Model-Mismatch Instability in Adaptive Control Systems

It has long been recognized that any adaptive controller can be characterized by an admissible controller set and a data-dependent cost function that partially orders these controllers. In this talk we discuss the unfalsified control concept, which involves expressing adaptive control cost functions in terms of certain controller-dependent `fictitious' signals used to evaluate stability and performance. We also define a new plant-independent property for adaptive controllers called cost-detectability. We prove that when cost-detectable unfalsified controllers are constructed using hysteresis-type adaptive algorithms, then closedloop stability of the adaptive control system is guaranteed with no assumption on the plant other than the trivial assumption of feasibility, i.e., that there exists a controller in the candidate controller set that would stabilize the plant if it were known. Cost detectable adaptive control designs circumvent the robustness problems and model-mismatch instability risks inherent with other popular adaptive design methods. Design studies and simulations demonstrate remarkably rapid convergence with unfalsified adaptive designs, often within a fraction of a plant time constant.