Stochastic model predictive control with bounded control inputs: a vector space approach

TL;DR

This paper develops a convex optimization-based stochastic model predictive control method for linear systems with unbounded disturbances, ensuring control input bounds and bounded state variance.

Contribution

It introduces a vector space approach to design receding horizon controllers that handle unbounded disturbances with hard input constraints, providing tractable solutions.

Findings

The control strategy guarantees bounded state variance under input constraints.

The optimization problems can be efficiently solved offline.

The approach is validated through illustrative examples.

Abstract

We design receding horizon control strategies for stochastic discrete-time linear systems with additive (possibly) unbounded disturbances, while obeying hard bounds on the control inputs. We pose the problem of selecting an appropriate optimal controller on vector spaces of functions and show that the resulting optimization problem has a tractable convex solution. Under the assumption that the zero-input and zero-noise system is asymptotically stable, we show that the variance of the state is bounded when enforcing hard bounds on the control inputs, for any receding horizon implementation. Throughout the article we provide several examples that illustrate how quantities needed in the formulation of the resulting optimization problems can be calculated off-line, as well as comparative examples that illustrate the effectiveness of our control strategies.