Prescribed Performance Adaptive Control for a Class of Non-affine Uncertain Systems with State and Input Constraints

For a class of non-affine nonlinear systems with state constraints, input constraint, uncertain parameters and unknown external disturbance, a back-stepping control scheme is proposed based on mean value theorem, nonlinear mapping and prescribed performance bounds (PPB). The non-affine system is first transformed into a time-varying system with a linear structure by using the mean value theorem, and the intervals of the time-varying uncertain parameters are calculated. The bounded time-varying parameters and external disturbance are estimated by adaptive algorithms with projection; the estimation error is compensated by employing nonlinear damping technology. To handle the state and input constraints, the nonlinear mapping technique (NMT), hyperbolic tangent function and Nussbaum function are employed. The prescribed performance control method improves the performance of the system. It is proved that the proposed control scheme can guarantee that all signals of the closed-loop system are bounded through the Lyapunov analysis. Simulation results are presented to demonstrate the effectiveness of the proposed control scheme.