Robust regret optimal control

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 infinity$$ {H}_{\infty } $$ 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 two examples: (i) a single-input, single-output (SISO) classical design, and (ii) an active suspension for a quarter car model. The SISO example is simple but is intended to provide insight about the robust regret control design. The quarter car example compares the robust regret controllers against regret controllers designed without plant uncertainty.