GRADUATE COURSE "Hybrid feedback control systems: Analysis and design"

COURSE DESCRIPTION

Hybrid control systems arise from controlling nonlinear systems with hybrid control algorithms — algorithms that involve logic variables, timers, computer program, and in general, states experiencing jumps at certain events — and also from controlling systems that are themselves hybrid, such as computer networks, power systems, and nonsmooth mechanical systems. Recent technological advances allowing for and utilizing the interplay between digital systems with the analog world (e.g., embedded computers, sensor networks, etc.) have increased the demand for a theory applicable to the resulting systems, which are of hybrid nature, and for design techniques that may guarantee, through hybrid control, performance, safety, and recovery specifications even in the presence of uncertainty.

This course presents recent advances in the analysis and design of hybrid control systems from a control theory viewpoint. The power of hybrid feedback control for robust stabilization will be displayed in several applications including power systems, robotic networks, underactuated rigid bodies, integrate-and-fire oscillators, neurons, and genetic networks.

This course is a natural follow-up to the introductory course on hybrid dynamical systems, to be taught previously through EECI and HYCON by A.R. Teel in 2010, by R.G. Sanfelice in 2011, 2013, and 2014, and by R. Goebel in 2015.

GRADING SCHEME

• Homework will be assigned at the end of the day.

• In-class activities will be proposed during some of the lectures.

• A final project is recommended for all participants, and is required for validation of the course. A short presentation outlining the ideas in each project is required on the last day of the coure. A final report in pdf using IEEE conference format will be due on May 1 midnight PST (e-mail submission)

COURSE CONTENT

PART 1: Introduction to hybrid control systems

• Overview of main modeling technique, robustness, and stability results

• Mathematical examples of hybrid systems

• Motivation to hybrid feedback control

References: [1], [2], [3], [4],

Slides: here

PART 2: Modeling hybrid control systems

• Modeling of hybrid plant and hybrid controller

• Basic notions and properties

• Examples

References: [1], [2], [3], [4], [5], [6], [7], [8], [9]

Slides: here

PART 3: Simulation of hybrid systems

• Introduction to simulation tools

• Examples

Slides: here

PART 4: Supervisory hybrid control

• General control architecture

• Uniting control (state and output feedback)

• Throw-and-catch control

• Examples

References: [10], [11], [12], [13], [14], [15], [16], [17]

Slides: here

PART 4: CLF-based control

• Control Lyapunov function concept

• Existence of continuous state feedbacks

• Minimum pointwise norm control

• Examples

References: [4], [18], [19], [20]

Slides: here

Forward invariance references: [21], [22], [23], [24]

PART 5: Passivity-based control

• General, Flow, and Jump passivity

• Link to Stability and Attractivity

• Synthesis of stabilizing feedback law

• Examples

Slides: here

Homework: here

PART 7: Invariance-based control

• Invariance notions

• Sufficient conditions

• Design of feedback law inducing invariance

• Examples

References: [4], [27], [28], [21], [22]

Slides: here

PART 8: Robustness

• Robustness to small perturbations

• Input to state stability

• Robustness to large perturbations by design

• Examples

References: [1], [2], [4], [29]

Slides: here

PART 9: Applications

• Juggling control

• Attitude control

• Power systems

• Spiking neurons

References: [30], [31], [32], [28], [20], [9]

Homework: here

Other references: [33], [34], [35], [36]

### References

- [65] Hybrid Dynamical Systems: Modeling, Stability, and Robustness, , Issue NULL, New Jersey, (2012)
- [34] Hybrid dynamical systems, , IEEE Control Systems Magazine, April, Volume 29, Issue NULL, Number 2, p.28-93, (2009)
- [103] Feedback Control of Hybrid Dynamical Systems, , Encyclopedia of Systems and Control, Issue NULL, (2015)
- [77] Control of Hybrid Dynamical Systems: An Overview of Recent Advances, , Hybrid Systems with Constraints, April, Issue NULL, p.146–177, (2013)
- [138] Computationally-Aware Switching Criteria for Hybrid Model Predictive Control Of Cyber-Physical Systems, , IEEE Transactions on Automation Science and Engineering, Volume 13, Issue 2, p.479--490, (2016)
- [140] On Distributed Intermittent Consensus for First-Order Systems with Robustness, , Proceedings of 10th IFAC Symposium on Nonlinear Control Systems, Issue NULL, p.146--151, (2016)
- [136] State Estimation of Linear Systems in the Presence of Sporadic Measurements, , Automatica, November, Volume 73, p.101--109, (2016)
- [105] Analysis and Design of Cyber-Physical Systems: A Hybrid Control Systems Approach, , Cyber Physical Systems: From Theory to Practice, p.3--31, (2015)
- [93] A Framework for Modeling and Analysis of Robust Stability for Spiking Neurons, , Proceedings of the American Control Conference, June, Issue NULL, p.1414-1419, (2014)
- [63] Switching System Model for Pinpoint Lunar Landing Guidance Using a Hybrid Control Strategy, , Proceedings of the AIAA Guidance, Navigation, and Control Conference, Issue NULL, (2012)
- [139] On Distributed Observers for Linear Time-invariant Systems Under Intermittent Information Constraints, , Proceedings of 10th IFAC Symposium on Nonlinear Control Systems, Issue NULL, p.666--671, (2016)
- [114] Interconnected Observers for Linear Systems to Improve Rate of Convergence and Robustness to Measurement Noise, , IEEE Transactions on Control of Network Systems, Volume 3, Issue 1, p.1--11, (2016)
- [33] Supervising a family of hybrid controllers for robust global asymptotic stabilization, , Proc. 47th IEEE Conference on Decision and Control, Issue NULL, p.4700–4705, (2008)
- [70] Robust Supervisory Control for Uniting Two Output-Feedback Hybrid Controllers with Different Objectives, , Automatica, July, Volume 49, Issue NULL, Number 7, p.1958–1969, (2013)
- [11] A ``throw-and-catch" hybrid control strategy for robust global stabilization of nonlinear systems, , Proc. 26th American Control Conference, Issue NULL, p.3470–3475, (2007)
- [152] Robust Global Trajectory Tracking for Underactuated {VTOL} Aerial Vehicles using Inner-Outer Loop Control Paradigms, , IEEE Transactions on Automatic Control, January, Volume 62, Number 1, p.97--112, (2017)
- [7] Robust hybrid controllers for continuous-time systems with applications to obstacle avoidance and regulation to disconnected set of points, , Proc. 25th American Control Conference, Issue NULL, p.3352–3357, (2006)
- [75] On the existence of control {L}yapunov functions and state-feedback laws for hybrid systems, , IEEE Transactions on Automatic Control, December, Volume 58, Issue NULL, Number 12, p.3242–3248, (2013)
- [85] Pointwise Minimum-norm Control Laws for Hybrid Systems, , Proceedings of the IEEE Conference on Decision and Control, Issue NULL, p.2665–2670, (2013)
- [110] Robust Global Stabilization of the {DC-DC} Boost Converter via Hybrid Control, , IEEE Transactions on Circuits and Systems I, April, Volume 62, Issue 4, p.1052--1061, (2015)
- [120] On Notions and Sufficient Conditions for Forward Invariance of Sets for Hybrid Dynamical Systems, , Proceedings of the 54th IEEE Conference on Decision and Control, December, p.2869-2874, (2015)
- [141] Results on Feedback Design for Forward Invariance of Sets in Hybrid Dynamical Systems, , Proceedings of the 55th IEEE Conference on Decision and Control, December, p.622--627, (2016)
- [23] On the optimality of {D}ubins paths across heterogeneous terrain, , Hybrid Systems: Computation and Control, Volume 4981, Issue NULL, p.457-470, (2008)
- [117] Hybrid Feedback Control Methods for Robust and Global Power Conversion, , Proceedings of the 5th Analysis and Design of Hybrid Systems, October, p.298-303, (2015)
- [69] Passivity-based Control for Hybrid Systems with Applications to Mechanical Systems Exhibiting Impacts, , Automatica, May, Volume 49, Number 5, p.1104–1116, (2013)
- [92] Sufficient Conditions for Passivity and Stability of Interconnections of Hybrid Systems using Sums of Storage Functions, , Proceedings of the 2014 American Control Conference, Issue NULL, p.1432-1437, (2014)
- [18] Invariance principles for hybrid systems with connections to detectability and asymptotic stability, , IEEE Transactions on Automatic Control, Volume 52, Issue NULL, Number 12, p.2282–2297, (2007)
- [91] A Robust Hybrid Control Algorithm for a Single-Phase DC/AC Inverter with Variable Input Voltage, , Proceedings of the 2014 American Control Conference, Issue NULL, p.1420-1425, (2014)
- [135] Robust Asymptotic Stabilization of Hybrid Systems using Control Lyapunov Functions, , Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control, April, p.235--244 , (2016)
- [17] A hybrid systems approach to trajectory tracking control for juggling systems, , Proc. 46th IEEE Conference on Decision and Control, Issue NULL, New Orleans, LA, p.5282–5287, (2007)
- [79] Juggling On A Bouncing Ball Apparatus Via Hybrid Control, , Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Issue NULL, p.1848–1853, (2013)
- [50] Quaternion-Based Hybrid Controller for Robust Global Attitude Tracking, , IEEE Transactions on Automatic Control, November, Volume 56, Issue NULL, Number 11, p.2555–2566, (2011)
- [20] Robust Hybrid Control Systems, , PhD. Thesis, Issue NULL, (2007)
- [113] Robust Global Trajectory Tracking for a Class of Underactuated Vehicles, , Automatica, August, Volume 58, Issue NULL, p.90-98, (2015)
- [40] Dynamical Properties of Hybrid Systems Simulators, , Automatica, Volume 46, Issue NULL, Number 2, p.239–248, (2010)
- [134] Computationally Tractable Implementations of Pointwise Minimum Norm State-Feedback Laws for Hybrid Systems, , Proceedings of American Control Conference, p.4257--4262, (2016)