Decentralized Control Based on FNNSMC for Interconnected Uncertain Nonlinear Systems

A new type controller, fuzzy neural networks sliding mode controller (FNNSMC), is developed for a class of large scale systems with unknown bounds of high order interconnections and disturbances. Although sliding mode control is simple and insensitive to uncertainties and disturbances, there are two main problems in the sliding mode controller (SMC): control input chattering and the assumption of known bounds of uncertainties and disturbances. The FNNSMC, which incorporates the fuzzy neural networks (FNN) and the SMC, can eliminate the chattering by using the continuous output of the FNN to replace the discontinuous sign term in the SMC. The bounds of uncertainties and disturbances are also not required in the FNNSMC design. The simulation results show that the FNNSMC has more robustness than the SMC.

Finite-Time Distributed Identification for Nonlinear Interconnected Systems

In this paper,a novel finite-time distributed identification method is introduced for nonlinear interconnected systems.A distributed concurrent learning-based discontinuous gradient descent update law is presented to learn uncertain interconnected subsystems’dynamics.The concurrent learning approach continually minimizes the identification error for a batch of previously recorded data collected from each subsystem as well as its neighboring subsystems.The state information of neighboring interconnected subsystems is acquired through direct communication.The overall update laws for all subsystems form coupled continuous-time gradient flow dynamics for which finite-time Lyapunov stability analysis is performed.As a byproduct of this Lyapunov analysis,easy-to-check rank conditions on data stored in the distributed memories of subsystems are obtained,under which finite-time stability of the distributed identifier is guaranteed.These rank conditions replace the restrictive persistence of excitation(PE)conditions which are hard and even impossible to achieve and verify for interconnected subsystems.Finally,simulation results verify the effectiveness of the presented distributed method in comparison with the other methods.

Nonlinear H_∞ filtering for interconnected Markovian jump systems

The problem of nonlinear H∞ filtering for interconnected Markovian jump systems is discussed. The aim of this note is the design of a nonlinear Markovian jump filter such that the resulting error system is exponentially meansquare stable and ensures a prescribed H∞ performance. A sufficient condition for the solvability of this problem is given in terms of linear matrix inequalities（LMIs）. A simulation example is presented to demonstrate the effectiveness of the proposed design approach.

Adaptive Fuzzy Observer Backstepping Control for a Class of Uncertain Nonlinear Systems with Unknown Time-delay

In this paper, a new adaptive fuzzy backstepping control approach is developed for a class of nonlinear systems with unknown time-delay and unmeasured states. Using fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy state observer is designed for estimating the unmeasured states. On the basis of the state observer and applying the backstepping technique, an adaptive fuzzy observer control approach is developed. The main features of the proposed adaptive fuzzy control approach not only guarantees that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded, but also contain less adaptation parameters to be updated on-line. Finally, simulation results are provided to show the effectiveness of the proposed approach.

Design of H_∞ robust fault detection filter for nonlinear time-delay systems

In this paper, the robust fault detection filter (RFDF) design problems are studied for nonlinear time-delay systems with unknown inputs. First, a reference residual model is introduced to formulate the RFDF design problem as an H∞ model-matching problem. Then appropriate input/output selection matrices are introduced to extend a performance index to the time-delay systems in time domain. The reference residual model designed according to the performance index is an optimal residual generator, which takes into account the robustness against disturbances and sensitivity to faults simultaneously. Applying robust H∞ optimization control technique, the existence conditions of the RFDF for nonlinear time-delay systems with unknown inputs are presented in terms of linear matrix inequality (LMI) formulation, independently of time delay. An illustrative design example is used to demonstrate the validity and applicability of the proposed approach.

Backstepping tracking control for nonlinear time-delay systems

Two design approaches of state feedback and output feedback tracking controllers are proposed for a class of strict feedback nonlinear time-delay systems by using backstepping technique. When the states of system cannot be observed, the time-delay state observer is designed to estimate the system states. Domination method is used to deal with nonlinear time-delay function under the assumption that the nonlinear time-delay functions of systems satisfy Lipschitz condition. The global asymptotical tracking of the reference signal is achieved and the bound of all signals of the resultant closed-loop system is also guaranteed. By constructing a Lyapunov-Krasoviskii functional, the stability of the closed-loop system is proved. The feasibility of the proposed approach is illustrated by a simulation example.

Adaptive Fuzzy Backstepping Output Feedback Control of Nonlinear Time-delay Systems with Unknown High-frequency Gain Sign

In this paper, an adaptive fuzzy robust feedback control approach is proposed for a class of single-input and singleoutput （SISO） strict-feedback nonlinear systems with unknown nonlinear functions, time delays, unknown high-frequency gain sign, and without the measurements of the states. In the backstepping recursive design, fuzzy logic systems are employed to approximate the unknown smooth nonlinear functions, K-filters is designed to estimate the unmeasured states, and Nussbaum gain functions are introduced to solve the problem of unknown sign of high-frequency gain. By combining adaptive fuzzy control theory and adaptive backstepping design, a stable adaptive fuzzy output feedback control scheme is developed. It has been proven that the proposed adaptive fuzzy robust control approach can guarantee that all the signals of the closed-loop system are uniformly ultimately bounded and the tracking error can converge to a small neighborhood of the origin by appropriately choosing design parameters. Simulation results have shown the effectiveness of the proposed method.

On stabilization for a class of nonlinear stochastic time-delay systems:a matrix inequality approach

This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.

Robust H_∞ controller design for a class of nonlinear fuzzy time-delay systems

The problem of fuzzy modeling for state and input time-delays systems with a class of nonlinear uncertainties by fuzzy T-S model is addressed.By using the linear matrix inequality（LMI） method, the problem of fuzzy robust H ∞ controller design for the system is studied.Assuming that the nonlinear uncertain functions in the model considered are gain-bounded, a sufficient condition for the robustly asymptotic stability of the closed-loop system is obtained via Lyapunov stability theory.By solving the LMI, a feedback control law which guarantees the robustly asymptotic stability of the closed-loop system is constructed and the effect of the disturbance input on the controlled output is ruduced to a prescribed level.

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.

ROBUST STABILIZATING FOR A OLASS OF UNOERTAIN NONLINEAR INTEROONNECTED SYSTEMS USING VARIABLE STRUCTURE CONTROL

The robust stabilizating control problem for a class of uncertain nonlinear large-scale systems is discussed. Based on the theory of both input/output (I/O) linearization and decentralized variable structure control (VSC),two-level and decentralized variable structure control laws for this kind of systems are presented respectively,which achieve asymptotically stabilization despite the uncertainties and disturbances. At last,sirnulation of the disturbed two-pendulum system is given to illustrate the feasibility of proposed technique.

Adaptive Output-feedback Regulation for Nonlinear Delayed Systems Using Neural Network

A novel adaptive neural network （NN） output-feedback regulation algorithm for a class of nonlinear time-varying timedelay systems is proposed. Both the designed observer and controller are independent of time delay. Different from the existing results, where the upper bounding functions of time-delay terms are assumed to be known, we only use an NN to compensate for all unknown upper bounding functions without that assumption. The proposed design method is proved to be able to guarantee semi-global uniform ultimate boundedness of all the signals in the closed system, and the system output is proved to converge to a small neighborhood of the origin. The simulation results verify the effectiveness of the control scheme.

Robust adaptive control for interval time-delay systems

This paper focuses on the robust adaptive control problems for a class of interval time-delay systems and a class of large-scale interconnected systems. The nonlinear uncertainties of the systems under study are bounded by high- order polynomial functions with unknown gains. Firstly, the adaptive feedback controller which can guarantee the stability of the closed-loop system in the sense of uniform ultimate boundedness is proposed. Then the proposed adaptive idea is extended to robust stabilizing designing method for a class of large-scale interconnected systems. Here, another problem we address is to design a decentralized feedback adaptive controller such that the closed-loop system is stable in the sense of uniform ultimate boundedness for all admissible uncertainties and time-delay. Finally, an illustrative example is given to show the validity of the proposed approach.

Exponential passive filtering for a class of nonlinear jump systems

The exponential passive filtering problem for a class of nonlinear Markov jump systems with uncertainties and time-delays is studied. The uncertain parameters are assumed unknown but norm bounded, and the nonlinearities satisfy the quadratic condition. Based on the passive filtering theory, the sufficient condition for the existence of the mode-dependent passive filter is given by analyzing the reconstructed observer system. By using the appropriate Lyapnnov-Krasovskii function and applying linear matrix inequalities, the design scheme of the passive filter is derived and described as an optimization one. The presented exponential passive filter makes the error dynamic systems exponentially stochastically stable for all the admissible uncertainties, time-delays and nonlinearities, has the better abilities of state tracking and satisfies the given passive norm index. Simulation results demonstrate the validity of the proposed approach.

Adaptive output-feedback control for MIMO nonlinear systems with time-varying delays using neural networks

An adaptive neural network output-feedback regulation approach is proposed for a class of multi-input-multi-output nonlinear time-varying delayed systems.Both the designed observer and controller are free from time delays.Different from the existing results,this paper need not the assumption that the upper bounding functions of time-delay terms are known,and only a neural network is employed to compensate for all the upper bounding functions of time-delay terms,so the designed controller procedure is more simplified.In addition,the resulting closed-loop system is proved to be semi-globally ultimately uniformly bounded,and the output regulation error converges to a small residual set around the origin.Two simulation examples are provided to verify the effectiveness of control scheme.

PARTIAL STABILITY ANALYSIS OF SOME CLASSES OF NONLINEAR SYSTEMS

A nonlinear differential equation system with nonlinearities of a sector type is studied. Using the Lyapunov direct method and the comparison method, conditions are derived under which the zero solution of the system is stable with respect to all variables and asymptotically stable with respect to a part of variables. Moreover, the impact of nonstationary perturbations with zero mean values on the stability of the zero solution is investigated. In addition, the corresponding time-delay system is considered for which delay-independent partial asymptotic stability conditions are found. Three examples are presented to demonstrate effectiveness of the obtained results.

Double Lipschitz Stability for Nonlinearly Perturbed Differential Systems with Multiple Delay

In this paper, firstly a new class of time-delay differential inequality is proved. Then as an application, the nonlinearly perturbed differential systems with multiple delay are considered and it is obtained that the trivial solution of the nonlinear systems with multiple delay has uniform stability and uniform exponential Lipschitz asymptotic stability with respect to partial variables. It is obvious that the above system is a generalization of the traditional differential systems. The aim of this paper is to investigate the double stability of time-delay differential equations, including Uniform stability and Uniform Lipschitz stability. The author uses the method of differential inequalities with time-delay and integral inequalities to establish double stability criteria. As a result, the partial stability of differential equations is widely used both in theory and in practice such as dynamic systems and control systems.

Parametric Estimation of Interconnected Nonlinear Systems Described by Input-output Mathematical Models

In this paper, two types of mathematical models are developed to describe the dynamics of large-scale nonlinear systems, which are composed of several interconnected nonlinear subsystems. Each subsystem can be described by an input-output nonlinear discrete-time mathematical model, with unknown, but constant or slowly time-varying parameters. Then, two recursive estimation methods are used to solve the parametric estimation problem for the considered class of the interconnected nonlinear systems. These methods are based on the recursive least squares techniques and the prediction error method. Convergence analysis is provided using the hyper-stability and positivity method and the differential equation approach. A numerical simulation example of the parametric estimation of a stochastic interconnected nonlinear hydraulic system is treated.

Decomposition Based Fuzzy Model Predictive Control Approaches for Interconnected Nonlinear Systems

This paper proposes fuzzy model predictive control(FMPC)strategies for nonlinear interconnected systems based mainly on a system decomposition approach.First,the Takagi-Sugeno(TS)fuzzy model is formulated in such a way to describe the behavior of the nonlinear system.Based on that description,a fuzzy model predictive control is determined.The system under consideration is decomposed into several subsystems.For each subsystem,the main idea consists of the decomposition of the control action into two parts:The decentralized part contains the parameters of the subsystem and the centralized part contains the elements of other subsystems.According to such decomposition,two strategies are defined aiming to circumvent the problems caused by interconnection bet ween subsystems.The feasibility and efficiency of the proposed method are illustrated through numerical examples.

Globally Asymptotic Stabilization for Nonlinear Time-delay Systems with ISS Inverse Dynamics

The output feedback stabilization is considered for a class of nonlinear time-delay systems with inverse dynamics in this paper.An appropriate state observer is constructed for the unmeasurable system states in order to realize the control objective.By adopting the backstepping and Lyapunov-Krasovskii functional methods,a systematic design procedure for a memoryless output feedback control law is presented.It is shown that the designed controller can make the closed-loop system globally asymptotically stable while keeping all signals bounded.An illustrative example is discussed to show the effectiveness of the proposed control strategy.