Guaranteed safe switching for switching adaptive control

Abstract

Adaptive control algorithms may not behave well in practice due to discrepancies between the theory and actual practice. The proposed results in this manuscript constitute an effort in providing algorithms which assure more reliable operation in practice. Our emphasis is on algorithms that will be safe in the sense of not permitting destabilizing controllers to be switched in the closed-loop and to prevent wild signal fluctuations to occur. Coping with the connection or possible connection of destabilizing controllers is indeed a daunting task. One of the most intuitive forms of adaptive control, gain scheduling, is an approach to control of non-linear systems which utilizes a family of linear controllers, each of which provides satisfactory control for a different operating point of the system. We provide a mechanism for guaranteeing closed-loop stability over rapid switching between controllers. Our proposed design provides a simplification using only finite number of pre-determined values for the controller gain, where the observer gain is computed via a table look-up method. In comparison to the original gain scheduling design which our procedure builds on, our design achieves similar performance but with much less computational burden. Many multi-controller adaptive switching algorithms do not explicitly rule out the possibility of switching a destabilizing controller into the closed-loop. Even if the new controller is ensured to be stabilizing, performance verification with the new controller is not straightforward. The importance of this arises in iterative identification and control algorithms and multiple model adaptive control (MMAC). We utilize a limited amount of experimental and possibly noisy data obtained from a closed-loop consisting of an existing known stabilizing controller connected to an unknown plant-to infer if the introduction of a prospective controller will stabilize the unknown plant. We propose analysis results in a nonlinear setting and provide data-based tests for verifying the closed-loop stability with the introduction of a new nonlinear controller to replace a linear controller. We also propose verification tools for the closed-loop performance with the introduction of a new stabilizing controller using a limited amount of data obtained from the existing stable closed-loop. The simulation results in different practical scenarios demonstrate efficacy and versatility of our results, and illustrate practicality of our novel data-based tests in addressing an instability problem in adaptive control algorithms. Show more