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For a class of nontriangular nonlinear systems in presence of unknown disturbances, we propose a predictor-based neural dynamic surface control (PNDSC) strategy in this paper. This nontriangular system is transformed via the mean value theorem, and a predictor is then constructed. To avoid an algebraic loop problem, partial state vectors are employed as input signals of neural networks (NNs) for approximating unknown dynamics, and compensation items are designed to compensate for approximation errors from NNs. Different from the traditional NDSC, the PNDSC in this paper utilizes prediction errors to update learning parameters for improving NNs’ learning behaviors with overlarge adaptive gains. On the basis of improved NNs’ approximation behaviors, a predictor-based NNs disturbance observer (PNNDO) is constructed for compensation for external disturbances and approximation errors from NNs. Furthermore, with predictors, a normalization method of weights is developed to reduce the number of online learning parameters. On the basis of the aforementioned result, measurement noises are taken into account in our predictor-based neural control strategy. We employ predictor states, rather than measurement information paralyzed by noises, in design of our control strategy. This reduces high-frequency oscillations in control input. A Lyapunov-based stability analysis shows that all signals are ultimately bounded in the closed-loop system. Finally, the effectiveness of the proposed control strategy is verified by a numerical example and a permanent magnet brushless DC motor system. [ABSTRACT FROM AUTHOR]

Backstepping control for fractional-order nonlinear systems (FONSs) requires the analytic calculation of fractional derivatives of certain complicated stabilizing functions, which becomes prohibitive as the order of the system increases. This article aims to facilitate the adaptive neural network (NN) backstepping control design for FONSs with actuator faults whose parameters and patterns are fully unknown. A fractional filtering approach, which obviates the requirement of analytic fractional differentiation, is used to generate command signals together with their fractional derivatives. Compensated tracking errors that can eliminate approximation errors of command signals are generated by fractional filters. The proposed adaptive NN command filtered backstepping control (ANNCFBC) approach, together with fractional adaptive laws, guarantees not only the boundedness of all involved variables but also the convergence of both the tracking error and the compensated tracking error to a sufficiently small region. Finally, simulation studies are given to indicate the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

This paper aims to give a design strategy on the prescribed performance $ {H_{\infty }}$ tracking control problem for a class of strict-feedback stochastic nonlinear systems based on the backstepping technique. Generally, by using the backstepping design method, the stochastic nonlinear systems can only be made to be bounded in probability and it is difficult to achieve the $ {H_{\infty }}$ performance criterion due to the positive constant term appeared in the stability analysis. Thus, a novel concept with regard to the bounded- $ {H_{\infty }}$ performance is proposed in this paper to overcome the design difficulty. By using the new concept and the adaptive neural network technique as well as Gronwall inequality, an adaptive neural network prescribed performance bounded- $ {H_{\infty }}$ tracking controller is designed. Therein, neural networks are used to approximate the unknown packaged nonlinear functions. The assumption that the approximation errors of neural networks are square-integrable in some literature is eliminated. The designed controller guarantees that all the signals in the closed-loop stochastic nonlinear systems are bounded in probability, the tracking error is constrained into an adjustable neighborhood of the origin with the prescribed performance bounds, and the controlled system has a given $ {H_{\infty }}$ disturbance attenuation performance for external disturbances. Finally, the simulation results are provided to illustrate the effectiveness and feasibility of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, for a general class of uncertain nonlinear (cascade) systems, including unknown dynamics, which are not feedback linearizable and cannot be solved by existing approaches, an innovative adaptive approximation-based regulation control (AARC) scheme is developed. Within the framework of adding a power integrator (API), by deriving adaptive laws for output weights and prediction error compensation pertaining to single-hidden-layer feedforward network (SLFN) from the Lyapunov synthesis, a series of SLFN-based approximators are explicitly constructed to exactly dominate completely unknown dynamics. By the virtue of significant advancements on the API technique, an adaptive API methodology is eventually established in combination with SLFN-based adaptive approximators, and it contributes to a recursive mechanism for the AARC scheme. As a consequence, the output regulation error can asymptotically converge to the origin, and all other signals of the closed-loop system are uniformly ultimately bounded. Simulation studies and comprehensive comparisons with backstepping- and API-based approaches demonstrate that the proposed AARC scheme achieves remarkable performance and superiority in dealing with unknown dynamics. [ABSTRACT FROM AUTHOR]

In order to stabilize a class of uncertain nonlinear strict-feedback systems with full-state constraints, an adaptive neural network control method is investigated in this paper. The state constraints are frequently emerged in the real-life plants and how to avoid the violation of state constraints is an important task. By introducing a barrier Lyapunov function (BLF) to every step in a backstepping procedure, a novel adaptive backstepping design is well developed to ensure that the full-state constraints are not violated. At the same time, one remarkable feature is that the minimal learning parameters are employed in BLF backstepping design. By making use of Lyapunov analysis, we can prove that all the signals in the closed-loop system are semiglobal uniformly ultimately bounded and the output is well driven to follow the desired output. Finally, a simulation is given to verify the effectiveness of the method. [ABSTRACT FROM AUTHOR]

Most of the available control schemes for pure-feedback systems are derived based on the backstepping technique. On the contrary, this paper presents a novel adaptive control design for nonlinear pure-feedback systems without using backstepping. By introducing a set of alternative state variables and the corresponding transform, state-feedback control of the pure-feedback system can be viewed as output-feedback control of a canonical system. Consequently, backstepping is not necessary and the previously encountered explosion of complexity and circular issue are also circumvented. To estimate unknown states of the newly derived canonical system, a high-order sliding mode observer is adopted, for which finite-time observer error convergence is guaranteed. Two adaptive neural controllers are then proposed to achieve tracking control. In the first scheme, a robust term is introduced to account for the neural approximation error. In the second scheme, a novel neural network with only a scalar weight updated online is constructed to further reduce the computational costs. The closed-loop stability and the convergence of the tracking error to a small compact set around zero are all proved. Comparative simulation and practical experiments on a servo motor system are included to verify the reliability and effectiveness. [ABSTRACT FROM AUTHOR]