Dampening parameter distributional shifts under robust control and gain scheduling

Abstract: Many traditional robust control approaches assume linearity of the system and independence between the system state-input and the parameters of its approximant low-order model. This assumption implies that robust control design introduces no distributional shifts in the parameters of this low-order model. This is generally not true when the underlying actual system is nonlinear, which admits typically state-input coupling with the parameters of the approximating model. Therefore, a robust controller has to be robust under the parameter distribution that will be experienced in the future data, after applying this control, not the parameter distribution seen in the learning data or assumed in the design. In this paper we seek a solution to this problem by restricting the newly designed closed-loop system to be consistent with the learning data and slowing down any distributional shifts in the state-input and parameter spaces. In computational terms, these objectives are formulated as convex semi-definite programs that standard software packages can efficiently solve. We evaluate the proposed approaches on a simple yet telling gain-scheduling problem, which can be equivalently posed as a robust control problem.