Analysis and design of adaptive control systems with unmodeled input dynamics via multiobjective convex optimization

A challenging problem for adaptive control systems is the accurate characterization of the transient response in the presence of dynamic uncertainties such as a partially known actuator. Considering an actuator modelled as a first order filter with an uncertain control effectiveness and using a projection mechanism for parameters adaptation, we show that the tracking error dynamics behaves as a linear system perturbed by bounded uncertainties. This brings the advantage that the stability analysis can be cast in terms of LMIs so that convex optimization tools can be used for analysis and design. In this framework we propose a mixed linear/adaptive control strategy whose parameters are computed via a convex multiobjective optimization in order to ensure, at the same time, the evolution of the error within a minimal size invariant set, while the added linear gain is minimized. A Numerical example is provided to demonstrate the efficacy of the method.