Input Hard Constrained Optimal Covariance Steering

TL;DR

This paper develops an optimal covariance steering method for stochastic linear systems that handles probabilistic state constraints and deterministic input hard constraints, validated through numerical simulations.

Contribution

It introduces a novel approach to covariance steering that combines chance constraints on states with hard constraints on inputs, addressing a gap in existing methods.

Findings

Successfully incorporates state chance constraints and input hard constraints.

Validated approach through numerical simulations demonstrating effectiveness.

Addresses unbounded noise effects in stochastic systems.

Abstract

We address the optimal covariance steering (OCS) problem for stochastic discrete linear systems with additive Gaussian noise under state chance constraints and input hard constraints. Because the system state can be unbounded due to the unbounded noise, the state constraints are formulated as probabilistic (chance) constraints, i.e., the maximum probability of constraint violation is constrained. In contrast, because it is hard to interpret the appropriate control action when the control command violates the constraints, probabilistically formulating the control constraints are difficult, and deterministic hard constraints are preferable. In this work we introduce an OCS approach subject to simultaneous state chance constraints and input hard constraints and validate the approach using numerical simulations.