An Improved Approach to Design Linear Parameter-Varying Controllers subject to Uncertain Parameter Measurements

摘要

This paper presents an improved approach for the design of linear parameter-varying controllers subject to uncertain parameter measurements. Specifically, we assume both additive and multiplicative uncertainty on the measured parameter, such that the parameter and its measurement assume values in a nonconvex domain. Closed-loop stability and performance is guaranteed by finding a parameter-dependent (PD) Lyapunov matrix such that a PD linear matrix inequality (LMI) is feasible on this nonconvex domain. We propose to express the nonconvex domain as the image of a polynomial spline, such that the PD LMI is equivalently expressed as a PD LMI on a hyperrectangle. To solve the resulting infinite-dimensional LMI problem, we propose a novel relaxation technique that exploits the properties of B-spline basis functions. An extensive numerical example demonstrates the merits of our approach compared to the state of the art.