Adjoint-based optimal control of the expected exit time for stochastic hybrid systems

Authors:
Robin L. Raffard;Jianghai Hu;Claire J. Tomlin
Affiliations:
Dept. of Aeronautics and Astronautics, Stanford University;School of Electrical and Computer Engineering, Purdue University;Dept. of Aeronautics and Astronautics, Stanford University
Venue:
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Year:
2005

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Abstract

In this paper, we study the problem of controlling the expected exit time from a region for a class of stochastic hybrid systems. That is, we find the least costly feedback control for a stochastic hybrid system that can keep its state inside a prescribed region for at least an expected amount of time. The stochastic hybrid systems considered are quite general: the continuous dynamics are governed by stochastic differential equations, and the discrete mode evolves according to a continuous time Markov chain. Instead of adopting the usual Hamilton-Jacobi viewpoint, we study the problem directly by formulating it as a PDE constrained optimization problem, and propose a solution using adjoint-based gradient descent methods. Numerical results of the proposed approach are presented for several representative examples, and, for the simple case, compared with analytical results.