Large-scale Stochastic Nonlinear Systems Research Articles

Command filter-based adaptive fuzzy decentralized control for stochastic nonlinear large-scale systems with saturation constraints and unknown disturbance

In this article, the problem of decentralized fuzzy adaptive control is addressed for a class of stochastic interconnected nonlinear large-scale systems including saturation and unknown disturbance. Fuzzy logic systems (FLSs) are used to estimate packaged nonlinear uncertainties. The command filter technique is presented to eliminate the “explosion of complexity” obstacle associated with the backstepping procedures and the corresponding error compensation mechanism is constructed to alleviate the effect of the errors generated by command filters. The influence of input saturation is compensated by introducing an auxiliary system. Meanwhile, an improved adaptive fuzzy decentralized controller is developed and it is able to minimize calculation time since there is no need for repeated differentiation for the virtual control laws. The presented control scheme not only assures the semi-global boundedness of all the signals in the closed-loop system, but also makes the output tracking errors reach a small neighborhood around the origin. Finally, both numerical and practical examples are provided to illustrate the efficiency and effectiveness of our theoretic result.

Adaptive neural smooth finite-time controller for large-scale stochastic nonlinear state-constrained systems with feasibility removal and time delays

This paper studies the adaptive smooth finite-time neural controller design for large-scale stochastic nonlinear systems subject to command filter and time-delay interactions. The main features are (1) the communication interconnection has the output delay between subsystems; (2) the smooth finite time strategy is given for stochastic disturbances; (3) all states are confined in the constrained space without feasibility conditions. First, the state time-delay interactions are tackled by the appropriate establishment of Lyapunov–Krasovskii functionals. Second, for full-state constraints, state-related mappings are employed to remove the feasibility. Then, by constructing the switching virtual control signals, the smooth fast finite-time feature is attached to the controller. Finally, based on finite-time stability theory in probability, command filter, and backstepping technique, the smooth fast finite-time neural controller is constructed to make that all system states converge in finite time, all closed-loop variables are bounded in probability, and full-state constraints are satisfied. Simulation results are provided to test the correctness of the method.

Decentralized stabilization of large-scale stochastic nonlinear systems with time-varying powers

In this paper, we study the decentralized stabilization problem for large-scale high-order stochastic nonlinear systems with time-varying powers. By using the backstepping design technique, a new decentralized state-feedback controller is constructed to ensure the closed-loop system is globally asymptotically stable (GAS) in probability. Then we further redesign a new optimal controller to solve the decentralized inverse optimal stabilization (IOS) problem. Specifically, our redesigned stabilizing backstepping controller is not only globally asymptotically stable for the closed-loop system but also optimal for the meaningful cost function. Finally, a simulation example is given to illustrate the effectiveness of the designed controllers.

Robust Adaptive Fuzzy Control via State-Dependent Function for Nonlinear Stochastic Large-Scale Systems Subject to Dead Zones

This paper concentrates on the adaptive fuzzy control problem for stochastic nonlinear large-scale systems with constraints and unknown dead zones. By introducing the state-dependent function, the constrained closed-loop system is transformed into a brand-new system without constraints, which can realize the same control objective. Then, fuzzy logic systems (FLSs) are used to identify the unknown nonlinear functions, the dead zone inverse technique is utilized to compensate for the dead zone effect, and a robust adaptive fuzzy control scheme is developed under the backstepping frame. Based on the Lyapunov stability theory, it is proved ultimately that all signals in the closed-loop system are bounded and the tracking errors converge to a small neighborhood of the origin. Finally, an example based on an actual system is given to verify the effectiveness of the proposed control scheme.

Sampled-Data Decentralized Output Feedback Control for a Class of Switched Large-Scale Stochastic Nonlinear Systems

In this article, a decentralized output feedback control problem for switched large-scale stochastic nonlinear systems subject to asynchronous switching is considered via sampled-data control. We design a state observer by only using the sampled information. Utilizing the average dwell time method, a sampled-data controller is constructed to ensure that the closed-loop system is globally asymptotically stable in mean square. Two examples are provided to demonstrate the developed strategy’s effectiveness.

Backstepping-based decentralized bounded-H∞ adaptive neural control for a class of large-scale stochastic nonlinear systems

In this paper, a novel decentralized adaptive neural control approach based on the backstepping technique is proposed to design a decentralized H∞ adaptive neural controller for a class of stochastic large-scale nonlinear systems with external disturbances and unknown nonlinear functions. RBF neural networks are utilized to approximate the packaged unknown nonlinearities. A novel concept with regard to bounded-H∞ performance is proposed. It can be applied to solve an H∞ control problem for a class of stochastic nonlinear systems. The constant terms appeared in stability analysis are dealt with by using Gronwall inequality, so that H∞ performance criterion is satisfied. The assumption that the approximation errors of neural networks must be square-integrable in some literature can be eliminated. The design process for decentralized bounded-H∞ controllers is given. The proposed control scheme guarantees that all the signals in the resulting closed-loop large-scale system are uniformly ultimately bounded in probability, and each subsystem possesses disturbance attenuation performance for external disturbances. Finally, the simulation results are provided to illustrate the effectiveness and feasibility of the proposed approach.

Decentralized adaptive tracking control for high-order interconnected stochastic nonlinear time-varying delay systems with stochastic input-to-state stable inverse dynamics by neural networks

The paper solves the problem of a decentralized adaptive state-feedback neural tracking control for a class of stochastic nonlinear high-order interconnected systems. Under the assumptions that the inverse dynamics of the subsystems are stochastic input-to-state stable (SISS) and for the controller design, Radial basis function (RBF) neural networks (NN) are used to cope with the packaged unknown system dynamics and stochastic uncertainties. Besides, the appropriate Lyapunov-Krosovskii functions and parameters are constructed for a class of large-scale high-order stochastic nonlinear strong interconnected systems with inverse dynamics. It has been proved that the actual controller can be designed so as to guarantee that all the signals in the closed-loop systems remain semi-globally uniformly ultimately bounded, and the tracking errors eventually converge in the small neighborhood of origin. Simulation example has been proposed to show the effectiveness of our results.

Observer-based multi-dimensional Taylor network decentralised adaptive tracking control of large-scale stochastic nonlinear systems

ABSTRACT In this paper, the problem of multi-dimensional Taylor network (MTN) decentralised adaptive output-feedback tracking control is investigated for large-scale stochastic nonlinear systems. MTNs are used to approximate the unknown nonlinear functions, and a MTN state observer is designed for estimating the unmeasured states. Based on the designed MTN state observer, and by combining the backstepping technique with dynamic surface control (DSC), an adaptive MTN decentralised output-feedback tracking control scheme is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded in probability, and the tracking errors converge to an arbitrarily small neighbourhood around the origin in the sense of mean quartic value. Finally, a numerical example is given to illustrate the effectiveness of the proposed design approach, and the simulation results demonstrate that the proposed method promises desirable real-time performance and tracking control.

Approximation-based decentralized output-feedback control for uncertain stochastic interconnected nonlinear time-delay systems with input delay and asymmetric input saturation

This paper proposes an adaptive observer-based neural controller for a class of uncertain large-scale stochastic nonlinear systems with actuator delay and time-delay nonlinear interactions, where drift and diffusion terms contain all state variables of their own subsystem. First, a state observer is established for estimating the unmeasured states, and a predictor-like term is utilized to transform the input delayed system into the delay-free system. Second, novel appropriate Lyapunov–Krasovskii functionals are used to compensate the time-delay terms, and neural networks are employed to approximate unknown nonlinear functions. At last, an output-feedback adaptive neural control scheme is constructed by using Lyapunov stability theory and backstepping technique. It is shown that the designed neural controller can ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error is driven to a small neighborhood of the origin. The simulation results are presented to further show the effectiveness of the proposed approach.

Decentralized adaptive neural control for high-order interconnected stochastic nonlinear time-delay systems with unknown system dynamics

This paper is concerned with the problem of decentralized adaptive backstepping state-feedback control for uncertain high-order large-scale stochastic nonlinear time-delay systems. For the control design of high-order large-scale nonlinear systems, only one adaptive parameter is constructed to overcome the over-parameterization, and neural networks are employed to cope with the difficulties raised by completely unknown system dynamics and stochastic disturbances. And then, the appropriate Lyapunov–Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown unmatched time-delay interactions of high-order large-scale systems for the first time. At last, on the basis of Lyapunov stability theory, the decentralized adaptive neural controller was developed, and it decreases the number of learning parameters. The actual controller can be designed so as to ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error converges in the small neighborhood of zero. The simulation example is used to further show the validity of the design method.

Decentralized adaptive neural control for interconnected stochastic nonlinear delay-time systems with asymmetric saturation actuators and output constraints

This paper investigates the problem of decentralized adaptive backstepping control for a class of large-scale stochastic nonlinear time-delay systems with asymmetric saturation actuators and output constraints. Firstly, the Gaussian error function is employed to represent a continuous differentiable asymmetric saturation nonlinearity, and barrier Lyapunov functions are designed to ensure that the output parameters are restricted. Secondly, the appropriate Lyapunov–Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown unmatched time-delay interactions, and the neural networks are employed to approximate the unknown nonlinearities. At last, based on Lyapunov stability theory, a decentralized adaptive neural control method is proposed, and the designed controller decreases the number of learning parameters. It is shown that the designed controller can ensure that all the closed-loop signals are 4-Moment (or 2 Moment) semi-globally uniformly ultimately bounded (SGUUB) and the tracking error converges to a small neighborhood of the origin. Two examples are provided to show the effectiveness of the proposed method.

Decentralized backstepping adaptive output tracking of large-scale stochastic nonlinear systems

The problem of decentralized adaptive output tracking control of a class ofinterconnected stochastic nonlinear systems is considered. In the control design, decentralized state observers and backstepping techniques are applied.To eliminate the influences of interactions with other subsystems, a differentiable function is employed. It is shown that the designed local adaptivecontrollers can ensure that all the signals in the closed-loop system arebounded in probability. Furthermore, the tracking errors can be limited to asmall residual set around the origin in the fourth moment sense and can be adjusted by choosing suitable design parameters.

Adaptive Fuzzy Output-Constrained Fault-Tolerant Control of Nonlinear Stochastic Large-Scale Systems With Actuator Faults.

The problem of adaptive fuzzy output-constrained tracking fault-tolerant control (FTC) is investigated for the large-scale stochastic nonlinear systems of pure-feedback form. The nonlinear systems considered in this paper possess the unstructured uncertainties, unknown interconnected terms and unknown nonaffine nonlinear faults. The fuzzy logic systems are employed to identify the unknown lumped nonlinear functions so that the problems of structured uncertainties can be solved. An adaptive fuzzy state observer is designed to solve the nonmeasurable state problem. By combining the barrier Lyapunov function theory, adaptive decentralized and stochastic control principles, a novel fuzzy adaptive output-constrained FTC approach is constructed. All the signals in the closed-loop system are proved to be bounded in probability and the system outputs are constrained in a given compact set. Finally, the applicability of the proposed controller is well carried out by a simulation example.

Decentralised output-feedback control for a class of large-scale stochastic high-order upper-triangular nonlinear systems

ABSTRACTUnder the weaker conditions on the drift and diffusion terms, this paper focuses on the global decentralised output-feedback control for a class of large-scale stochastic high-order upper-triangular nonlinear systems. By introducing an appropriate coordinate transformation, the original system is transformed into an equivalent one with tunable gain. After that, by reasonably combing the homogeneous domination approach with stochastic nonlinear systems stability criterion, and skillfully choosing the low gain scale, the decentralised output-feedback controller is constructed for each subsystem to ensure that the closed-loop system is globally asymptotically stable in probability. The simulation example is given to demonstrate the effectiveness of the proposed design scheme.

Global decentralized output-feedback stabilization of large-scale stochastic high-order nonlinear systems with multi-delays

Based on the stochastic nonlinear time-delay system stability criterion and homogeneous domination approach, this paper solves the global decentralized output-feedback stabilization problem for a class of large-scale stochastic high-order nonlinear systems with multi-delays. By skillfully choosing an appropriate Lyapunov–Krasoviskii functional and successfully overcoming some troublesome obstacles in the design and analysis procedure, the decentralized output-feedback controller and homogeneous observer are constructed for each subsystem to guarantee that the closed-loop system is globally asymptotically stable (GAS) in probability. The simulation example is given to verify the effectiveness of the proposed design scheme.

Design of Self-Tuning Regulator for Large-Scale Interconnected Hammerstein Systems

This paper deals with the self-tuning regulator for large-scale stochastic nonlinear systems, which are composed of several interconnected nonlinear monovariable subsystems. Each interconnected subsystem is described by discrete Hammerstein model with unknown and time-varying parameters. This self-tuning control is developed on the basis of the minimum variance approach and is combined by a recursive algorithm in the estimation step. The parametric estimation step is performed on the basis of the prediction error method and the least-squares techniques. Simulation results of the proposed self-tuning regulator for two interconnected nonlinear hydraulic systems show the reliability and effectiveness of the developed method.

Decentralized adaptive NN state-feedback control for large-scale stochastic high-order nonlinear systems

This paper solves the decentralized state-feedback control problem for a class of large-scale stochastic high-order nonlinear systems. By generalizing neural network (NN) approximation approach to this kind of systems, we completely remove the growth conditions on system nonlinearities and the power order restriction. It is shown that through using dynamic surface control (DSC) and backstepping technique, an adaptive state-feedback controller is constructed, which guarantees the closed-loop system to be semi-globally uniformly ultimately bounded (SGUUB). Finally, a simulation example is given to demonstrate the effectiveness of the proposed control scheme.

Decentralised adaptive output feedback stabilisation for stochastic time-delay systems via LaSalle-Yoshizawa-type theorem

ABSTRACTThis paper deals with the decentralised output feedback stabilisation problem for a class of large-scale stochastic time-delay nonlinear systems. A general theorem is firstly given to guarantee the global existence and uniqueness of the solution for stochastic time-delay systems. In addition, a stochastic version of the well-known LaSalle-Yoshizawa theorem with time-varying delay is initially proposed for the controller design and stability analysis. Then, for a class of large-scale stochastic systems with time-varying delays, totally decentralised adaptive delay-dependent controllers are designed by using K-filter and backstepping approach. Via LaSalle-Yoshizawa-type theorem and constructing a general Lyapunov function, it is shown that all signals in the closed-loop system are bounded almost surely and the solution is almost surely asymptotically stable. Finally, a simulation example is given to illustrate the effectiveness of the results of this paper.

Decentralized adaptive fuzzy output feedback control of stochastic nonlinear large-scale systems with dynamic uncertainties

In this paper, centralized and decentralized adaptive fuzzy output feedback control schemes are investigated for a class of stochastic nonlinear interconnected large-scale systems with dynamic uncertainties and unmeasured states. Fuzzy systems are used to approximate the unknown nonlinear functions. Decentralized K-filters are designed to estimate the unmeasured states. An available dynamic signal is introduced to dominate the unmodeled dynamics. By combining dynamic surface control (DSC) technique with backstepping design, the condition in which the approximation errors are assumed to be bounded is avoided. Using the defined compact set in the stability analysis, the unknown smooth interconnections and black box functions are effectively dealt with. Using Itoˆ formula and Chebyshev’s inequality, it is shown that all the signals in the closed-loop system are bounded in probability, and the error signals are semi-globally uniformly ultimately bounded in mean square or the sense of four-moment. Simulation results demonstrate the effectiveness of the proposed approach.

Decentralized robust adaptive output feedback control of stochastic nonlinear interconnected systems with dynamic interactions

For a class of stochastic nonlinear large-scale systems with output dynamic interactions, the problem of robust adaptive control is researched in this paper. Under the assumptions that the inverse dynamics of the subsystems are stochastic input-to-state stable, a decentralized robust adaptive output feedback controller is designed by combining the backstepping method and changing supply functions technique. Under some milder conditions, it is shown that the outputs can be regulated into an arbitrarily small neighborhood of the origin in probability and the other signals in the closed-loop system are globally bounded in probability by tuning design parameters. Moreover, when the drift and diffusion terms vanish at the origin, the equilibrium of the closed-loop system is globally stable in probability and the outputs tend to the origin almost surely. A simulation example is presented to demonstrate the effectiveness of the designed controller.