Fuzzy neural network-based adaptive control for a class of uncertain nonlinear stochastic systems

Robust Adaptive Neural Tracking Control for a Class of Stochastic Nonlinear Interconnected Systems

In this paper, an adaptive neural decentralized control approach is proposed for a class of multiple input and multiple output uncertain stochastic nonlinear strong interconnected systems. Radial basis function neural networks are used to approximate the packaged unknown nonlinearities, and backstepping technique is utilized to construct an adaptive neural decentralized controller. The proposed control scheme can guarantee that all signals of the resulting closed-loop system are semiglobally uniformly ultimately bounded in the sense of fourth moment, and the tracking errors eventually converge to a small neighborhood around the origin. The main feature of this paper is that the proposed approach is capable of controlling the stochastic systems with strong interconnected nonlinearities both in the drift and diffusion terms that are the functions of all states of the overall system. Simulation results are used to illustrate the effectiveness of the suggested approach.

Adaptive Neural Network Control of an Uncertain Robot With Full-State Constraints

This paper studies the tracking control problem for an uncertain n -link robot with full-state constraints. The rigid robotic manipulator is described as a multiinput and multioutput system. Adaptive neural network (NN) control for the robotic system with full-state constraints is designed. In the control design, the adaptive NNs are adopted to handle system uncertainties and disturbances. The Moore-Penrose inverse term is employed in order to prevent the violation of the full-state constraints. A barrier Lyapunov function is used to guarantee the uniform ultimate boundedness of the closed-loop system. The control performance of the closed-loop system is guaranteed by appropriately choosing the design parameters. Simulation studies are performed to illustrate the effectiveness of the proposed control.

Adaptive Fuzzy Tracking Control for a Class of MIMO Nonlinear Systems in Nonstrict-Feedback Form

This paper focuses on the problem of fuzzy adaptive control for a class of multiinput and multioutput (MIMO) nonlinear systems in nonstrict-feedback form, which contains the strict-feedback form as a special case. By the condition of variable partition, a new fuzzy adaptive backstepping is proposed for such a class of nonlinear MIMO systems. The suggested fuzzy adaptive controller guarantees that the proposed control scheme can guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking errors eventually converge to a small neighborhood around the origin. The main advantage of this paper is that a control approach is systematically derived for nonlinear systems with strong interconnected terms which are the functions of all states of the whole system. Simulation results further illustrate the effectiveness of the suggested approach.

Adaptive Robust Output Feedback Control for a Marine Dynamic Positioning System Based on a High-Gain Observer

This paper develops an adaptive robust output feedback control scheme for dynamically positioned ships with unavailable velocities and unknown dynamic parameters in an unknown time-variant disturbance environment. The controller is designed by incorporating the high-gain observer and radial basis function (RBF) neural networks in vectorial backstepping method. The high-gain observer provides the estimations of the ship position and heading as well as velocities. The RBF neural networks are employed to compensate for the uncertainties of ship dynamics. The adaptive laws incorporating a leakage term are designed to estimate the weights of RBF neural networks and the bounds of unknown time-variant environmental disturbances. In contrast to the existing results of dynamic positioning (DP) controllers, the proposed control scheme relies only on the ship position and heading measurements and does not require a priori knowledge of the ship dynamics and external disturbances. By means of Lyapunov functions, it is theoretically proved that our output feedback controller can control a ship's position and heading to the arbitrarily small neighborhood of the desired target values while guaranteeing that all signals in the closed-loop DP control system are uniformly ultimately bounded. Finally, simulations involving two ships are carried out, and simulation results demonstrate the effectiveness of the proposed control scheme.

A New Framework for Analysis on Stability and Bifurcation in a Class of Neural Networks With Discrete and Distributed Delays

This paper studies the stability and Hopf bifurcation in a class of high-dimension neural network involving the discrete and distributed delays under a new framework. By introducing some virtual neurons to the original system, the impact of distributed delay can be described in a simplified way via an equivalent new model. This paper extends the existing works on neural networks to high-dimension cases, which is much closer to complex and real neural networks. Here, we first analyze the Hopf bifurcation in this special class of high dimensional model with weak delay kernel from two aspects: one is induced by the time delay, the other is induced by a rate parameter, to reveal the roles of discrete and distributed delays on stability and bifurcation. Sufficient conditions for keeping the original system to be stable, and undergoing the Hopf bifurcation are obtained. Besides, this new framework can also apply to deal with the case of the strong delay kernel and corresponding analysis for different dynamical behaviors is provided. Finally, the simulation results are presented to justify the validity of our theoretical analysis.

Output-feedback adaptive neural control for stochastic nonlinear time-varying delay systems with unknown control directions

This paper presents an adaptive output-feedback neural network (NN) control scheme for a class of stochastic nonlinear time-varying delay systems with unknown control directions. To make the controller design feasible, the unknown control coefficients are grouped together and the original system is transformed into a new system using a linear state transformation technique. Then, the Nussbaum function technique is incorporated into the backstepping recursive design technique to solve the problem of unknown control directions. Furthermore, under the assumption that the time-varying delays exist in the system output, only one NN is employed to compensate for all unknown nonlinear terms depending on the delayed output. Moreover, by estimating the maximum of NN parameters instead of the parameters themselves, the NN parameters to be estimated are greatly decreased and the online learning time is also dramatically decreased. It is shown that all the signals of the closed-loop system are bounded in probability. The effectiveness of the proposed scheme is demonstrated by the simulation results.

Universal fuzzy models and universal fuzzy controllers for discrete-time nonlinear systems

This paper investigates the problems of universal fuzzy model and universal fuzzy controller for discrete-time nonaffine nonlinear systems (NNSs). It is shown that a kind of generalized T-S fuzzy model is the universal fuzzy model for discrete-time NNSs satisfying a sufficient condition. The results on universal fuzzy controllers are presented for two classes of discrete-time stabilizable NNSs. Constructive procedures are provided to construct the model reference fuzzy controllers. The simulation example of an inverted pendulum is presented to illustrate the effectiveness and advantages of the proposed method. These results significantly extend the approach for potential applications in solving complex engineering problems.

Adaptive NN controller design for a class of nonlinear MIMO discrete-time systems

An adaptive neural network tracking control is studied for a class of multiple-input multiple-output (MIMO) nonlinear systems. The studied systems are in discrete-time form and the discretized dead-zone inputs are considered. In addition, the studied MIMO systems are composed of N subsystems, and each subsystem contains unknown functions and external disturbance. Due to the complicated framework of the discrete-time systems, the existence of the dead zone and the noncausal problem in discrete-time, it brings about difficulties for controlling such a class of systems. To overcome the noncausal problem, by defining the coordinate transformations, the studied systems are transformed into a special form, which is suitable for the backstepping design. The radial basis functions NNs are utilized to approximate the unknown functions of the systems. The adaptation laws and the controllers are designed based on the transformed systems. By using the Lyapunov method, it is proved that the closed-loop system is stable in the sense that the semiglobally uniformly ultimately bounded of all the signals and the tracking errors converge to a bounded compact set. The simulation examples and the comparisons with previous approaches are provided to illustrate the effectiveness of the proposed control algorithm.

Reinforcement learning design-based adaptive tracking control with less learning parameters for nonlinear discrete-time MIMO systems

Based on the neural network (NN) approximator, an online reinforcement learning algorithm is proposed for a class of affine multiple input and multiple output (MIMO) nonlinear discrete-time systems with unknown functions and disturbances. In the design procedure, two networks are provided where one is an action network to generate an optimal control signal and the other is a critic network to approximate the cost function. An optimal control signal and adaptation laws can be generated based on two NNs. In the previous approaches, the weights of critic and action networks are updated based on the gradient descent rule and the estimations of optimal weight vectors are directly adjusted in the design. Consequently, compared with the existing results, the main contributions of this paper are: 1) only two parameters are needed to be adjusted, and thus the number of the adaptation laws is smaller than the previous results and 2) the updating parameters do not depend on the number of the subsystems for MIMO systems and the tuning rules are replaced by adjusting the norms on optimal weight vectors in both action and critic networks. It is proven that the tracking errors, the adaptation laws, and the control inputs are uniformly bounded using Lyapunov analysis method. The simulation examples are employed to illustrate the effectiveness of the proposed algorithm.

Local synchronization of chaotic neural networks with sampled-data and saturating actuators

This paper investigates the problem of local synchronization of chaotic neural networks with sampled-data and actuator saturation. A new time-dependent Lyapunov functional is proposed for the synchronization error systems. The advantage of the constructed Lyapunov functional lies in the fact that it is positive definite at sampling times but not necessarily between sampling times, and makes full use of the available information about the actual sampling pattern. A local stability condition of the synchronization error systems is derived, based on which a sampled-data controller with respect to the actuator saturation is designed to ensure that the master neural networks and slave neural networks are locally asymptotically synchronous. Two optimization problems are provided to compute the desired sampled-data controller with the aim of enlarging the set of admissible initial conditions or the admissible sampling upper bound ensuring the local synchronization of the considered chaotic neural networks. A numerical example is used to demonstrate the effectiveness of the proposed design technique.