Nonlinear learning control for a class of nonlinear systems

Based on the Lyapunov's direct method, a new learning control design is proposed. The proposed technique can be applied in two ways: it is either the standard backward recursive design or its extension. In the first case, the design yields a class of learning control with a difference learning law, under which the class of nonlinear systems is guaranteed to be asymptotically stable with respect to the number of trials in performing repeated tasks. However, implementation of the difference learning control requires derivative measurement of the state for guaranteed stability and performance, as required by most of the existing linear learning control laws. To overcome this difficulty, the proposed design extends the recursive design by employing a new state transformation and a new Lyapunov function, and it yields a class of learning control with a difference-differential learning law. Compared with the existing design methods most of which are based on linear analysis and design, the extension not only guarantees global stability and good performance but also removes such limitations as derivative measurement, Lipschitz condition, and resetting of initial conditions. In addition, the proposed design does not rely on the property of a system under consideration such as the input–output passivity.