Asymptotic tracking control with preassigned transient performance for strict-feedback systems in the presence of unknown control directions

Abstract This paper is devoted to tracking control for a class of strict-feedback time-varying nonlinear systems with unknown control directions. Currently, most existing control methods for strict-feedback nonlinear systems can realize asymptotic tracking while neglecting the transient performance; or they can guarantee the preassigned transient performance, but merely ultimately bounded tracking error is reached. By introducing smooth compensating terms in a function form of tracking errors, an innovative control algorithm is proposed that can ensure preassigned bounds of overshoot and convergence rate without a priori knowledge of control directions while achieving asymptotic tracking and global uniform boundedness of all the closed-loop signals. Furthermore, the adaptive σ-modification control algorithm for the parameter estimates is developed, which renders smaller parameter estimates and thus results in lower shocks on the control input without compromising the preassigned transient performance and asymptotic tracking convergence. The proposed control algorithms obviate the need for analytic calculation of the partial derivatives of the stabilizing functions (virtual controllers) that is typically employed in controlling of strict-feedback systems, and are therefore more easily derived and implemented. Simulations are provided to verify the theoretical findings.