Min-max piecewise constant optimal control for multi-model linear systems

TL;DR

This paper develops a min-max optimal control method for finite-horizon linear systems with uncertain parameters modeled as a finite set, using a multi-model Riccati approach and a numerical algorithm for implementation.

Contribution

It introduces a novel multi-model Riccati-based approach for min-max control of systems with finite parametric uncertainty.

Findings

The control law is explicitly derived using a discrete Riccati equation.

A numerical algorithm effectively computes the optimal control.

Simulations demonstrate the method's effectiveness in uncertain scenarios.

Abstract

The present work addresses a finite-horizon linear-quadratic optimal control problem for uncertain systems driven by piecewise constant controls. The precise values of the system parameters are unknown, but assumed to belong to a finite set (i.e., there exist only finitely many possible models for the plant). Uncertainty is dealt with using a min-max approach (i.e., we seek the best control for the worst possible plant). The optimal control is derived using a multi-model version of Lagrange's multipliers method, which specifies the control in terms of a discrete-time Riccati equation and an optimization problem over a simplex. A numerical algorithm for computing the optimal control is proposed and tested by simulation.