Backstepping Nussbaum gain dynamic surface control for a class of input and state constrained systems with actuator faults

Abstract

This paper presents a novel constructive control design applicable for uncertain dynamic systems subject to input and state saturations, unknown direction, and actuation faults. The controller is based on the direct Lyapunov method, which by use of the Nussbaum-type function, provides an adaptive control scheme that can handle the effect of unknown control direction. The violation of constraints is avoided by relying on the bounding of the Lyapunov function in the closed-loop system using the barrier Lyapunov function (BLF). The time-varying cotangent-type BLF is constructed, and by introducing a novel flexible technique to generate state constraints, general constraints are formed systematically to relax different initial conditions. Proper input saturation is utilized, and it is shown that under the proposed control all the signals in the closed-loop system are bounded without violating the constraints, in both fault-free and faulty actuation. The performance of the theoretical results is illustrated using numerical simulations. Also, a comparison is made with the results of well-known logarithm BLF and traditional quadratic Lyapunov functions to further evaluate the effectiveness of the proposed controller.