Safe Switching Adaptive Control : Stability and Convergence

This thesis is concerned with the control of highly uncertain systems. A formal theoretical explanation of the model-mismatch instability problem often associated with adaptive control design schemes is proposed, and a generic solution is provided. A primary task of adaptive control is formulated as finding an asymptotically optimal, stabilizing controller, given the feasibility of adaptive control problem. Feasibility is defined as the existence of a stabilizing solution in a continuously parametrized candidate controller set. The multi-faceted adaptive control problem is thus placed in a setting of a standard optimization problem. The proposed solution, called safe adaptive control, robustly achieves this goal without any assumptions other than feasibility. Specifically, a list of the required plant-independent properties of the cost function is formulated. The result extends previous theoretical results in multiple model adaptive control, and provides a significant generalization by allowing the class of candidate controllers to have arbitrary cardinality, structure or dimensionality, and by strengthening the concept of tunability. The problem is motivated by a model-mismatch stability failure associated with a multitude of adaptive control schemes, exemplified by several simulation results.