Multi-Objective Optimal Control Modification Adaptive Control Method for Systems with Input and Unmatched Uncertainties

This paper presents a recent development of a new model-reference adaptive control method based on a multi-objective optimal control formulation for systems with control input uncertainty and unmatched uncertainty. Previously, a bi-objective optimal control modification method has been developed for systems with matched uncertainty and unmatched uncertainty using a predictor model for estimating the control input uncertainty and matched uncertainty. In this work, we develop an extension for unmatched uncertain systems. In the presence of unmatched uncertainty, the uncertainty cannot be completely canceled, but its effect can be minimized to maintain a certain degree of tracking performance and robustness. In this study, we develop a technique to decompose the unmatched uncertainty into a matched component and unmatched component. The matched component is designed to be canceled out by adaptive control to improve tracking performance, while the unmatched component is to be minimized to provide robustness of closed-loop systems. The optimal control formulation includes a third objective cost function which is the minimization of the decomposition error of the unmatched uncertainty in addition to the first two objective functions in the previous bi-objective optimal control modification method for minimization of the tracking error norm and predictor error norm. The approach is a multi-objective optimal control formulation. The resulting multi-objective optimal control modification adaptive control method cancels out the matched component while ensuring robustness by estimating the unmatched component for use in the adaptive laws to bound adaptive parameters. Flight control simulations are performed to illustrate the effectiveness of the multi-objective optimal control modification adaptive laws for unmatched uncertain systems.