Minimal Control Synthesis Adaptive Control of Continuous Bimodal Piecewise Affine Systems

This paper is concerned with the derivation of a model reference adaptive control (MRAC) scheme for bimodal piecewise-affine (PWA) continuous systems. The algorithm is based on an extension of the minimal control synthesis algorithm, originally developed as an MRAC for smooth systems. The resulting adaptive algorithm is a switched feedback controller able to cope with uncertain continuous PWA systems. The proof of stability, based on the newly developed passivity theory for hybrid systems, is provided and the effectiveness of the new proposed control is shown on a representative example.