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.

Fuzzy Adaptive Quantized Control for a Class of Stochastic Nonlinear Uncertain Systems

In this paper, a fuzzy adaptive approach for stochastic strict-feedback nonlinear systems with quantized input signal is developed. Compared with the existing research on quantized input problem, the existing works focus on quantized stabilization, while this paper considers the quantized tracking problem, which recovers stabilization as a special case. In addition, uncertain nonlinearity and the unknown stochastic disturbances are simultaneously considered in the quantized feedback control systems. By putting forward a new nonlinear decomposition of the quantized input, the relationship between the control signal and the quantized signal is established, as a result, the major technique difficulty arising from the piece-wise quantized input is overcome. Based on fuzzy logic systems' universal approximation capability, a novel fuzzy adaptive tracking controller is constructed via backstepping technique. The proposed controller guarantees that the tracking error converges to a neighborhood of the origin in the sense of probability and all the signals in the closed-loop system remain bounded in probability. Finally, an example illustrates the effectiveness of the proposed control approach.

Neural Controller Design-Based Adaptive Control for Nonlinear MIMO Systems With Unknown Hysteresis Inputs

This paper studies an adaptive neural control for nonlinear multiple-input multiple-output systems in interconnected form. The studied systems are composed of N subsystems in pure feedback structure and the interconnection terms are contained in every equation of each subsystem. Moreover, the studied systems consider the effects of Prandtl-Ishlinskii (PI) hysteresis model. It is for the first time to study the control problem for such a class of systems. In addition, the proposed scheme removes an important assumption imposed on the previous works that the bounds of the parameters in PI hysteresis are known. The radial basis functions neural networks are employed to approximate unknown functions. The adaptation laws and the controllers are designed by employing the backstepping technique. The closed-loop system can be proven to be stable by using Lyapunov theorem. A simulation example is studied to validate the effectiveness of the scheme.

Resilient Asynchronous H∞ Filtering for Markov Jump Neural Networks With Unideal Measurements and Multiplicative Noises

This paper is concerned with the resilient H∞ filtering problem for a class of discrete-time Markov jump neural networks (NNs) with time-varying delays, unideal measurements, and multiplicative noises. The transitions of NNs modes and desired mode-dependent filters are considered to be asynchronous, and a nonhomogeneous mode transition matrix of filters is used to model the asynchronous jumps to different degrees that are also mode-dependent. The unknown time-varying delays are also supposed to be mode-dependent with lower and upper bounds known a priori. The unideal measurements model includes the phenomena of randomly occurring quantization and missing measurements in a unified form. The desired resilient filters are designed such that the filtering error system is stochastically stable with a guaranteed H∞ performance index. A monotonicity is disclosed in filtering performance index as the degree of asynchronous jumps changes. A numerical example is provided to demonstrate the potential and validity of the theoretical results.

Observed-Based Adaptive Fuzzy Tracking Control for Switched Nonlinear Systems With Dead-Zone

In this paper, the problem of adaptive fuzzy output-feedback control is investigated for a class of uncertain switched nonlinear systems in strict-feedback form. The considered switched systems contain unknown nonlinearities, dead-zone, and immeasurable states. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, a switched fuzzy state observer is designed and thus the immeasurable states are obtained by it. By applying the adaptive backstepping design principle and the average dwell time method, an adaptive fuzzy output-feedback tracking control approach is developed. It is proved that the proposed control approach can guarantee that all the variables in the closed-loop system are bounded under a class of switching signals with average dwell time, and also that the system output can track a given reference signal as closely as possible. The simulation results are given to check the effectiveness of the proposed approach.

Multiagent Learning of Coordination in Loosely Coupled Multiagent Systems

Multiagent learning (MAL) is a promising technique for agents to learn efficient coordinated behaviors in multiagent systems (MASs). In MAL, concurrent multiple distributed learning processes can make the learning environment nonstationary for each individual learner. Developing an efficient learning approach to coordinate agents' behaviors in this dynamic environment is a difficult problem, especially when agents do not know the domain structure and have only local observability of the environment. In this paper, a coordinated MAL approach is proposed to enable agents to learn efficient coordinated behaviors by exploiting agent independence in loosely coupled MASs. The main feature of the proposed approach is to explicitly quantify and dynamically adapt agent independence during learning so that agents can make a trade-off between a single-agent learning process and a coordinated learning process for an efficient decision making. The proposed approach is employed to solve two-robot navigation problems in different scales of domains. Experimental results show that agents using the proposed approach can learn to act in concert or independently in different areas of the environment, which results in great computational savings and near optimal performance.

Composite Adaptive Fuzzy Output Feedback Control Design for Uncertain Nonlinear Strict-Feedback Systems With Input Saturation

In this paper, a composite adaptive fuzzy output-feedback control approach is proposed for a class of single-input and single-output strict-feedback nonlinear systems with unmeasured states and input saturation. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a fuzzy state observer is designed to estimate the unmeasured states. By utilizing the designed fuzzy state observer, a serial-parallel estimation model is established. Based on adaptive backstepping dynamic surface control technique and utilizing the prediction error between the system states observer model and the serial-parallel estimation model, a new fuzzy controller with the composite parameters adaptive laws are developed. It is proved that all the signals of the closed-loop system are bounded and the system output can follow the given bounded reference signal. A numerical example and simulation comparisons with previous control methods are provided to show the effectiveness of the proposed approach.

Approximation-Based Adaptive Tracking Control for MIMO Nonlinear Systems With Input Saturation

In this paper, an approximation-based adaptive tracking control approach is proposed for a class of multiinput multioutput nonlinear systems. Based on the method of neural network, a novel adaptive controller is designed via backstepping design process. Furthermore, by introducing Nussbaum function, the issue of unknown control directions is handled. In the backstepping design process, the dynamic surface control technique is employed to avoid differentiating certain nonlinear functions repeatedly. Moreover, in order to reduce the number of adaptation laws, we do not use the neural networks to directly approximate the unknown nonlinear functions but the desired control signals. Finally, we provide two examples to illustrate the effectiveness of the proposed approach.

Dynamic Surface Control Using Neural Networks for a Class of Uncertain Nonlinear Systems With Input Saturation

In this paper, a dynamic surface control (DSC) scheme is proposed for a class of uncertain strict-feedback nonlinear systems in the presence of input saturation and unknown external disturbance. The radial basis function neural network (RBFNN) is employed to approximate the unknown system function. To efficiently tackle the unknown external disturbance, a nonlinear disturbance observer (NDO) is developed. The developed NDO can relax the known boundary requirement of the unknown disturbance and can guarantee the disturbance estimation error converge to a bounded compact set. Using NDO and RBFNN, the DSC scheme is developed for uncertain nonlinear systems based on a backstepping method. Using a DSC technique, the problem of explosion of complexity inherent in the conventional backstepping method is avoided, which is specially important for designs using neural network approximations. Under the proposed DSC scheme, the ultimately bounded convergence of all closed-loop signals is guaranteed via Lyapunov analysis. Simulation results are given to show the effectiveness of the proposed DSC design using NDO and RBFNN.

Adaptive Neural Output Feedback Control of Output-Constrained Nonlinear Systems With Unknown Output Nonlinearity

This paper addresses the problem of adaptive neural output-feedback control for a class of special nonlinear systems with the hysteretic output mechanism and the unmeasured states. A modified Bouc-Wen model is first employed to capture the output hysteresis phenomenon in the design procedure. For its fusion with the neural networks and the Nussbaum-type function, two key lemmas are established using some extended properties of this model. To avoid the bad system performance caused by the output nonlinearity, a barrier Lyapunov function technique is introduced to guarantee the prescribed constraint of the tracking error. In addition, a robust filtering method is designed to cancel the restriction that all the system states require to be measured. Based on the Lyapunov synthesis, a new neural adaptive controller is constructed to guarantee the prescribed convergence of the tracking error and the semiglobal uniform ultimate boundedness of all the signals in the closed-loop system. Simulations are implemented to evaluate the performance of the proposed neural control algorithm in this paper.

Exponential H∞ filtering for discrete-time switched neural networks with random delays

This paper addresses the exponential H∞ filtering problem for a class of discrete-time switched neural networks with random time-varying delays. The involved delays are assumed to be randomly time-varying which are characterized by introducing a Bernoulli stochastic variable. Effects of both variation range and distribution probability of the time delays are considered. The nonlinear activation functions are assumed to satisfy the sector conditions. Our aim is to estimate the state by designing a full order filter such that the filter error system is globally exponentially stable with an expected decay rate and a H∞ performance attenuation level. The filter is designed by using a piecewise Lyapunov-Krasovskii functional together with linear matrix inequality (LMI) approach and average dwell time method. First, a set of sufficient LMI conditions are established to guarantee the exponential mean-square stability of the augmented system and then the parameters of full-order filter are expressed in terms of solutions to a set of LMI conditions. The proposed LMI conditions can be easily solved by using standard software packages. Finally, numerical examples by means of practical problems are provided to illustrate the effectiveness of the proposed filter design.

Adaptive NN tracking control of uncertain nonlinear discrete-time systems with nonaffine dead-zone input

In the paper, an adaptive tracking control design is studied for a class of nonlinear discrete-time systems with dead-zone input. The considered systems are of the nonaffine pure-feedback form and the dead-zone input appears nonlinearly in the systems. The contributions of the paper are that: 1) it is for the first time to investigate the control problem for this class of discrete-time systems with dead-zone; 2) there are major difficulties for stabilizing such systems and in order to overcome the difficulties, the systems are transformed into an n-step-ahead predictor but nonaffine function is still existent; and 3) an adaptive compensative term is constructed to compensate for the parameters of the dead-zone. The neural networks are used to approximate the unknown functions in the transformed systems. Based on the Lyapunov theory, it is proven that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to a small neighborhood of zero. Two simulation examples are provided to verify the effectiveness of the control approach in the paper.

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.

Adaptive fuzzy output feedback dynamic surface control of interconnected nonlinear pure-feedback systems

In this paper, an adaptive fuzzy decentralized output feedback control design is presented for a class of interconnected nonlinear pure-feedback systems. The considered nonlinear systems contain unknown nonlinear uncertainties and the states are not necessary to be measured directly. Fuzzy logic systems are employed to approximate the unknown nonlinear functions, and then a fuzzy state observer is designed and the estimations of the immeasurable state variables are obtained. Based on the adaptive backstepping dynamic surface control design technique, an adaptive fuzzy decentralized output feedback control scheme is developed. It is proved that all the variables of the resulting closed-loop system are semi-globally uniformly ultimately bounded, and also that the observer and tracking errors are guaranteed to converge to a small neighborhood of the origin. Some simulation results and comparisons with the existing results are provided to illustrate the effectiveness and merits of the proposed approach.

Adaptive synchronization for neutral-type neural networks with stochastic perturbation and Markovian switching parameters

In this paper, the problem of adaptive synchronization is investigated for stochastic neural networks of neutral-type with Markovian switching parameters. Using the M-matrix approach and the stochastic analysis method, some sufficient conditions are obtained to ensure three kinds of adaptive synchronization for the stochastic neutral-type neural networks. These three kinds of adaptive synchronization include the almost sure asymptotical synchronization, exponential synchronization in p th moment and almost sure exponential synchronization. Some numerical examples are provided to illustrate the effectiveness and potential of the proposed design techniques.

Adaptive neural control for a class of nonlinear time-varying delay systems with unknown hysteresis

This paper investigates the fusion of unknown direction hysteresis model with adaptive neural control techniques in face of time-delayed continuous time nonlinear systems without strict-feedback form. Compared with previous works on the hysteresis phenomenon, the direction of the modified Bouc-Wen hysteresis model investigated in the literature is unknown. To reduce the computation burden in adaptation mechanism, an optimized adaptation method is successfully applied to the control design. Based on the Lyapunov-Krasovskii method, two neural-network-based adaptive control algorithms are constructed to guarantee that all the system states and adaptive parameters remain bounded, and the tracking error converges to an adjustable neighborhood of the origin. In final, some numerical examples are provided to validate the effectiveness of the proposed control methods.

Exponential stabilization for sampled-data neural-network-based control systems

This paper investigates the problem of sampled-data stabilization for neural-network-based control systems with an optimal guaranteed cost. Using time-dependent Lyapunov functional approach, some novel conditions are proposed to guarantee the closed-loop systems exponentially stable, which fully use the available information about the actual sampling pattern. Based on the derived conditions, the design methods of the desired sampled-data three-layer fully connected feedforward neural-network-based controller are established to obtain the largest sampling interval and the smallest upper bound of the cost function. A practical example is provided to demonstrate the effectiveness and feasibility of the proposed techniques.

Novel neural networks-based fault tolerant control scheme with fault alarm

In this paper, the problem of adaptive active fault-tolerant control for a class of nonlinear systems with unknown actuator fault is investigated. The actuator fault is assumed to have no traditional affine appearance of the system state variables and control input. The useful property of the basis function of the radial basis function neural network (NN), which will be used in the design of the fault tolerant controller, is explored. Based on the analysis of the design of normal and passive fault tolerant controllers, by using the implicit function theorem, a novel NN-based active fault-tolerant control scheme with fault alarm is proposed. Comparing with results in the literature, the fault-tolerant control scheme can minimize the time delay between fault occurrence and accommodation that is called the time delay due to fault diagnosis, and reduce the adverse effect on system performance. In addition, the FTC scheme has the advantages of a passive fault-tolerant control scheme as well as the traditional active fault-tolerant control scheme's properties. Furthermore, the fault-tolerant control scheme requires no additional fault detection and isolation model which is necessary in the traditional active fault-tolerant control scheme. Finally, simulation results are presented to demonstrate the efficiency of the developed techniques.

Adaptive GSA-based optimal tuning of PI controlled servo systems with reduced process parametric sensitivity, robust stability and controller robustness

This paper suggests a new generation of optimal PI controllers for a class of servo systems characterized by saturation and dead zone static nonlinearities and second-order models with an integral component. The objective functions are expressed as the integral of time multiplied by absolute error plus the weighted sum of the integrals of output sensitivity functions of the state sensitivity models with respect to two process parametric variations. The PI controller tuning conditions applied to a simplified linear process model involve a single design parameter specific to the extended symmetrical optimum (ESO) method which offers the desired tradeoff to several control system performance indices. An original back-calculation and tracking anti-windup scheme is proposed in order to prevent the integrator wind-up and to compensate for the dead zone nonlinearity of the process. The minimization of the objective functions is carried out in the framework of optimization problems with inequality constraints which guarantee the robust stability with respect to the process parametric variations and the controller robustness. An adaptive gravitational search algorithm (GSA) solves the optimization problems focused on the optimal tuning of the design parameter specific to the ESO method and of the anti-windup tracking gain. A tuning method for PI controllers is proposed as an efficient approach to the design of resilient control systems. The tuning method and the PI controllers are experimentally validated by the adaptive GSA-based tuning of PI controllers for the angular position control of a laboratory servo system.

Adaptive fuzzy output-feedback controller design for nonlinear systems via backstepping and small-gain approach

This paper focuses on an input-to-state practical stability (ISpS) problem of nonlinear systems which possess unmodeled dynamics in the presence of unstructured uncertainties and dynamic disturbances. The dynamic disturbances depend on the states and the measured output of the system, and its assumption conditions are relaxed compared with the common restrictions. Based on an input-driven filter, fuzzy logic systems are directly used to approximate the unknown and desired control signals instead of the unknown nonlinear functions, and an integrated backstepping technique is used to design an adaptive output-feedback controller that ensures robustness with respect to unknown parameters and uncertain nonlinearities. This paper, by applying the ISpS theory and the generalized small-gain approach, shows that the proposed adaptive fuzzy controller guarantees the closed-loop system being semi-globally uniformly ultimately bounded. A main advantage of the proposed controller is that it contains only three adaptive parameters that need to be updated online, no matter how many states there are in the systems. Finally, the effectiveness of the proposed approach is illustrated by two simulation examples.

Adaptive neural network output feedback control for stochastic nonlinear systems with unknown dead-zone and unmodeled dynamics

This paper discusses the problem of adaptive neural network output feedback control for a class of stochastic nonlinear strict-feedback systems. The concerned systems have certain characteristics, such as unknown nonlinear uncertainties, unknown dead-zones, unmodeled dynamics and without the direct measurements of state variables. In this paper, the neural networks (NNs) are employed to approximate the unknown nonlinear uncertainties, and then by representing the dead-zone as a time-varying system with a bounded disturbance. An NN state observer is designed to estimate the unmeasured states. Based on both backstepping design technique and a stochastic small-gain theorem, a robust adaptive NN output feedback control scheme is developed. It is proved that all the variables involved in the closed-loop system are input-state-practically stable in probability, and also have robustness to the unmodeled dynamics. Meanwhile, the observer errors and the output of the system can be regulated to a small neighborhood of the origin by selecting appropriate design parameters. Simulation examples are also provided to illustrate the effectiveness of the proposed approach.

Adaptive dynamic surface control for uncertain nonlinear systems with interval type-2 fuzzy neural networks

This paper presents a new robust adaptive control method for a class of nonlinear systems subject to uncertainties. The proposed approach is based on an adaptive dynamic surface control, where the system uncertainties are approximately modeled by interval type-2 fuzzy neural networks. In this paper, the robust stability of the closed-loop system is guaranteed by the Lyapunov theorem, and all error signals are shown to be uniformly ultimately bounded. In addition to simulations, the proposed method is applied to a real ball-and-beam system for performance evaluations. To highlight the system robustness, different initial settings of ball-and-beam parameters are considered. Simulation and experimental results indicate that the proposed control scheme has superior responses, compared to conventional dynamic surface control.