Safe Adaptive Control, 2011
Data-driven Stability Analysis and Robust Synthesis
Lecture Notes in Control and Information Sciences Series, Vol. 405

Safe Adaptive Control gives a formal and complete algorithm for assuring the stability of a switched control system when at least one of the available candidate controllers is stabilizing. The possibility of having an unstable switched system even in the presence of a stabilizing candidate controller is demonstrated by referring to several well-known adaptive control approaches, where the system goes unstable when a large mismatch between the unknown plant and the available models exists ("plant-model mismatch instability"). Sufficient conditions for this possibility to be avoided are formulated, and a "recipe" to be followed by the control system designer to guarantee stability and desired performance is provided. The problem is placed in a standard optimization setting. Unlike the finite controller sets considered elsewhere, the candidate controller set is allowed to be continuously parametrized so that it can deal with plants with a very large range of uncertainties.

Introduction.- Definitions and Preliminary Facts.- Stability Results.- Generalization to the Time-varying Case.- Switched Adaptive Controller: Robust Synthesis.- Comparison with Other Switching Adaptive Schemes.- Conclusion.

Helps the reader achieve rapid plant adaptation in quickly-changing environments and fast convergence to target parameter values

Provides the reader with rigorous treatment of adaptive system stability

Gives the reader a method of analysing "model-mismatch" instability with a view to avoiding it