Adaptive State-Quantized Control of Uncertain Lower-Triangular Nonlinear Systems with Input Delay

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.

Further Results on the Input-to-State Stability of a Linear Disturbed System with Control Delay

“…In the work [30], it is demonstrated that the Wirtinger inequality encompasses Jensen's inequality and facilitates, if it is used, the reduction of conservatism. The approach from [31] allows an extension to various practical systems, such as jet engines, flight systems and robots, if the mathematical models are presented in a lower triangular form. Finally, in a recent paper [32], the probabilistic control of discrete-time stochastic systems with multiple control inputs and state delays was considered.…”