@book {65, title = {Hybrid Dynamical Systems: Modeling, Stability, and Robustness}, year = {2012}, publisher = {Princeton University Press}, organization = {Princeton University Press}, address = {New Jersey}, keywords = {hybrid systems}, doi = {http://www.u.arizona.edu/~sricardo/index.php?n=Main.Books}, author = {R. Goebel and R. G. Sanfelice and A. R. Teel} } @inbook {36, title = {Hybrid Control Systems}, booktitle = {Encyclopedia of Complexity and Systems Science}, series = {NULL}, year = {2009}, publisher = {Springer}, organization = {Springer}, abstract = {This article will present a general framework for modeling hybrid control systems and studying their dynamical properties. It will put forth basic tools for studying asymptotic stability properties of hybrid systems. Then, particular aspects of hybrid control will be described, as well as approaches to control objectives that can be successfully achieved via hybrid control even if they are not solvable with classical methods.}, keywords = {hybrid systems}, author = {A. R. Teel and R. G. Sanfelice and R. Goebel} } @inbook {21, title = {Hybrid systems: limit sets and zero dynamics with a view toward output regulation}, booktitle = {Analysis and Design of Nonlinear Control Systems}, year = {2008}, pages = {241-261}, publisher = {Springer-Verlag}, organization = {Springer-Verlag}, chapter = {Hybrid systems: limit sets and zero dynamics with a view toward output regulation}, abstract = {

We present results on omega-limit sets and minimum phase zero dynamics for hybrid dynamical systems. Moreover, we give pointers to how these results may be useful in the future for solving the output regulation problem for hybrid systems. We highlight the main attributes of omega-limit sets and we show, under mild conditions, that they are asymptotically stable. We define a minimum phase notion in terms of omega-limit sets and establish an equivalent Lyapunov characterization. Then we study the feedback stabilization problem for a class of minimum phase, relative degree one hybrid systems. Finally, we discuss output regulation for this class of hybrid systems. We illustrate the concepts with examples throughout the paper.

}, keywords = {hybrid systems}, doi = {http://www.springer.com/west/home/generic/search/results?http://www.springerlink.com/content/r00r175353435104/fulltext.pdf}, url = {https://hybrid.soe.ucsc.edu/files/preprints/21.pdf}, author = {C. Cai and R. Goebel and R. G. Sanfelice and A. R. Teel}, editor = {A. Astolfi and L. Marconi and A. Astolfi and L. Marconi} } @article {349, title = {Stochastic Approximation of Hybrid Systems: Boundedness and Asymptotic Behavior}, journal = {Annual Reviews in Control}, year = {2025}, author = {A. R. Teel and R. G. Sanfelice and R. Goebel} } @article {348, title = {Lyapunov-like Descriptions of Strong Forward Invariance for Differential Inclusions}, journal = {SIAM Journal on Control and Optimization}, year = {2025}, author = {R. Goebel and R. G. Sanfelice and A. R. Teel} } @article {237, title = {Robust Coordinated Hybrid Source Seeking with Obstacle Avoidance in Multi-Vehicle Autonomous Systems}, journal = {IEEE Transactions on Automatic Control}, volume = {67}, number = {2}, year = {2022}, month = {February}, pages = {706-721}, author = {J. I. Poveda and M. Benosman and A. R. Teel and R. G. Sanfelice} } @article {68, title = {On Path-Lifting Mechanisms and Unwinding in Quaternion-based Attitude Control}, journal = {IEEE Transactions on Automatic Control}, volume = {58}, number = {5}, year = {2013}, month = {May}, pages = {1179{\textendash}1191}, keywords = {attitude control}, doi = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6389715}, author = {C. G. Mayhew and R. G. Sanfelice and A. R. Teel} } @article {58, title = {Quaternion-Based Hybrid Feedback for Robust Global Attitude Synchronization}, journal = {IEEE Transactions on Automatic Control}, volume = {57}, number = {8}, year = {2012}, month = {August}, pages = {2122{\textendash}2127}, keywords = {attitude control}, doi = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6111242}, url = {https://hybrid.soe.ucsc.edu/files/preprints/58.pdf}, author = {C. G. Mayhew and R. G. Sanfelice and J. Sheng and M. Arcak and A. R. Teel} } @article {50, title = {Quaternion-Based Hybrid Controller for Robust Global Attitude Tracking}, journal = {IEEE Transactions on Automatic Control}, volume = {56}, number = {11}, year = {2011}, month = {November}, pages = {2555{\textendash}2566}, keywords = {attitude control}, doi = {http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=5701762}, url = {https://hybrid.soe.ucsc.edu/files/preprints/50.pdf}, author = {C. G. Mayhew and R. G. Sanfelice and A. R. Teel} } @article {45, title = {On singular perturbations due to fast actuators in hybrid control systems}, journal = {Automatica}, volume = {47}, number = {4}, year = {2011}, month = {April}, pages = {692{\textendash}701}, keywords = {hybrid systems}, doi = {http://www.sciencedirect.com/science/article/pii/S0005109811000707}, url = {https://hybrid.soe.ucsc.edu/files/preprints/45.pdf}, author = {R. G. Sanfelice and A. R. Teel} } @article {40, title = {Dynamical Properties of Hybrid Systems Simulators}, journal = {Automatica}, volume = {46}, number = {2}, year = {2010}, pages = {239{\textendash}248}, abstract = {This paper analyzes the dynamical properties of a class of hybrid systems simulators. A hybrid system is a dynamical system with a state that can both ?ow and jump. Its simulator attempts to generate its solutions approximately. The paper presents mild regularity conditions on the hybrid system and its simulator to guarantee that simulated solutions are close to actual solutions on compact (hybrid) time intervals, and that asymptotically stable compact sets are preserved, in a semiglobal practical sense, under simulation. In fact, it is established that asymptotically stable compact sets are continuous in the integration step size parameter of the simulator; that is, as the step size of the simulator converges to zero, the asymptotically stable set observed in simulations approaches the asymptotically stable compact set of the true hybrid system. Examples are used to illustrate concepts and results.}, keywords = {simulation}, doi = {http://www.sciencedirect.com/science/article/pii/S0005109809004361}, url = {https://hybrid.soe.ucsc.edu/files/preprints/40.pdf}, author = {R. G. Sanfelice and A. R. Teel} } @article {35, title = {Asymptotic stability in hybrid systems via nested {M}atrosov functions}, journal = {IEEE Transactions on Automatic Control}, volume = {54}, number = {7}, year = {2009}, pages = {1569{\textendash}1574}, abstract = {A theorem on nested Matrosov functions is extended to time-varying hybrid systems. It provides suf?cient conditions for uniform global asymptotic stability of a compact set. An application to parameter identi?cation with state resets is made and illustrated on an example.}, keywords = {hybrid systems}, doi = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5071164}, url = {https://hybrid.soe.ucsc.edu/files/preprints/35.pdf}, author = {R. G. Sanfelice and A. R. Teel} } @article {22, title = {Invariance principles for switching systems via hybrid systems techniques}, journal = {Systems \& Control Letters}, volume = {57}, number = {12}, year = {2008}, month = {December}, pages = {980-986}, abstract = {Invariance principles and sufficient conditions for asymptotic stability for switching systems are given. Multiple Lyapunov-like functions are used, and dwell-time, persistent dwell-time, and weak dwell-time switching signals are considered. The invariance principles are derived from general invariance principles for hybrid systems. Asymptotic stability is concluded under observability assumptions or common bounds on the Lyapunov-like functions.}, keywords = {hybrid systems}, doi = {http://www.sciencedirect.com/science/article/pii/S0167691108001035}, url = {https://hybrid.soe.ucsc.edu/files/preprints/22.pdf}, author = {R. Goebel and R. G. Sanfelice and A. R. Teel} } @article {18, title = {Invariance principles for hybrid systems with connections to detectability and asymptotic stability}, journal = {IEEE Transactions on Automatic Control}, volume = {52}, number = {12}, year = {2007}, pages = {2282{\textendash}2297}, abstract = {The paper shows several versions of the (LaSalle{\textquoteright}s) invariance principle for general hybrid systems. The broad framework allows for nonuniqueness of solutions, Zeno behaviors, and does not insist on continuous dependence of solutions on initial conditions. Instead, only a mild structural property involving graphical convergence of solutions is posed. The general invariance results are then specified to hybrid systems given by set-valued data. Further results involving invariance as well as observability, detectability, and asymptotic stability are given.}, keywords = {hybrid systems}, doi = {http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=04395187}, url = {https://hybrid.soe.ucsc.edu/files/preprints/18.pdf}, author = {R. G. Sanfelice and R. Goebel and A. R. Teel} } @conference {340, title = { Stochastic Approximations of Differential Inclusions: Almost Sure Boundedness and Asymptotic Convergence}, booktitle = {13th IFAC Symposium on Nonlinear Control Systems (NOLCOS)}, year = {2025}, month = {August}, author = {A. R. Teel and R. Goebel and R. G. Sanfelice} } @conference {324, title = {Stochastic Approximation Results for Hybrid Inclusions}, booktitle = {Proceedings of the 63rd IEEE Conference on Decision and Control}, year = {2024}, month = {December}, pages = {7822-7827}, author = {A. R. Teel and R. Goebel and R. G. Sanfelice and M. F. Crisafulli} } @conference {320, title = {Some Converse Lyapunov-Like Results for Strong Forward Invariance}, booktitle = {Proceedings of the 63rd IEEE Conference on Decision and Control}, year = {2024}, month = {December}, pages = {3605-3610}, author = {R. Goebel and R. G. Sanfelice and A. R. Teel} } @conference {297, title = {Multi-Channel Hybrid Time Domains and Clustering Protocols for Large-Scale Interconnections}, booktitle = {Proceedings of the 62nd IEEE Conference on Decision and Control}, year = {2023}, month = {December}, pages = {2847-2852}, author = {A. R. Teel and R. Goebel and R. G. Sanfelice} } @conference {296, title = {On Invariants for Open Hybrid Systems and their Interconnections}, booktitle = {Proceedings of the 62nd IEEE Conference on Decision and Control}, year = {2023}, month = {December}, pages = {1859-1864}, author = {R. G. Sanfelice and A. R. Teel} } @conference {167, title = {A Hybrid Adaptive Feedback Law for Robust Obstacle Avoidance and Coordination in Multiple Vehicle Systems}, booktitle = {Proceedings of the American Control Conference}, year = {2018}, month = {August}, pages = {616-621}, author = {J. I. Poveda and M. Benosman and A. R. Teel and R. G. Sanfelice} } @conference {54, title = {Further results on synergistic {L}yapunov functions and hybrid feedback design through backstepping}, booktitle = {Proc. Joint Conference on Decision and Control and European Control Conference}, series = {NULL}, year = {2011}, pages = {7428{\textendash}7433}, keywords = {hybrid systems}, doi = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6161283}, author = {C. G. Mayhew and R. G. Sanfelice and A. R. Teel} } @conference {49, title = {Synergistic {L}yapunov functions and backstepping hybrid feedbacks}, booktitle = {Proc. 30th American Control Conference}, series = {NULL}, year = {2011}, pages = {3203{\textendash}3208}, keywords = {hybrid systems}, doi = {http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=5991021}, author = {C. G. Mayhew and R. G. Sanfelice and A. R. Teel} } @conference {48, title = {On the Non-Robustness of Memoryless Path-Lifting Schemes for Quaternion-Based Attitude Control}, booktitle = {Proc. 30th American Control Conference}, series = {NULL}, year = {2011}, pages = {1003{\textendash}1008}, keywords = {attitude control}, doi = {http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=5991359}, author = {C. G. Mayhew and R. G. Sanfelice and A. R. Teel} } @conference {47, title = {On Quaternion-Based Attitude Control and the Unwinding Phenomenon}, booktitle = {Proc. 30th American Control Conference}, series = {NULL}, year = {2011}, pages = {299{\textendash}304}, keywords = {attitude control}, doi = {http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=5991127}, author = {C. G. Mayhew and R. G. Sanfelice and A. R. Teel} } @conference {41, title = {Robust Global Asymptotic Attitude Synchronization by Hybrid Control}, booktitle = {Proc. 29th American Control Conference}, series = {NULL}, year = {2010}, pages = {3666{\textendash}3671}, keywords = {attitude control}, doi = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=\&arnumber=5530428}, author = {C. G. Mayhew and R. G. Sanfelice and M. Arcak and A. R. Teel} } @conference {38, title = {Robust Global Asymptotic Attitude Stabilization of a Rigid Body by Quaternion-based Hybrid Feedback}, booktitle = {Proc. 46th Conference on Decision and Control}, series = {NULL}, year = {2009}, pages = {2522{\textendash}2527}, abstract = {Global asymptotic stabilization of the attitude of a rigid body is made difficult by several topological obstructions. In fact, this task is impossible to accomplish with discontinuous state feedback. Moreover, when the attitude is parameterized with unit quaternions, it becomes impossible to design a globally stabilizing state feedback (even discontinuous) that is robust to measurement noise. In this paper, we present a quaternion-based hysteretic hybrid feedback that robustly globally asymptotically stabilizes the attitude of a rigid body. The hybrid control laws are derived through Lyapunov analysis in kinematic and dynamic settings. In the dynamic setting, we provide two control laws: one derived from a simple Lyapunov function, and another based on backstepping. Analyzing the change in these Lyapunov functions due to jumps of the hysteretic logic variable yields a straightforward form for state-based hysteretic switching points. A simulation study demonstrates robustness to measurement noise in the proposed control laws and differences between the non-backstepping and backstepping control laws.}, keywords = {attitude control}, doi = {http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=\&arnumber=5400431}, url = {https://hybrid.soe.ucsc.edu/files/preprints/38.pdf}, author = {C. G. Mayhew and R. G. Sanfelice and A. R. Teel} } @conference {37, title = {Robust Global Asymptotic Stabilization of a 6-DOF Rigid Body by Quaternion-based Hybrid Feedback}, booktitle = {Proc. 46th Conference on Decision and Control}, series = {NULL}, year = {2009}, pages = {1094{\textendash}1099}, abstract = {The problem of robust, global asymptotic stabilization of a rigid body is hampered by major topological obstructions. These obstructions prevent a continuous state feedback from solving the problem and also lead to robustness issues when discontinuous feedback is applied. In this paper, we extend a hybrid control strategy proposed in a companion paper for robust, global asymptotic stabilization of rigid body attitude to the case where translation is also considered. The quaternion-based hysteretic hybrid feedback laws are developed in the kinematic and dynamic settings. In the dynamic setting, two control laws are derived, one of which is based on backstepping. Robustness to measurement noise is asserted by employing recently developed stability theory for hybrid systems. The hybrid feedback is found to have desirable robustness properties.}, keywords = {attitude control}, doi = {http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=\&arnumber=5400338}, url = {https://hybrid.soe.ucsc.edu/files/preprints/37.pdf}, author = {C. G. Mayhew and R. G. Sanfelice and A. R. Teel} } @conference {33, title = {Supervising a family of hybrid controllers for robust global asymptotic stabilization}, booktitle = {Proc. 47th IEEE Conference on Decision and Control}, series = {NULL}, year = {2008}, pages = {4700{\textendash}4705}, abstract = {This paper describes an algorithm for achieving robust, global asymptotic stabilization in nonlinear control systems by supervising the actions of a family of hybrid controllers. The family is such that the regions over which they operate cover the state space in an appropriate sense. Moreover, their behavior is such that they can be scheduled to move the state of the system toward a desirable region, whether it be an equilibrium point or a compact set. In establishing our main result, we use the concept of ?events? for hybrid systems and show that, under mild assumptions, stability of a system without events is preserved when a ?nite number of events are incorporated. The algorithm is applied to robust, global stabilization problems involving vehicle orientation, position and orientation of a mobile robot, and the inverted con?guration of a pendulum.}, keywords = {hybrid systems}, doi = {http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=\&arnumber=4739481\&isnumber=4738560}, url = {https://hybrid.soe.ucsc.edu/files/preprints/33.pdf}, author = {R. G. Sanfelice and A. R. Teel and R. Goebel} } @conference {32, title = {Analysis of hybrid systems resulting from hysteresis and saturation: a {L}yapunov approach}, booktitle = {Proc. 47th IEEE Conference on Decision and Control}, series = {NULL}, year = {2008}, pages = {2764{\textendash}2769}, abstract = {This paper studies a class of hybrid systems with linear (or linear plus saturated linear) continuous and discrete dynamics, which are determined by a ?ow map and jump map, and state-triggered jumps. One motivation for considering this class of systems is that they can model control systems with a relay-type hysteresis element. Based on Lyapunov theorems for hybrid systems, a Lyapunov function is constructed that effectively incorporates the feature of the jumps. Global asymptotic stability analysis is presented for the case when the ?ow map is linear, and local asymptotic stability analysis is presented for the case when the ?ow map is linear plus saturated linear. The stability conditions are derived as matrix inequalities. A numerical example is presented to illustrate the hybrid modeling process for a system experiencing hysteresis. Simulations con?rm the effectiveness of the proposed analysis tools and demonstrate the potential of the Lyapunov function.}, keywords = {hybrid systems}, doi = {http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=\&arnumber=4739453\&isnumber=4738560}, url = {https://hybrid.soe.ucsc.edu/files/preprints/32.pdf}, author = {D. Dai and R. G. Sanfelice and T. Hu and A. R. Teel} } @conference {30, title = {Robust hybrid source-seeking algorithms based on directional derivatives and their approximations}, booktitle = {Proc. 47th IEEE Conference on Decision and Control}, series = {NULL}, year = {2008}, pages = {1735{\textendash}1740}, abstract = {A family of hybrid control algorithms is developed that steer a nonholonomic autonomous vehicle to the source of a scalar signal present in the environment. In an idealized setting, we develop a general hybrid control scheme that globally asymptotically stabilizes the vehicle position about the source. Pursuing a practical implementation, a series of perturbations to the family of controllers is introduced, resulting in a semiglobal practical stability of the vehicle position about the source. An example of a recently developed conjugate direction-based controller ?tting into this family is developed and demonstrated by simulation and experiment.}, keywords = {hybrid systems}, doi = {http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=\&arnumber=4739392\&isnumber=4738560}, url = {https://hybrid.soe.ucsc.edu/files/preprints/30.pdf}, author = {C. G. Mayhew and R. G. Sanfelice and A. R. Teel} } @conference {28, title = {On robust, global stabilization of the attitude of an underactuated rigid body using hybrid feedback}, booktitle = {Proc. 27th American Control Conference}, series = {NULL}, year = {2008}, pages = {2909{\textendash}2914}, abstract = {A hybrid feedback is developed for robust, global stabilization of the attitude of an underactuated rigid body. For the case where two angular velocities are considered as controls, this objective is achieved. For the case where the two controls are torques, the objective is achieved in a {\textquoteleft}{\textquoteleft}practical" sense, i.e., robust, global asymptotic stability of some arbitrarily small neighborhood of the desired attitude is achieved. To assist with the exposition, a robustly, globally stabilizing hybrid controller is also developed for the case where three angular velocities are considered as controls. This solution provides an alternative to one that has recently appeared in the literature.}, keywords = {attitude control}, doi = {http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=\&arnumber=4586937\&isnumber=4586444}, url = {https://hybrid.soe.ucsc.edu/files/preprints/28.pdf}, author = {A. R. Teel and R. G. Sanfelice} } @conference {27, title = {A Nested {M}atrosov Theorem for Hybrid Systems}, booktitle = {Proc. 27th American Control Conference}, series = {NULL}, year = {2008}, pages = {2915{\textendash}2920}, abstract = {We present a sufficient condition for uniform global asymptotic stability of compact sets for hybrid systems. Uniform global asymptotic stability (UGAS {\textendash} in the sense that bounds on the solutions and on the convergence time depend only on the distance to the compact set of interest) are introduced for a large class of hybrid systems which are given by a flow map, flow set, jump map, and jump set. We show that uniform global stability of a compact set plus the existence of Lyapunov-like functions and continuous functions satisfying a nested condition on the flow and jump sets imply uniform global asymptotic stability of the compact set. The required nested condition for hybrid systems turns out to be a combination of the conditions in nested Matrosov theorems for time-varying continuous-time and discrete-time available in the literature. Our result also show that Matrosov{\textquoteright}s theorem are a reasonable alternative to LaSalle{\textquoteright}s invariance principle for time-invariant systems when additional functions with certain decreasing properties are available. We illustrate the application of our main result in several examples, including the so-called bouncing ball system.}, keywords = {hybrid systems}, doi = {http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=\&arnumber=4586938\&isnumber=4586444:PDF;SLIDES:Talks/ACC2008-ThB14-5.pdf:PowerPoint}, url = {https://hybrid.soe.ucsc.edu/files/preprints/27.pdf}, author = {R. G. Sanfelice and A. R. Teel} } @conference {25, title = {Robust global swing-up of the pendubot via hybrid control}, booktitle = {Proc. 27th American Control Conference}, series = {NULL}, year = {2008}, pages = {1424{\textendash}1429}, abstract = {Combining local state-feedback laws and open-loop schedules, we design a hybrid control algorithm for robust global stabilization of the pendubot to the upright configuration (both links straight up with zero velocity). Our hybrid controller performs the swing-up task robustly by executing a decision-making algorithm designed to work under the presence of perturbations. The hybrid control algorithm features logic variables, timers, and hysteresis. We explicitly design the control strategy and implement it in a real pendubot system using Matlab/Simulink with Real-time Workshop. Experimental results show the main capabilities of our hybrid controller.}, keywords = {hybrid systems}, doi = {http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=\&arnumber=4586692\&isnumber=4586444:PDF;SLIDES:Talks/ACC2008-WeC05-4.pdf:PowerPoint}, url = {https://hybrid.soe.ucsc.edu/files/preprints/25.pdf}, author = {R. O{\textquoteright}Flaherty and R. G. Sanfelice and A. R. Teel} } @conference {24, title = {Robust source-seeking hybrid controllers for nonholonomic vehicles}, booktitle = {Proc. 27th American Control Conference}, series = {NULL}, year = {2008}, pages = {2722{\textendash}2727}, abstract = {We consider the problem of steering a nonholonomic vehicle to the source of a radiation-like signal with only measurements of the signal. We propose a general control strategy for vehicle steering which is based on an optimization algorithm for minimization of nonlinear functions without gradient information. We state the main properties of the strategy and specialize it to the control of nonholonomic vehicles. We discuss its implementation in a hybrid controller which coordinates vehicle steering and logic elements. We present global convergence and stability results for the closed-loop system. We also discuss two possible modifications to our algorithm that improve its performance when applied to real-world environments.}, keywords = {hybrid systems}, doi = {http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=\&arnumber=4586904\&isnumber=4586444}, url = {https://hybrid.soe.ucsc.edu/files/preprints/24.pdf}, author = {C. G. Mayhew and R. G. Sanfelice and A. R. Teel} } @conference {19, title = {Hybrid {MPC}: Open-minded but not Easily Swayed}, booktitle = {Assessment and Future Directions of Nonlinear Model Predictive Control}, series = {NULL}, volume = {Lecture Notes in Control and Information Sciences 358}, year = {2007}, pages = {17{\textendash}34}, publisher = {Springer Berlin / Heidelberg}, organization = {Springer Berlin / Heidelberg}, chapter = {Hybrid {MPC}: Open-minded but not Easily Swayed}, abstract = {The robustness of asymptotic stability with respect to measurement noise for discrete-time feedback control systems is discussed. It is observed that, when attempting to achieve obstacle avoidance or regulation to a disconnected set of points for a continuous-time system using sample and hold state feedback, the noise robustness margin necessarily vanishes with the sampling period. With this in mind, we propose two modifications to standard model predictive control (MPC) to enhance robustness to measurement noise. The modifications involve the addition of dynamical states that make large jumps. Thus, they have a hybrid flavor. The proposed algorithms are well suited for situations where control algorithms must respond quickly to large changes in operating conditions but not be easily confused by moderately large measurement noise and similar disturbances.}, keywords = {hybrid systems}, doi = {http://www.springerlink.com/content/22236583418rr285/fulltext.pdf}, url = {https://hybrid.soe.ucsc.edu/files/preprints/19.pdf}, author = {S. E. Tuna and R. G. Sanfelice and M. J. Messina and A. R. Teel} } @conference {17, title = {A hybrid systems approach to trajectory tracking control for juggling systems}, booktitle = {Proc. 46th IEEE Conference on Decision and Control}, series = {NULL}, year = {2007}, pages = {5282{\textendash}5287}, address = {New Orleans, LA}, abstract = {From a hybrid systems point of view, we provide a modeling framework and a trajectory tracking control design methodology for juggling systems. We present the main ideas and concepts in a one degree-of-freedom juggler, which consists of a ball bouncing on an actuated robot. We design a hybrid control strategy that, with only information of the ball{\textquoteright}s state at impacts, controls the ball to track a reference rhythmic pattern with arbitrary precision. We extend this hybrid control strategy to the case of juggling multiple balls with different rhythmic patterns. Simulation results for juggling of one and three balls with a single actuated robot are presented.}, keywords = {hybrid systems}, doi = {http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=\&arnumber=4435010\&isnumber=4434000:PDF;SLIDES:Users/ricardo/public_html.MIT/Talks/CDC2007-FrB04-4.pdf:PowerPoint}, url = {https://hybrid.soe.ucsc.edu/files/preprints/17.pdf}, author = {R. G. Sanfelice and A. R. Teel and R. Sepulchre} } @conference {14, title = {{H}ybrid {S}ystems: stability and control}, booktitle = {Proc. 26th Chinese Control Conference}, series = {NULL}, year = {2007}, chapter = {Hybrid systems: limit sets and zero dynamics with a view toward output regulation}, abstract = {We present results on omega-limit sets and minimum phase zero dynamics for hybrid dynamical systems. Moreover, we give pointers to how these results may be useful in the future for solving the output regulation problem for hybrid systems. We highlight the main attributes of omega-limit sets and we show, under mild conditions, that they are asymptotically stable. We define a minimum phase notion in terms of omega-limit sets and establish an equivalent Lyapunov characterization. Then we study the feedback stabilization problem for a class of minimum phase, relative degree one hybrid systems. Finally, we discuss output regulation for this class of hybrid systems. We illustrate the concepts with examples throughout the paper.}, keywords = {hybrid systems}, url = {https://hybrid.soe.ucsc.edu/files/preprints/14.pdf}, author = {C. Cai and R. Goebel and R. G. Sanfelice and A. R. Teel} } @conference {13, title = {A hybrid control strategy for robust contact detection and force regulation}, booktitle = {Proc. 26th American Control Conference}, series = {NULL}, year = {2007}, pages = {1461{\textendash}1466}, abstract = {We present an innovative hybrid control strategy for contact detection and force regulation of robotic manipulators. This hybrid architecture controls the robotic manipulator during the following stages of interaction with the work environment: the free motion, the transition phase, and the constrained motion. The proposed control strategy is to switch between a position and a force controller with hysteresis relying only on contact force measurements. We implement this strategy in a hybrid controller and provide a design procedure which depends on the viscoelastic parameters of the work environment. Our controller guarantees contact detection and force regulation without bounce-off effects between the robotic manipulator and the work environment from compact sets of initial conditions. Additionally, the resulting closed-loop system is robust to measurement noise. We include simulations that show how the proposed hybrid control strategy guarantees good performance in the cases of stiff and compliant work environments, and in the presence of measurement noise.}, keywords = {hybrid systems}, doi = {http://ieeexplore.ieee.org/iel5/4282134/4282135/04283119.pdf?tp=\&isnumber=4282135\&arnumber=4283119\&punumber=\%3Cb\%3E\%3Cfont\%20color=990000\%3E4282134\%3C/font\%3E\%3C/b\%3E}, url = {https://hybrid.soe.ucsc.edu/files/preprints/13.pdf}, author = {R. Carloni and R. G. Sanfelice and A. R. Teel and C. Melchiorri} } @conference {12, title = {Robust source seeking hybrid controllers for autonomous vehicles}, booktitle = {Proc. 26th American Control Conference}, series = {NULL}, year = {2007}, pages = {1185{\textendash}1190}, abstract = {

We consider the problem of steering an autonomous vehicle to locate a radiation source utilizing measurements of the radiation intensity only. We propose a control algorithm that locates the source through a sequence of line minimizations of the radiation intensity. We implement in a hybrid controller, with sample-and-hold and logic variables, a discretized version of the algorithm suitable for steering a point-mass vehicle. The algorithm confers global convergence and practical stability properties to the closed-loop hybrid system. We discuss these properties and characterize the region of convergence for the vehicle. Convergence and stability results are supplemented with simulations.

}, keywords = {hybrid systems}, doi = {http://www.scivee.tv/node/2725,http\://ieeexplore.ieee.org/iel5/4282134/4282135/04283016.pdf?tp=\&isnumber=4282135\&arnumber=4283016\&punumber=\%3Cb\%3E\%3Cfont\%20color=990000\%3E4282134\%3C/font\%3E\%3C/b\%3E}, url = {https://hybrid.soe.ucsc.edu/files/preprints/12.pdf}, author = {C. G. Mayhew and R. G. Sanfelice and A. R. Teel} } @conference {11, title = {A {\textquoteleft}{\textquoteleft}throw-and-catch" hybrid control strategy for robust global stabilization of nonlinear systems}, booktitle = {Proc. 26th American Control Conference}, series = {NULL}, year = {2007}, pages = {3470{\textendash}3475}, abstract = {We present a control strategy that combines local state feedback laws and open-loop schedules to robustly globally asymptotically stabilize a compact subset (typically a point) of the state space for a nonlinear system. The control algorithm is illustrated on the problem of global stabilization of the upright position of the pendubot and implemented in a hybrid controller containing logic variables and logic rules with hysteresis. We also present the design procedure of the hybrid controller for general nonlinear systems. Recent results in the literature on robustness of asymptotic stability in hybrid systems are used in establishing that the closed-loop system is robust to measurement noise and other external disturbances.}, keywords = {hybrid systems}, doi = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4282778}, url = {https://hybrid.soe.ucsc.edu/files/preprints/11.pdf}, author = {R. G. Sanfelice and A. R. Teel} } @conference {10, title = {On the robustness to measurement noise and unmodeled dynamics of stability in hybrid systems}, booktitle = {Proc. 25th American Control Conference}, series = {NULL}, year = {2006}, pages = {4061{\textendash}4066}, abstract = {

Results on robustness to measurement noise and unmodeled dynamics of stability in hybrid systems are presented. We show that arbitrarily small measurement noise can lead to lack of existence of solutions in hybrid systems. One solution to this problem is to pass the measurements through a filter. Robustness to measurement noise using this filtering is shown explicitly. We also study the effect of unmodeled sensor/actuator dynamics in the closed loop and we demonstrate that stability is robust to a class of singular perturbations. The results are illustrated for the inverted pendulum on a cart system when attempting to globally asymptotically stabilize the inverted position of the pendulum and the neutral cart position.

}, keywords = {hybrid systems}, doi = {http://ieeexplore.ieee.org/iel5/11005/34689/01657354.pdf?tp=\&arnumber=1657354\&isnumber=34689}, url = {https://hybrid.soe.ucsc.edu/files/preprints/10.pdf}, author = {R. G. Sanfelice and A. R. Teel and R. Goebel and C. Prieur} } @conference {9, title = {{L}yapunov analysis of sample-and-hold hybrid feedbacks}, booktitle = {Proc. 45th IEEE Conference on Decision and Control}, series = {NULL}, year = {2006}, pages = {4879{\textendash}4884}, abstract = {

For hybrid closed-loop systems arising from hybrid control of nonlinear systems, we show that the sampleand-hold implementation of the hybrid controller preserves (semiglobally and practically) the stability properties of the closed-loop system. We provide a general model for the hybrid closed-loop system where the hybrid controller is implemented digitally and it is interfaced to the nonlinear system through sample and hold devices. We model the sample device and the digital controller/hold device as single asynchronous hybrid systems with independent timing constants and data. The main result is established by means of a Lyapunov function for the hybrid closed-loop system resulting from the interconnection of its hybrid and nonlinear subsystems.

}, keywords = {hybrid systems}, doi = {http://ieeexplore.ieee.org/iel5/4176992/4176993/04177901.pdf?tp=\&isnumber=4176993\&arnumber=4177901\&punumber=\%3Cb\%3E\%3Cfont\%20color=990000\%3E4176992\%3C/font\%3E\%3C/b\%3E}, url = {https://hybrid.soe.ucsc.edu/files/preprints/9.pdf}, author = {R. G. Sanfelice and A. R. Teel} } @conference {8, title = {On the continuity of asymptotically stable compact sets for simulations of hybrid systems}, booktitle = {Proc. 45th IEEE Conference on Decision and Control}, series = {NULL}, year = {2006}, pages = {270{\textendash}275}, abstract = {

We propose a hybrid model for simulations of hybrid systems and we establish conditions on its data so that the asymptotically stable sets observed in simulations are continuous. The most important components of the hybrid model for simulations are a discrete integration scheme for the computation of the flows and an approximated jump mapping for the computation of the jumps. Our main result is built on the facts that, on compact hybrid time domains, every simulation to a hybrid system is arbitrarily close (in the graphical sense) to some solution to the actual hybrid system, and that asymptotically stable compact sets of hybrid systems are semiglobally practically asymptotically stable compact sets for the hybrid model for simulations. We present these results and illustrate them in simulations of the bouncing ball system.

}, keywords = {simulation}, doi = {http://ieeexplore.ieee.org/iel5/4176992/4176993/04177840.pdf?tp=\&isnumber=4176993\&arnumber=4177840\&punumber=\%3Cb\%3E\%3Cfont\%20color=990000\%3E4176992\%3C/font\%3E\%3C/b\%3E:PDF}, url = {https://hybrid.soe.ucsc.edu/files/preprints/8.pdf}, author = {R. G. Sanfelice and A. R. Teel} } @conference {7, title = {Robust hybrid controllers for continuous-time systems with applications to obstacle avoidance and regulation to disconnected set of points}, booktitle = {Proc. 25th American Control Conference}, series = {NULL}, year = {2006}, pages = {3352{\textendash}3357}, abstract = {

We give an elementary proof of the fact that, for continuous-time systems, it is impossible to use (even discontinuous) pure state feedback to achieve robust global asymptotic stabilization of a disconnected set of points or robust global regulation to a target while avoiding an obstacle. Indeed, we show that arbitrarily small, piecewise constant measurement noise can keep the trajectories away from the target. We give a constructive, Lyapunov-based hybrid state feedback that achieves robust regulation in the above mentioned settings.

}, keywords = {hybrid systems}, doi = {http://ieeexplore.ieee.org/iel5/11005/34689/01657236.pdf?tp=\&isnumber=\&arnumber=1657236}, url = {https://hybrid.soe.ucsc.edu/files/preprints/7.pdf}, author = {R. G. Sanfelice and M. J. Messina and S. E. Tuna and A. R. Teel} } @conference {5, title = {On hybrid controllers that induce input-to-state stability with respect to measurement noise}, booktitle = {Proc. 44th IEEE Conference on Decision and Control and European Control Conference}, series = {NULL}, year = {2005}, pages = {4891{\textendash}4896}, abstract = {

For a class of nonlinear systems affine in controls and with unknown high frequency gain, we develop a hybrid control strategy that guarantees (practical) global input-to-state stability (ISS) with respect to measurement noise. We provide a design procedure for the hybrid controller and apply it to Freeman{\textquoteright}s counterexample and minimum-phase relative degree one systems.

}, keywords = {hybrid systems}, doi = {http://ieeexplore.ieee.org/iel5/10559/33412/01582936.pdf?tp=\&arnumber=1582936\&isnumber=33412}, url = {https://hybrid.soe.ucsc.edu/files/preprints/5.pdf}, author = {R. G. Sanfelice and A. R. Teel} }