Guaranteeing Safety of Switching Adaptive Control Systems

This paper addresses 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 (the existence of a stabilizing solution in a continuously parametrized candidate controller set). The result extends previous theoretical results in hysteresis switching control, and provides a generalization by allowing the class of candidate controllers to have arbitrary cardinality, structure or dimensionality, and by strengthening the concept of tunability