Low-Complexity Adaptive Tracking Control for Unknown Pure Feedback Nonlinear Systems With Multiple Constraints

A low-complexity adaptive tracking control strategy for a class of pure feedback nonlinear systems is developed in the presence of completely unknown non-affine nonlinearities, prescribed tracking performance constraints, full states constraints, and input saturation constraint. To handle the input saturation nonlinearity and the constrained states without pre-calculating the bound of virtual controllers, a new coordinate transformation approach is presented with an arc-tangent function and an auxiliary first-order dynamics. Subsequently, to deal with the completely unknown non-affine nonlinearities and the problem of prescribed performance, an inverse hyperbolic tangent function and a Nussbaum function are introduced at each step of back-stepping design, which can guarantee the control errors to vary with prescribed performance functions in time and avoid the “explosion of complexity” issue simultaneously. Then, an adaptive controller is derived from the recursive design procedure without the use of any approximators. The semi-globally uniformly ultimate boundedness of all signals in the closed-loop system and the satisfaction of all constraints are rigorously proved through Lyapunov stability analysis. Finally, the simulation studies on a hypersonic flight vehicle system are worked out to demonstrate the effectiveness and the applicability of the investigated approach.