Stochastic receding horizon control with output feedback and bounded control inputs

TL;DR

This paper develops a convex, receding horizon control approach for stochastic systems with output feedback and bounded inputs, ensuring mean-square boundedness and computational efficiency.

Contribution

It introduces a novel control policy framework that guarantees stability and feasibility for stochastic systems with output feedback and input constraints.

Findings

Finite-horizon optimization is convex and successively feasible.

The control scheme ensures mean-square boundedness of the system.

Off-line computation reduces real-time processing requirements.

Abstract

We provide a solution to the problem of receding horizon control for stochastic discrete-time systems with bounded control inputs and imperfect state measurements. For a suitable choice of control policies, we show that the finite-horizon optimization problem to be solved on-line is convex and successively feasible. Due to the inherent nonlinearity of the feedback loop, a slight extension of the Kalman filter is exploited to estimate the state optimally in mean-square sense. We show that the receding horizon implementation of the resulting control policies renders the state of the overall system mean-square bounded under mild assumptions. Finally, we discuss how some of the quantities required by the finite-horizon optimization problem can be computed off-line, reducing the on-line computation, and present some numerical examples.