Dynamic learning from adaptive neural control with predefined performance for a class of nonlinear systems

In this paper, a neural learning mechanism is presented for a class of single-input-single-output (SISO) uncertain nonlinear systems, which can achieve knowledge acquisition, storage and reuse of the unknown system dynamics as well as the predefined tracking error behavior bound. Using the novel transformed function, the constrained tracking control problem of the original nonlinear system is transformed into the stabilization problem of an augmented system. By combining a filter tracking error with the universal approximation capabilities of radial basis function (RBF) neural networks (NNs), a stable adaptive neural control (ANC) scheme is proposed to guarantee the ultimate boundedness of all the signals in the closed-loop system and the prescribed transient and steady tracking control performance. In the steady control process, a partial persistent excitation (PE) condition of RBF NNs is satisfied during tracking control to recurrent reference orbits. Consequently, it is shown that the proposed ANC scheme can acquire and store knowledge of the unknown system dynamics. The stored knowledge is reused to develop neural learning control, so that the improved control performance with the faster tracking convergence rate and the less computational burden is achieved, while guaranteeing the prescribed transient and steady tracking performance when the initial condition satisfies the prescribed performance bound. Simulation studies are performed to demonstrate and verify the effectiveness of the proposed scheme.