Model‐Based Learning Controls And Their Comparisons Using Lyapunov Direct Method

ABSTRACT Model‐based learning control of nonlinear systems is studied. Two types of learning algorithms, described by differential equations and/or difference equations to learn unknown time functions, are designed and compared using the Lyapunov's direct method. The time functions to be learned are classified into several classes according to their properties such as continuity, periodicity, and value at the origin of the state space. Conditions are found for iterative learning controls to achieve asymptotic stability and asymptotic learning convergence. For a comparative study, learning capability of a control is defined and, using the criterion, other model‐based controls with learning capability such as adaptive controls and robust controls are investigated. Through the study, iterative learning control is shown to be the one best suited for learning unknown time functions of known period. Finally, it is shown for the first time that an iterative learning control is directly applicable to systems described by nonlinear partial differential equation.