In this paper we extend the work presented in our previous papers (2001) where we considered optimal control of a linear, discrete time system subject to input constraints and stochastic disturbances. Here we basically look at the same problem but we additionally consider state constraints. We discuss several approaches for incorporating state constraints in a stochastic optimal control problem. We consider in particular a soft-constraint on the state constraints where constraint violation is punished by a hefty penalty in the cost function. Because of the stochastic nature of the problem, the penalty on the state constraint violation can not be made arbitrary high. We derive a condition on the growth of the state violation cost that has to be satisfied for the optimization problem to be solvable. This condition gives a link between the problem that we consider and the well known $H_\infty$ control problem.
|Number of pages||6|
|Publication status||Published - Dec 2002|
|Event||41st IEEE Conference on Decision and Control, CDC 2002 - Las Vegas, United States|
Duration: 10 Dec 2002 → 13 Dec 2002
Conference number: 41
|Conference||41st IEEE Conference on Decision and Control, CDC 2002|
|Period||10/12/02 → 13/12/02|