Approximations of maximal controlled safe sets for hybrid systems

In the determination of the ”maximal safe set” for a hybrid system, the core problem consists in the computation of a maximal controlled invariant set contained in a constraint set for a continuous time dynamical system. In the case of a linear system, we propose a procedure that, on the basis of a controlled invariant set for the exponential discretization of the continuous time system, leads to an arbitrarily good approximation of the maximal controlled invariant set for the continuous time system. The approximating set has the interesting property that the constraints can be satis...ed by means of a piecewise constant control. An example of application of the proposed procedure to idle control is illustrated. keywords: controlled invariant sets, safe sets, linear systems

[1]  Morishigekimura.  Preservation of stabilizability of a continuous time-invariant linear system after discretization , 1990 .

[2]  Jean-Claude Hennet,et al.  COMPUTATION OF MAXIMAL ADMISSIBLE SETS OF CONSTRAINED LINEAR SYSTEMS , 1996 .

[3]  Franco Blanchini,et al.  Ultimate boundedness control for uncertain discrete-time systems via set-induced Lyapunov functions , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[4]  Maria Domenica Di Benedetto,et al.  Idle speed controller synthesis using an assume-guarantee approach , 2003 .

[5]  F. Blanchini,et al.  Constrained Control for Systems with Unknown Disturbances , 1992 .

[6]  E. De Santis,et al.  Controlled safe sets for continuous time linear systems , 2001, 2001 European Control Conference (ECC).

[7]  F. Blanchini,et al.  Constrained stabilization of continuous-time linear systems , 1996 .

[8]  M. Cwikel,et al.  Admissible sets and feedback control for discrete-time linear dynamical systems with bounded controls and states , 1984 .

[9]  C. Pinello,et al.  Automotive engine control and hybrid systems: challenges and opportunities , 2000, Proceedings of the IEEE.

[10]  Jean-Pierre Aubin,et al.  Viability theory , 1991 .

[11]  Luca Benvenuti,et al.  Invariant polytopes of linear systems , 1998 .

[12]  E. D. Santis,et al.  Inner approximations of domains of attraction for constrained continuous time linear systems , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[13]  Maria Domenica Di Benedetto,et al.  Invariant Sets and Control Synthesis for Switching Systems with Safety Specifications , 2000, HSCC.

[14]  Franco Blanchini,et al.  Nonquadratic Lyapunov functions for robust control , 1995, Autom..