Filtering adaptive neural network controller for multivariable nonlinear systems with mismatched uncertainties

Abstract

This paper synthesizes a filtering adaptive neural network controller for multivariable nonlinear systems with mismatched uncertainties. The multivariable nonlinear systems under consideration have both matched and mismatched uncertainties, which satisfy the semiglobal Lipschitz condition. The nonlinear uncertainties are approximated by a Gaussian radial basis function (GRBF)-based neural network incorporated with a piecewise constant adaptive law, where the adaptive law will generate adaptive parameters by solving the error dynamics between the real system and the state predictor with the neglection of unknowns. The combination of GRBF-based neural network and piecewise constant adaptive law relaxes hardware limitations (CPU). A filtering control law is designed to handle the nonlinear uncertainties and deliver a good tracking performance with guaranteed robustness. The matched uncertainties are cancelled directly by adopting their opposite in the control signal, whereas a dynamic inversion of the system is required to eliminate the effect of the mismatched uncertainties on the output. Since the virtual reference system defines the best performance that can be achieved by the closed-loop system, the uniform performance bounds are derived for the states and control signals via comparison. To validate the theoretical findings, comparisons between the model reference adaptive control method and the proposed filtering adaptive neural network control architecture with the implementation of different sampling time are carried out.

Finite‐time adaptive tracking control for a class of nonstrict feedback nonlinear systems with full state constraints

“…As a valid method in dealing with unknown uncertainties, [1][2][3] adaptive backstepping control has found wide applications in nonlinear control systems in the past few years. [4][5][6][7] To better deal with unknown uncertainties, some powerful methods are proposed, including neural network method [8][9][10] and fuzzy logic method. 11,12 Adaptive neural networks (ANNs)/fuzzy logics controllers are constructed to stabilize the considered nonlinear systems.…”

Combined adaptive neural network and regressor‐based trajectory tracking control of flexible joint robots

“…In [56], the authors proposed a trajectory tracking controller for a class of uncertain non-linear systems with time delay by using command filtered-based event-triggered adaptive neural network control. A filtering adaptive neural network-based controller with Gaussian radial basis function was developed in [57] to compensate mismatched uncertainties in multivariable non-linear systems. A backstepping-based controller with adaptive neural networks was proposed in [58] for non-strict-feedback systems with input delays.…”

Disturbance observer‐based two‐Layer control strategy design to deal with both matched and mismatched uncertainties

“…Due to their unique features, designing a controller that be able to optimally and robustly manage nonlinear systems subjected to mismatched uncertainties has been the desire of researchers. In this respect, different control methods have been proposed to make nonlinear systems immune against mismatched uncertainties; such as robust control methods, 14‐20 adaptive control schemes, 21‐24 and hybrid control systems 25‐33 . In dealing with mismatched uncertainties, an appropriate controller should make an uncertain nonlinear system robust, while achieving a desired performance.…”

“…For managing multivariable nonlinear plants against mismatched uncertainties, a filtering adaptive neural network (NN) control strategy was devised in Reference 22. In that work, fast adaptation was achieved through the integration of Gaussian radial basis function and piecewise constant adaptive rule.…”