Optimal sliding‐mode control of linear systems with uncertainties and input constraints using projection neural network

Abstract

Summary In this paper, an optimal sliding‐mode control (SMC) method based on the projection recurrent neural networks for a class of linear systems with uncertainties and input constraint is developed. The chattering in the SMC is eliminated by introducing a performance index for minimizing the sliding‐surface variations and the control effort. Moreover, the constraints on the actuators are considered in the optimization problem, which is solved using projection recurrent neural network. The main advantages of the proposed method are obtaining an optimal and chattering‐free control law in a feasible space. Moreover, the parameters of the proposed control method are determined based on the closed‐loop stability and robustness analysis. The performance of the proposed method is evaluated by considering uncertainties and input constraints in the system and is compared with the conventional and a second‐order SMC in the view of chattering, input saturation, and robustness.

Near‐optimal control of a class of output‐constrained systems using recurrent neural network: A control‐barrier function approach

“…The following lemma provides a theoretical analysis on how () attains the optimal solution of the problem.Lemma Consider QP in () with constant vectors and matrices $$$ \hat{\mathbf{p}} $$$, $$$ {\hat{\overline{\mathbf{Y}}}}_n $$$, $$$ {\hat{\underset{\_}{\mathbf{Y}}}}_n $$$, $$$ \mathbf{Q} $$$, and $$$ \overline{\Theta} $$$. Then, the RNN in () with these parameters is stable and its output equation is convergent to the optimal solution of the QP. Proof Theoretical analysis of RNNs, including (), are addressed in References 36 and 37. Nevertheless, since the final Lyapunov inequality is required for the next section, a brief analysis with a minor modification is provided here.…”

Observer‐based control with enlarged domain of attraction for one‐sided Lipschitz systems subject to input saturation

“…Therefore, the effect of input saturation should be taken into consideration in the controller design. In the last years, the input saturation control problem has received the attention of many authors 38‐42 . However, less attention has been paid to the OBC design problem for OSL systems subject to input saturation in the literature.…”

Adaptive block compensation trajectory tracking control based on LuGre friction model

“…Jung 11 presented a neural network control technique to improve the tracking performance of a three-link rotary robot manipulator, where a neural network compensator is used to deal with the stability and performance more intelligently. Toshani and Farrokhi 12 developed an optimal sliding mode control method based on the projection recurrent neural networks for a class of linear systems. Nguyen et al 13 proposed a neural network-based adaptive sliding mode control method for tracking of a nonholonomic wheeled mobile robot subject to unknown wheel slips, model uncertainties, and unknown bounded disturbances, where self-recurrent wavelet neural networks are employed to approximate unknown nonlinear functions.…”

“…Some scholars have studied the sliding mode control method based on neural network. 1 –15 For example, Vikas 1 studied wavelet neural networks controller based on fast terminal sliding mode control, where the wavelet neural network is used to compensate the unknown robot dynamics. Wai and Muthusamy 2 proposed a sliding mode controller based on fuzzy neural network genetic algorithm, where a projection algorithm is used to derive the adaptive adjustment algorithm of network parameters.…”