# Optimal control of linear, stochastic systems with state and input constraints

Ivo Batina, Antonie Arij Stoorvogel, Siep Weiland

30 Citations (Scopus)

## Abstract

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.
Original language Undefined 1564-1569 6 Published - Dec 2002 41st IEEE Conference on Decision and Control, CDC 2002 - Las Vegas, United StatesDuration: 10 Dec 2002 → 13 Dec 2002Conference number: 41

### Conference

Conference 41st IEEE Conference on Decision and Control, CDC 2002 CDC United States Las Vegas 10/12/02 → 13/12/02

• EWI-16650
• IR-69045