Abstract
In this paper, we investigate the adaptive state-quantized control problem of uncertain lower-triangular systems with input delay. It is assumed that all state variables are quantized for the feedback control design. The error transformation method using an auxiliary time-varying signal is presented to deal with the compensation problem of input delay. Based on the error surfaces with the auxiliary variable, a neural-network-based adaptive state-quantized control scheme is constructed with the design of the input delay compensator. Different from existing results in the literature, the proposed method exhibits the following features: (i) compensating for the input delay effect by using quantized states; and (ii) establishing the stability of the adaptive quantized feedback control system in the presence of input delay. Furthermore, the boundedness of all the signals in the closed-loop and the convergence of the tracking error are analyzed. The effectiveness of the developed control strategy is demonstrated through the simulation on a hydraulic servo system.
Highlights
Owing to theoretical challenges and several practical applications, the feedback control problems of triangular nonlinear systems have been actively addressed in the control community
This paper provides a theoretical basis for the adaptive state-quantized control design of uncertain lower-triangular systems with input delay
This paper develops the adaptive state-quantized control strategy to compensate for the input delay of uncertain nonlinear lower-triangular systems with state quantization
Summary
Owing to theoretical challenges and several practical applications, the feedback control problems of triangular nonlinear systems have been actively addressed in the control community (see [1,2,3] and references therein). To approximate unknown and unmatched nonlinearities in nonlinear systems, a neural-network-based quantized feedback control result is presented in [24] This approach has been extended to nonlinear strict-feedback systems with state delays [25] where the Lyapunov–Krasovskii functional technique is employed to remove the effects of state delays. We aim at addressing the adaptive state-quantized control problem in the presence of input delay in uncertain triangular nonlinear systems with unknown nonlinearities and external disturbances. Different from the existing quantized feedback control results [22,23,24,25], our primary contribution is to establish an input delay compensation strategy using quantized states in the state-quantized control framework while ensuring the robustness against unknown nonlinearities and external disturbances To this end, an error coordinated transformation using the auxiliary variable is derived to design the delay compensator and the neural-network-based adaptive controller.
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