Robust Regret Optimal Control

TL;DR

This paper introduces a method for designing robust controllers that minimize regret relative to an optimal non-causal controller, ensuring performance despite uncertainties in linear systems.

Contribution

It develops a synthesis approach linking robust regret minimization to $H_$ performance, using DK-iteration for controller design in uncertain LTI systems.

Findings

Successfully applied to classical, aerospace, and vehicle suspension examples.

Demonstrated improved robustness over regret controllers without uncertainty considerations.

Validated the method's effectiveness through comparative simulations.

Abstract

This paper presents a synthesis method for robust, regret optimal control. The plant is modeled in discrete-time by an uncertain linear time-invariant (LTI) system. An optimal non-causal controller is constructed using the nominal plant model and given full knowledge of the disturbance. Robust regret is defined relative to the performance of this optimal non-causal control. It is shown that a controller achieves robust regret if and only if it satisfies a robust $H_\infty$ performance condition. DK-iteration can be used to synthesize a controller that satisfies this condition and hence achieve a given level of robust regret. The approach is demonstrated three examples: (i) a simple single-input, single-output classical design, (ii) a longitudinal control for a simplified model for a Boeing 747 model, and (iii) an active suspension for a quarter car model. All examples compare the robust regret optimal against regret optimal controllers designed without uncertainty.