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A note on an LQG regulator with Markovian switching and pathwise average cost. (English) Zbl 0843.93090

A parametrized linear system perturbed by white noise is studied. The parameters are randomly switching from one state to the other and are modeled as a finite state Markov chain. The actual values of the parameter and the state of the linear system are assumed to be known to the controller. The objective is to minimze a quadratic cost over the infinite planning horizon. Under certain conditions, a linear feedback control is found which is almost surely optimal for the pathwise average cost over the infinite planning horizon.

MSC:

93E20 Optimal stochastic control
60J27 Continuous-time Markov processes on discrete state spaces
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