Closed-loop stability and performance optimization in LPV control based on a reduced parameter set

Abstract

A difficulty encountered in applying linear parameter-varying (LPV) control is the complexity of synthesis and implementation for large numbers of scheduling parameters. Often, heuristic solutions involve neglecting individual scheduling parameters, such that LPV controller synthesis methods become applicable. However, stability and performance guarantees are rendered void, if a controller design based on an approximate model is implemented on the original plant. In this paper, a posteriori conditions are proposed to assess closed-loop stability and performance and possibly recover guarantees. The controller - synthesized based on a reduced parameter set - is first transformed back to depend on the original parameters. Then analysis is performed with respect to the original plant model, which is considered to be accurate. Moreover, an iterative approach for optimizing controllers with few scheduling parameters is sketched. A two-degrees-of-freedom (2-DOF) robotic manipulator is considered as an illustrative example. Experimental results indicate a significant increase in performance.