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

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