TA1 Hybrid Systems II (invited)

Organized by: Pappas G. - University of Pennsylvania, USA Lygeros J., University of California at Berkeley, USA Antsaklis P., University of Notre Dame, USA

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Stabilizing Supervisory Control of Hybrid Systems based on Piecewise-Linear Lyapunov Functions

Authors:

Koutsoukos X., University of Notre Dame, USA

Antsaklis P., University of Notre Dame, USA

ABSTRACT

In this paper, the stability of discrete-time piecewise linear hybrid systems is in-vestigated using piecewise linear Lyapunov functions. In particular, we consider switched discrete-time linear systems and we identify classes of switching sequences that result in stable trajectories. Given a switched linear system, we present a systematic methodology for computing switching laws that guarantee stability based on the matrices of the system. In the proposed approach, we assume that each individual subsystem is stable and admits a piece-wise linear Lyapunov function. Based on these Lyapunov functions, we compose “global” Lyapunov functions that guarantee stability of the switched linear system. A large class of stabilizing switching sequences for switched linear systems is characterized by computing conic partitions of the state space.

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Minimum-Time Reachability for Timed Automata

Authors:

Niebert P., VERIMAG, France

Tripakis S., VERIMAG, France

Yovine S. - VERIMAG, France

ABSTRACT

The problem of minimum-time reachability for timed automata is: given an automaton, and initial state q0 and a target state qf , find whether a run from q0 to qf exists, and if yes, a minimum time run. We show that this problem can be solved by examining acyclic paths in a forward reachability graph generated on-the- y from the timed automaton. Based on this result, we then propose three algorithms with different complex- ities.

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Analysis of Controlled Hybrid Processing Systems based on Approximation by Timed Automata using Interval Arithmetic

Authors:

Stursberg O., University of Dortmund, Germany

Kowaleski S. - University of Dortmund, Germany

ABSTRACT

This contribution describes an approach to investigate reachability properties for a class of controlled hybrid systems. The continuous dynamics of these so-called Switched Continuous Systems (SCS) is selected by the discrete output of a logic controller. While reachability analysis is in general undecidable for this class of systems, the analysis is known to terminate for the class of Timed Automata (TA). In order to make reachability analysis amenable to the control structure, we propose an approximating algorithm to convert a SCS into a TA. Different modifications and extensions of the procedure are given and the approach is illustrated by the application to a chemical reaction system.

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Parameter Synthesis in Robot Motion Planning using Symbolic Reachability Computations

Authors:

Lafferriere G. - Portland State University, USA

Pappas G. - University of Pennsylvania, USA

Schneider G., VERIMAG, France

Yovine S., VERIMAG, France

ABSTRACT

A well known problem in robotics is the motion planning problem in the presence of static obstacles. The trajectory of the robot must satisfy a linear differential equation as well as possible input and state constraints. In this paper, we explore the use of symbolic reachability algorithms to decide whether the motion planning problem is feasible or not. In the case where it is feasible, it computes a feasible nominal input pro le satisfying all system constraints. Our algorithm is based on quantifier elimination techniques in the ordered field of the reals, which have been recently applied to compute the reachable space for classes of linear hybrid systems.

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