Optimal Control for Discrete-Time Systems under Bounded Disturbances

TL;DR

This paper presents a new optimal control method for linear discrete-time systems with bounded disturbances, leveraging a duality between reachable and observable sets, and provides the first optimal output-feedback solution with improved computational efficiency.

Contribution

It introduces the first optimal output-feedback control solution for discrete-time systems with bounded disturbances, based on a novel duality approach.

Findings

Exact solutions for state-feedback control and filtering.

Numerical simulations show improved performance over previous methods.

First known optimal output-feedback control solution for these systems.

Abstract

This paper introduces a novel approach to the optimal control of linear discrete-time systems subject to bounded disturbances. Our approach is based on the newly established duality between ellipsoidal approximations of reachable and hardly observable sets. We provide exact solutions for state-feedback control and filtering problems, aligning with existing methods while offering improved computational efficiency. Moreover, our main contribution is the optimal solution to the output-feedback control problem for discrete-time systems which was not known before. Numerical simulations demonstrate the superiority of this result over previous sub-optimal ones.