Quadratic optimal control of switched linear stochastic systems

This paper studies the quadratic optimal control problem for the discrete-time switched linear stochastic system with nonautonomous subsystems perturbed by Gaussian random noises. The goal is to jointly design a deterministic switching sequence and a continuous feedback law to minimize the expectation of a finite-horizon quadratic cost function. Both the value function and the optimal control strategy are characterized analytically. A numerical relaxation framework is developed to efficiently compute a control strategy with a guaranteed performance upper bound. It is also proved that by choosing the relaxation parameter sufficiently small, the performance of the resulting control strategy can be made arbitrarily close to the optimal one.