Stochastic optimal control for hybrid systems with uncertain discrete dynamics

This paper considers the task of computing (sub-) optimal continuous and discrete control trajectories for hybrid systems with a probabilistic discrete transition structure. The discrete inputs are used to block undesired transitions and to realize evolutions that are goal-attaining with high probability. An approach is proposed which combines the computation of discrete shortest-paths for given probability-levels with embedded continuous optimal control problems to fix the continuous controls. The result is a control strategy which leads to a system evolution that maximizes a weighted sum of performance and probability of success. The approach is illustrated for an automated transportation scenario.

[1]  O. V. Stryk,et al.  HYBRID OPTIMAL CONTROL OF MOTORIZED TRAVELING SALESMEN AND BEYOND , 2002 .

[2]  Peter E. Caines,et al.  On the Optimal Control of Hybrid Systems: Optimization of Trajectories, Switching Times, Location Schedules , 2003, HSCC.

[3]  P. Ramadge,et al.  Supervisory control of a class of discrete event processes , 1987 .

[4]  V. Borkar,et al.  A unified framework for hybrid control: model and optimal control theory , 1998, IEEE Trans. Autom. Control..

[5]  S. Sastry,et al.  Optimal control for a class of stochastic hybrid systems , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[6]  G. Zhai,et al.  Optimal persistent disturbance attenuation control for linear hybrid systems , 2006 .

[7]  Olaf Stursberg,et al.  Control of Switched Hybrid Systems Based on Disjunctive Formulations , 2002 .

[8]  Dimitri P. Bertsekas,et al.  Dynamic Programming and Optimal Control, Two Volume Set , 1995 .

[9]  Oskar von Stryk,et al.  User's guide for DIRCOL (Version 2.1): a direct collacation method for the numerical solution of optimal control problems , 1999 .

[10]  O. Stursberg,et al.  A graph search algorithm for optimal control of hybrid systems , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[11]  A. Rantzer,et al.  Optimal control of hybrid systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[12]  Alberto Bemporad,et al.  Optimal Control of Discrete Hybrid Stochastic Automata , 2005, HSCC.

[13]  Masahiro Ono,et al.  Robust, Optimal Predictive Control of Jump Markov Linear Systems Using Particles , 2007, HSCC.