Opti mal higher order learning adaptive control approach for a class of SISO nonlinear systems

In this paper, an optimal higher order learning adaptive control approach is developed for a class of SISO nonlinear systems. This design is model-free and depends directly on pseudo-partial-derivatives derived on-line from the input and output information of the system. A novel weighted one-step-ahead control criterion function is proposed for the control law. The convergence analysis shows that the proposed control law can guarantee the convergence under the assumption that the desired output is a set point. Simulation examples are provided for nonlinear systems to illustrate the better performance of the higher order learning adaptive control.

Event-Triggered Asymmetric Bipartite Consensus Tracking for Nonlinear Multi-Agent Systems Based on Model-Free Adaptive Control

In this paper,an asymmetric bipartite consensus problem for the nonlinear multi-agent systems with cooperative and antagonistic interactions is studied under the event-triggered mechanism.For the agents described by a structurally balanced signed digraph,the asymmetric bipartite consensus objective is firstly defined,assigning the agents'output to different signs and module values.Considering with the completely unknown dynamics of the agents,a novel event-triggered model-free adaptive bipartite control protocol is designed based on the agents'triggered outputs and an equivalent compact form data model.By utilizing the Lyapunov analysis method,the threshold of the triggering condition is obtained.Subsequently,the asymptotic convergence of the tracking error is deduced and a sufficient condition is obtained based on the contraction mapping principle.Finally,the simulation example further demonstrates the effectiveness of the protocol.

Fuzzy Adaptive Control of Stochastic Nonlinear Systems with Unknown Virtual Control Gain Function

The problem of track control is studied for a class of strict-feedback stochastic nonlinear systems in which unknown virtual control gain function is the main feature. First, the so-called stochastic LaSalle theory is extended to some extent, and accordingly, the results of global ultimate boundedness for stochastic nonlinear systems are developed. Next, a new design scheme of fuzzy adaptive control is proposed. The advantage of it is that it does not require priori knowledge of virtual control gain function sign, which is usually demanded in many designs. At the same time, the track performance of closed-loop systems is improved by adaptive modifying the estimated error upper bound. By theoretical analysis, the signals of closed-loop systems are globally ultimately bounded in probability and the track error converges to a small residual set around the origin in 4th-power expectation.

Output-feedback Adaptive Control for a Class of Nonlinear Systems with Unknown Control Directions

在这份报纸，产量反馈适应稳定与未知控制方向为非线性的系统的一个班被调查。首先通过线性州的转变，未知控制系数在一起是 lumped，原来的系统被转变到控制设计为变得可行的一个新系统。在为状态和参数估计的一个观察员和一个评估者的介绍以后，分别地，然后，一个建设性的设计过程为产量反馈被给使用综合者 backstepping 并且调节功能技术的适应稳定控制器。而所有另外的靠近环的系统状态被围住，设计的控制器保证状态集成到起源的原来的系统，这被显示出而所有另外的靠近环的系统状态被围住。模拟结果被说明显示出建议途径的有效性。

Neural-network adaptive controller for nonlinear systems and its application in pneumatic servo systems

In this paper, a novel control law is presented, which uses neural-network techniques to approximate the affine class nonlinear system having unknown or uncertain dynamics and noise disturbances. It adopts an adaptive control law to adjust the network parameters online and adds another control component according to H-infinity control theory to attenuate the disturbance. This control law is applied to the position tracking control of pneumatic servo systems. Simulation and experimental results show that the tracking precision and convergence speed is obviously superior to the results by using the basic BP-network controller and self-tuning adaptive controller.

Fuzzy Adaptive Control of Delayed High Order Nonlinear Systems

This paper deals with the problem of tracking control for a class of high order nonlinear systems with input delay. The unknown continuous functions of the system are estimated by fuzzy logic systems （FLS）. A state conversion method is introduced to eliminate the delayed input item. By means of the backstepping algorithm, the property of semi-globally uniformly ultimately bounded （SGUUB） of the closed-loop system is achieved. The stability of the closed-loop system is proved according to Lyapunov second theorem on stability. The tracking error is proved to be bounded which ultimately converges to an adequately small compact set. Finally, a computer simulation example of high order nonlinear systems is presented, which illustrates the effectiveness of the control scheme.

Identification and Adaptive Control of Dynamic Nonlinear Systems Using Sigmoid Diagonal Recurrent Neural Network

The goal of this paper is to introduce a new neural network architecture called Sigmoid Diagonal Recurrent Neural Network (SDRNN) to be used in the adaptive control of nonlinear dynamical systems. This is done by adding a sigmoid weight victor in the hidden layer neurons to adapt of the shape of the sigmoid function making their outputs not restricted to the sigmoid function output. Also, we introduce a dynamic back propagation learning algorithm to train the new proposed network parameters. The simulation results showed that the (SDRNN) is more efficient and accurate than the DRNN in both the identification and adaptive control of nonlinear dynamical systems.

Robust adaptive fuzzy tracking control for a class of strict-feedback nonlinear systems based on backstepping technique

In this paper, the robust adaptive fuzzy tracking control problem is discussed for a class of perturbed strict-feedback nonlinear systems. The fuzzy logic systems in Mamdani type are used to approximate unknown nonlinear functions. A design scheme of the robust adaptive fuzzy controller is proposed by use of the backstepping technique. The proposed controller guarantees semi-global uniform ultimate boundedness of all the signals in the derived closed-loop system and achieves the good tracking performance. The possible controller singularity problem which may occur in some existing adaptive control schemes with feedback linearization techniques can be avoided. In addition, the number of the on-line adaptive parameters is not more than the order of the designed system. Finally, two simulation examples are used to demonstrate the effectiveness of the proposed control scheme.

Adaptive Robust Control for a Class of Uncertain MIMO Non-affine Nonlinear Systems

In this paper, the adaptive robust tracking control scheme is proposed for a class of multi-input and multi-output (MIMO) non-affine systems with uncertain structure and parameters, unknown control direction and unknown external disturbance based on backstepping technique. The MIMO non-affine system is first transformed into a time-varying system with strict feedback structure using the mean value theorem, and then the bounded time-varying parameters are estimated by adaptive algorithms with projection. To handle the possible 'controller singularity' problem caused by unknown control direction, a Nussbaum function is employed, and the dynamic surface control (DSC) method is applied to solve the problem of 'explosion of complexity' in backstepping control. It is proved that the proposed control scheme can guarantee that all signals of the closed-loop system are bounded through Lyapunov stability theorem and decoupled backstepping method. Simulation results are presented to illustrate the effectiveness of the proposed control scheme. © 2014 Chinese Association of Automation.

Adaptive H~∞ Control of Nonlinear Systems with Neural Networks

The discussion is devoted to the adaptive H ∞ control method based on RBF neural networks for uncertain nonlinear systems in this paper. The controller consists of an equivalent controller and an H ∞ controller. The RBF neural networks are used to approximate the nonlinear functions and the approximation errors of the neural networks are used in the adaptive law to improve the performance of the systems. The H ∞ controller is designed for attenuating the influence of external disturbance and neural network approximation errors. The controller can not only guarantee stability of the nonlinear systems, but also attenuate the effect of the external disturbance and neural networks approximation errors to reach performance indexes. Finally, an example validates the effectiveness of this method.

Adaptive control using interval Type-2 fuzzy logic for uncertain nonlinear systems

A new adaptive Type-2 （T2） fuzzy controller was developed and its potential performance advantage over adaptive Type-1 （T1） fuzzy control was also quantified in computer simulation. Base on the Lyapunov method, the adaptive laws with guaranteed system stability and convergence were developed. The controller updates its parameters online using the laws to control a system and tracks its output command trajectory. The simulation study involving the popular inverted pendulum control problem shows theoretically predicted system stability and good tracking performance. And the comparison simulation experiments subjected to white noige or step disturbance indicate that the T2 controller is better than the T1 controller by 0--18%, depending on the experiment condition and performance measure.

Observer-based Adaptive Optimal Control for Unknown Singularly Perturbed Nonlinear Systems With Input Constraints

This paper introduces an observer-based adaptive optimal control method for unknown singularly perturbed nonlinear systems with input constraints. First, a multi-Time scales dynamic neural network MTSDNN observer with a novel updating law derived from a properly designed Lyapunov function is proposed to estimate the system states. Then, an adaptive learning rule driven by the critic NN weight error is presented for the critic NN, which is used to approximate the optimal cost function. Finally, the optimal control action is calculated by online solving the Hamilton-Jacobi-Bellman HJB equation associated with the MTSDNN observer and critic NN. The stability of the overall closed-loop system consisting of the MTSDNN observer, the critic NN and the optimal control action is proved. The proposed observer-based optimal control approach has an essential advantage that the system dynamics are not needed for implementation, and only the measured input U+002F output data is needed. Moreover, the proposed optimal control design takes the input constraints into consideration and thus can overcome the restriction of actuator saturation. Simulation results are presented to confirm the validity of the investigated approach. © 2014 Chinese Association of Automation.

Adaptive Decentralized Asymptotic Tracking Control for Large-Scale Nonlinear Systems With Unknown Strong Interconnections

An adaptive decentralized asymptotic tracking control scheme is developed in this paper for a class of large-scale nonlinear systems with unknown strong interconnections,unknown time-varying parameters,and disturbances.First,by employing the intrinsic properties of Gaussian functions for the interconnection terms for the first time,all extra signals in the framework of decentralized control are filtered out,thereby removing all additional assumptions imposed on the interconnec-tions,such as upper bounding functions and matching conditions.Second,by introducing two integral bounded functions,asymptotic tracking control is realized.Moreover,the nonlinear filters with the compensation terms are introduced to circumvent the issue of“explosion of complexity”.It is shown that all the closed-loop signals are bounded and the tracking errors converge to zero asymptotically.In the end,a simulation example is carried out to demonstrate the effectiveness of the proposed approach.

Nonlinear adaptive switching control for a class of non-affine nonlinear systems

An improved nonlinear adaptive switching control method is presented to relax the assumption on the higher order nonlinear terms of a class of discrete-time non-affine nonlinear systems. The proposed control strategy is composed of a linear adaptive controller, a neural network(NN) based nonlinear adaptive controller and a switching mechanism. An incremental model is derived to represent the considered system and an improved robust adaptive law is chosen to update the parameters of the linear adaptive controller. A new performance criterion of the switching mechanism is designed to select the proper controller. Using this control scheme, all the signals in the system are proved to be bounded. Numerical examples verify the effectiveness of the proposed algorithm.

Adaptive L_2 control of nonlinear systems using neural networks

An adaptive neural network controller is developed to achieve output-tracking of a class of nonlinear systems. The global L 2 stability of the closed-loop system is established. The proposed control design overcomes the limitation of the conventional adaptive neural control design where the modeling error brought by neural networks is assumed to be bounded over a compact set. Moreover, the generalized matching conditions are also relaxed in the proposed L 2 control design as the gains for the external disturbances entering the system are allowed to have unknown upper bounds.

Adaptive switching control of a class of nonlinear systems based on mixed multiple models

The transient behaviors of traditional adaptive control may be very poor in general. A practically feasible approach to improve the transient performances is the adoption of adaptive switc- hing control. For a typical class of nonlinear systems disturbed by random noises, mixed multiple models consisting of adaptive model and fixed models were considered to design the switching con- trol law. Under certain assumptions, the nonlinear system with the switching control law was proved rigorously to be stable and optimal A simulation example was provided to compare the performance of the switching control and the traditional adaptive control.

Dissipative-based adaptive neural control for nonlinear systems

A dissipative-based adaptive neural control scheme was developed for a class of nonlinear uncertain systems with unknown nonlinearities that might not be linearly parameterized. The major advantage of the present work was to relax the requirement of matching condition, i.e., the unknown nonlinearities appear on the same equation as the control input in a state-space representation, which was required in most of the available neural network controllers. By synthesizing a state-feedback neural controller to make the closed-loop system dissipative with respect to a quadratic supply rate, the developed control scheme guarantees that the L2-gain of controlled system was less than or equal to a prescribed level. And then, it is shown that the output tracking error is uniformly ultimate bounded. The design scheme is illustrated using a numerical simulation.

ADAPTIVE H-INFINITY CONTROL OF A CLASS OF UNCERTAIN NONLINEAR SYSTEMS

It is concerned with the problem of disturbance attenuation with stability for uncertain nonlinear systems by adaptive output feedback. By a partial-state observer and Backstepping technique, an adaptive output feedback controller was constructed, which can solve the standard gain disturbance attenuation problem with internal stability.

Adaptive Neuro-fuzzy Controller Design for Non-affine Nonlinear Systems

An adaptive neuro-fuzzy control is investigated for a class of non-affine nonlinear systems.To do so,rigorous description and quantification of the approximation error of the neuro-fuzzy controller are firstly discussed.Applying this result and Lyapunov stability theory,a novel updating algorithm to adapt the weights,centers,and widths of the neuro-fuzzy controller is presented.Consequently,the proposed design method is able to guarantee the stability of the closed-loop system and the convergence of the tracking error.Simulation results illustrate the effectiveness of the proposed adaptive neuro-fuzzy control scheme.

Fuzzy Adaptive Tracking Control of Uncertain Strict-Feedback Nonlinear Systems with Disturbances Based on Generalized Fuzzy Hyperbolic Model

In this paper, a fuzzy adaptive tracking control for uncertain strict-feedback nonlinear systems with unknown bounded disturbances is proposed. The generalized fuzzy hyperbolic model (GFHM) with better approximation performance is used to approximate the unknown nonlinear function in the system. The dynamic surface control (DSC) is used to design the controller, which not only avoids the “explosion of complexity” problem in the process of repeated derivation, but also makes the control system simpler in structure and lower in computational cost because only one adaptive law is designed in the controller design process. Through the Lyapunov stability analysis, all signals in the closed loop system designed in this paper are semi-globally uniformly ultimately bounded (SGUUB). Finally, the effectiveness of the method is verified by a simulation example.