# Sparse and Constrained Stochastic Predictive Control for Networked Systems

## TL;DR

This paper introduces a new class of sparse, constrained stochastic predictive control policies for networked linear systems with packet dropouts and noise, ensuring stability and boundedness through convex optimization.

## Contribution

It proposes a novel affine control policy with sparsity promotion and stability guarantees for networked systems affected by stochastic packet drops and disturbances.

## Key findings

- Control policies ensure mean-square boundedness of states.
- Convex quadratic programs enable online implementation.
- Policies are robust to packet dropouts and noise.

## Abstract

This article presents a novel class of control policies for networked control of Lyapunov-stable linear systems with bounded inputs. The control channel is assumed to have i.i.d. Bernoulli packet dropouts and the system is assumed to be affected by additive stochastic noise. Our proposed class of policies is affine in the past dropouts and saturated values of the past disturbances. We further consider a regularization term in a quadratic performance index to promote sparsity in control. We demonstrate how to augment the underlying optimization problem with a constant negative drift constraint to ensure mean-square boundedness of the closed-loop states, yielding a convex quadratic program to be solved periodically online. The states of the closed-loop plant under the receding horizon implementation of the proposed class of policies are mean square bounded for any positive bound on the control and any non-zero probability of successful transmission.