Abstract
This article focuses on controlling single-input-single-output (SISO) nonlinear systems with actuator failures via sliding mode control (SMC) and composite learning SMC (CLSMC). In the design of the SMC, an integer-order sliding surface is proposed, and an adaptive law is constructed to update the parameter evaluation in the actuator failure. The SMC method can achieve the tracking error approaching zero if a strict permanent excitation (PE) condition is satisfied. To mitigate this requirement, by using all data recorded while the controller works, we construct prediction errors that are utilized to produce a composite learning adaptive law. Then, the proposed CLSMC method not only drives the tracking error to zero but also realizes the accurate evaluation of the unmatched unknown parameter in the actuator failure. In addition, in the proposed CLSMC method, we only need to satisfy an interval excitation (IE) condition. Simulation results are presented to indicate the validity of our methods.
Highlights
It is commonly recognized that actuator failures in the control of nonlinear systems usually makes the control process more complicated and reduces the control performance
To deal with this problem, fault-tolerant control (FTC) was proposed, for example, an FTC method was proposed for SISO system with actuator failures in [1], where only matched system uncertainty is taken into consideration
In this work, we study the sliding mode control (SMC) and the composite learning SMC (CLSMC) for nonlinear systems with actuator failures. e SMC with adaptive law is designed to ensure the convergence of tracking error but cannot accurately evaluate the parameter
Summary
It is commonly recognized that actuator failures in the control of nonlinear systems usually makes the control process more complicated and reduces the control performance. Erefore, to accelerate the convergence speed and achieve accurate estimation of an unknown parameter, composite adaptive control (CAC) was introduced by combining tracking error and prediction error in [13]. In above literature, a strict condition, i.e., the permanent excitation (PE), should be satisfied to guarantee the convergence of the adaptive parameters To relax this limitation, a more powerful control method called composite learning control (CLC) was proposed in [17], where only a condition named interval excitation (IE) must be satisfied. In order to obtain accurate parameter evaluation, the CLSMC method with composite learning adaptive law is designed. E contributions to this article are as follows: (1) a sliding surface is designed for strict-feedback nonlinear systems to facilitate the CLC design; (2) actuator failures with mismatched parameters are discussed, and a CLSMC method is proposed to obtain the accurate estimation of parametric uncertainties under the IE condition.
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