NN/RISE-based controller design for a class of uncertain nonlinear systems with time-varying constraints

This paper presents a novel adaptive control strategy for the tracking control of a class of uncertain nonlinear systems with external disturbances as well as for placing arbitrary user-defined time-varying constraints on the system state. As such, our contribution is a step forward beyond the usual stabilization result to show that the states of the plant not only converge asymptotically, but also remain within user- defined, time-varying bound functions. To prove our new results, an error transformed technique is firstly established to generate a new uncertain nonlinear system, whose asymptotic stability guarantees both the satisfaction of the time-varying restrictions and the asymptotic tracking performance of the original system. The uncertainties of the transformed system are overcome by an online neural network (NN) approximator, while the external disturbances and NN reconstruction error are compensated by the robust integral of the sign of the error (RISE) signal. Via standard Lyapunov method, semi-global asymptotic tracking performance is theoretically guaranteed, and all the closed-loop signals are bounded. The requirement for a prior knowledge of bounds of uncertain terms is relaxed. Finally, simulation results demonstrate the merits of the proposed controller.