Overtaking optimal regulation and tracking of piecewise diffusion linear systems

The infinite horizon optimal control of linear stochastic systems with quadratic cost integrand is studied, and the tracking of a periodic signal on an infinite time interval is considered. The system is exposed to three types of noises and is modeled by a nonhomogeneous linear stochastic control plant with modal and diffusion disturbances, where the dynamics switch at random times within a finite number of descriptions according to a Markov chain.The overtaking optimality criterion is employed. Considering the expected cost, the existence of a unique optimal control is established for the above noisy control systems with partial information. This is realized as an affine feedback control of the best estimate of the state. Moreover, in the case of partial information, this feedback control is proved to be also almost surely overtaking optimal.

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