On Stochastic Model Predictive Control with Bounded Control Inputs

TL;DR

This paper develops a convex, tractable stochastic model predictive control method for discrete-time systems with bounded control inputs and unbounded noise, ensuring stability and bounded state variance.

Contribution

It introduces a nonlinear feedback policy that guarantees convexity and tractability in control design under noise and input constraints.

Findings

Convex solution for control optimization problem.

Bounded state variance under stability assumptions.

Numerical methods for offline matrix computation.

Abstract

This paper is concerned with the problem of Model Predictive Control and Rolling Horizon Control of discrete-time systems subject to possibly unbounded random noise inputs, while satisfying hard bounds on the control inputs. We use a nonlinear feedback policy with respect to noise measurements and show that the resulting mathematical program has a tractable convex solution in both cases. Moreover, under the assumption that the zero-input and zero-noise system is asymptotically stable, we show that the variance of the state, under the resulting Model Predictive Control and Rolling Horizon Control policies, is bounded. Finally, we provide some numerical examples on how certain matrices in the underlying mathematical program can be calculated off-line.