Adaptive tracking control for nonlinear time-varying delay systems with full state constraints and unknown control coefficients

Abstract

This paper proposes an adaptive tracking control approach for a class of nonlinear state-constrained and time-varying delay systems with unknown time-varying control coefficients. As far as we know, there is no control method for such systems at present. To stabilize such a class of systems, the neural networks and a backstepping technique are utilized to structure an adaptive tracking controller. The Nussbaum gain technique is utilized to solve the problem of unknown time-varying control coefficients, and the Lyapunov–Krasovskii functionals (LKFs) are employed to eliminate the effect of unknown time-varying delays. In addition, the states are guaranteed to remain within their constraint sets based on the Barrier Lyapunov functions (BLFs). Finally, it can be proved that all signals in the closed-loop systems are bounded, the state constraints are never violated and the tracking errors fluctuate within the predetermined compact range around the zero. The simulation results are provided to illustrate the effectiveness of the proposed control strategy.