Abstract
This paper presents a continuous composite control scheme to achieve fixed-time stabilization for nonlinear systems with mismatched disturbances. The composite controller is constructed in two steps: First, uniformly finite time exact disturbance observers are proposed to estimate and compensate the disturbances. Then, based on adding a power integrator technique and fixed-time stability theory, continuous fixed-time stable state feedback controller and Lyapunov functions are constructed to achieve global fixed-time system stabilization. The proposed control method extends the existing fixed-time stable control results to high order nonlinear systems with mismatched disturbances and achieves global fixed-time system stabilization. Besides, the proposed control scheme improves the disturbance rejection performance and achieves performance recovery of nominal system. Simulation results are provided to show the effectiveness, the superiority and the applicability of the proposed control scheme.
Highlights
Disturbances widely exist in many practical systems [1] and could degrade system control performance, cause damages to equipment and result in system instability
Great efforts have been taken in designing control strategies to counteract the mismatched disturbances and several control schemes have been proposed, such as, integral sliding mode control [6], adaptive radial basis function (RBF) neural network based control [7], Riccati approach [8], fuzzy control [9]
The composite control scheme is composed of uniformly finite time exact disturbance observer and continuous fixed-time state feedback controller, which can ensure exact disturbance estimation and system convergence within finite time bounded by a constant independent of initial condition
Summary
Disturbances widely exist in many practical systems [1] and could degrade system control performance, cause damages to equipment and result in system instability. A composite control method is presented to achieve fixed-time stabilization for a class of high order nonlinear systems with matched and mismatched disturbances in this paper. The composite control scheme is composed of uniformly finite time exact disturbance observer and continuous fixed-time state feedback controller, which can ensure exact disturbance estimation and system convergence within finite time bounded by a constant independent of initial condition. (2) The proposed control strategy overcomes the drawback of the existing finite time disturbance observers and finite time control methods, and achieves exact disturbance estimation and system stabilization within finite time upper bounded by a constant independent of initial condition. The proposed control scheme achieves uniformly finite time exact disturbance estimation, fixed-time system stabilization and performance recovery of nominal system. N) and 1⁄2Áa 1⁄4 j Á jasignðÁÞ; a > 0
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