Model Predictive Control of Hybrid Dynamical Systems
Organisers
- Berk Altın
- Ricardo Sanfelice
- Francesco Ferrante
- Mohamed Adlene Maghenem
The workshop will run on 11 July 2020 from 10:00 until 17:00 Berlin time (10am until 5pm CEST/UTC+2h). The presentations will also be available for streaming from 10 July until 31 August 2020 for registered participants.
Please contact Berk Altın (berkaltin@ucsc.edu) and Ricardo G. Sanfelice (ricardo@ucsc.edu) for details about the live sessions and to be added to the discussion forum.
The slides of the workshop are available on the external workshop website.
Speakers
- Berk Altın, University of California, Santa Cruz, USA
- Francesco Ferrante, GIPSA Lab, Université Grenoble Alpes
- Ricardo G. Sanfelice, University of California, Santa Cruz, USA
- Mohamed A. Maghenem, University of California, Santa Cruz, USA
Summary
Hybrid systems model the behavior of dynamical systems where the
states can evolve continuously as well as instantaneously. Such systems
arise when control algorithms that involve digital devices are applied
to continuous-time systems, or due to the intrinsic dynamics (e.g.
mechanical systems with impacts, switching electrical circuits). Hybrid
control may be used for improved performance and robustness properties
compared to conventional control, and hybrid dynamics may be unavoidable
due to the interplay between digital and analog components of a
system.
This workshop is a complete course on the analysis and
design of model predictive control (MPC) schemes for hybrid systems. It
presents recently developed results on asymptotically stabilizing MPC
for hybrid systems based on control Lyapunov functions. The workshop
provides a detailed overview of the state of the art on hybrid MPC, and
a short tutorial on a powerful hybrid systems framework (hybrid
inclusions) that can model hybrid dynamics described in other frameworks
(e.g. switched systems, hybrid automata, impulsive systems). Key
analysis tools in this setting are demonstrated, along with several
advantages over other frameworks. This background is then used to lay
the theoretical foundations of a general MPC framework for hybrid
systems, with guaranteed stability and feasibility. The ideas are
illustrated in several applications.
The workshop targets a broad
audience in academia and industry, including graduate students, looking
for an introduction to an active area of research and some modern
mathematical analysis tools; control practitioners interested in novel
design techniques; researchers in dynamical systems in pursuit of
relevant applications; and researchers in industry and labs applying
hybrid predictive control methods to engineering systems. The required
background is basic familiarity with continuous- and discrete-time
nonlinear systems. The lectures are closely related to each other and
not meant to be independent research presentations.
Programme
10:00 Welcome Remarks, Berk Altın and Ricardo G. Sanfelice
10:05 Introduction to Hybrid Dynamical Systems: Modeling,
Examples, Asymptotic Stability, Francesco Ferrante
A short tutorial on a powerful hybrid systems framework called hybrid inclusions is provided. The generality of this framework is demonstrated by showing that several classes of hybrid systems often described in other frameworks (e.g. switched systems, hybrid automata, impulsive systems) can be reformulated as hybrid inclusions. The notion of solutions are presented, along with conditions guaranteeing existence and uniqueness. Asymptotic stability of such systems are formalized, sufficient Lyapunov conditions for asymptotic stability are demonstrated.
11:40 Background on Hybrid Model Predictive Control:
Models, Methods, and Open Questions, Ricardo G. Sanfelice
This module discusses several MPC strategies in the literature that have a hybrid flavor, which, due to the diverse use of the term hybrid, span a wide range of control settings. This module provides a unified presentation of these strategies with the purpose of serving as a self contained summary of the state of the art in hybrid MPC, and as a motivator for research on MPC of hybrid inclusions.
12:30 Overview of Model Predictive Control for Hybrid
Dynamical Systems, Berk Altın
An MPC algorithm that asymptotically stabilizes a closed set of interest for a given hybrid dynamical system is introduced. An overview of the salient features of the algorithm and the underlying optimal control problem is presented in comparison to continuous- and discrete-time MPC.
12:45 Lunch Break
13:30 Model Predictive Control for Hybrid Dynamical
Systems: Feasibility, Value Function Properties, Lyapunov Stability
Analysis, Berk Altın
Feasibility and stability properties of the aforementioned MPC algorithm under appropriate conditions are presented, along with the relevant properties of the optimal control problem. The key stabilizing ingredient of the algorithm, which comes from the consideration of the terminal cost as a control Lyapunov function over the terminal constraint set, is revealed. It is shown that when trajectories of the system persistently flows or jumps, the cost functional defining the underlying optimal control problem simplifies considerably.
13:50 Control Lyapunov Functions for Hybrid MPC, Ricardo G.
Sanfelice
The notion of control Lyapunov functions for hybrid inclusions is
formalized in the context of MPC and terminal cost functions. Sufficient
conditions for the existence of control Lyapunov functions are provided.
Methods to construct continuous feedback controllers from such functions
are presented.
14:25 Forward Invariance Tools for Hybrid MPC, Mohamed Maghenem
Notions of forward invariance for hybrid inclusions are presented. Various analysis and synthesis tools to ensure forward invariance, including barrier functions, are demonstrated in the context of MPC and the terminal constraint set.
15:15 Evaluating the Cost of Hybrid MPC without Computing,
Francesco Ferrante
The problem of evaluation the cost of the optimal control problem arising in the MPC algorithm is considered. It is shown that the value function can be estimated with Lyapunov-like inequalities. In addition, it is shown that when the terminal cost of the problem satisfies the sufficient Lyapunov conditions for asymptotic stability, it is an upper bound on the value function of the corresponding infinite horizon optimal control problem. The results are interpreted in the context of MPC for hybrid inclusions with nonunique solutions.
15:50 Coffee Break
16:05 Discretizing Hybrid Dynamical Systems to Solve the
Hybrid MPC Problem, Berk Altın
A computationally tractable counterpart of the MPC algorithm for hybrid inclusions is introduced, which relies on the time-discretization of the underlying continuous-time dynamics. Feasibility and stability properties of the nondiscretized hybrid MPC algorithm presented before are extended to the discretized case. Computational methods to solve the optimal control problem, such as mixed integer nonlinear programming, are presented. As the discretization of hybrid dynamical systems is a nontrivial problem, appropriate discretization techniques are demonstrated.
16:25 Hybrid MPC Applications, Ricardo G. Sanfelice,
Mohamed Maghenem, and Francesco Ferrante
A general methodology for the design of the cost functions required for the MPC algorithm is presented. The presented methodology shows a systematic way of satisfying the sufficient conditions for asymptotic stability. The methodology is demonstrated via three different applications with inherently hybrid dynamics.
16:50 Open Problems and Concluding Remarks, Ricardo G. Sanfelice and Berk Altın
(live discussions will be held after the last session)