Decentralised indirect adaptive output feedback fuzzy H ∞ tracking design for a class of large-scale nonlinear systems

A novel decentralised indirect adaptive output feedback fuzzy controller with a compensation controller and an H _∞ tracking controller is presented for a class of uncertain large-scale nonlinear systems in this article. The compensator adaptively compensates for interconnections between subsystems as well as mismatched errors, while the H _∞ controller suppresses the effect of external disturbances. Based upon the combination of fuzzy inference systems, a state observer, H _∞ tracking technique and the strictly positive real condition, the proposed overall observer-based decentralised algorithm guarantees not only asymptotical tracking of reference trajectories but also an arbitrary small attenuation level of the unmodelled error dynamics including the disturbances on the tracking control. Simulation results substantiate the effectiveness of the proposed scheme.     

Error-based adaptive optimal tracking control of nonlinear discrete-time systems

In this paper,for the output tracking problem of nonlinear discrete-time systems,a performance index is newly defined using the adaptive dynamic programming(ADP) technique to completely eliminate tracking errors in theory.In contrast to traditional definitions of performance indices in other ADP-based methods,the proposed performance index is not only designed from the perspective of output tracking errors but also introduced errors of system states and control inputs at adjacent stages,which is...     

Reliable observer-based H∞ control of uncertain state-delayed systems

This paper is concerned with the reliable H_∞ control design problem for linear state-delayed system using observed-based output feedback. It proposes a reliable control design scheme for the case of possibly a simultaneous presence of actuator failures and sensor failures. Modified algebraic Riccati inequalities are developed to solve the problem addressed. Based on this approach, observer-based feedback control laws are designed that guarantee closed-loop asymptotic stability and reduction of the effect of an augmented disturbance input on the controlled output of a prescribed level, not only when the system is operating properly, but also under actuator and sensor failures. A numerical example is presented to demonstrate the applicability and effectiveness of the proposed approach.     

Robust adaptive control of a class of nonlinear uncertain systems

A smooth robust dynamic feedback controller is constructed, and the problem of robust H∞ almost disturbance attenuation with internal stability is solved for high-order nonlinear systems with parameter uncertainties. Finally, illustrative example and simulation results demonstrate the effectiveness of the proposed method.     

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

1IntroductionMany dynamic systems to be controlled have constant orslowly_varying uncertain parameters .Adaptive control is apopular approachtothe control ofsuchsystems [1] .Inthepast two decades ,significant progress has been made in theresearch and design of adaptive control systems [2,3] .Fairly complete and comprehensive guidelines are nowavailable for both design and implementation of adaptivecontrollers inthe cases where the systemunder control canbe adequately modeled as a linear dynami…     

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.     

Reliable H ∞ control of a class of uncertain interconnected systems: an LMI approach

The aim of this work is to study the reliable control design problem for parameter-dependent interconnected systems in the presence of actuator failures. Moreover, the control ensures H _∞ performance in front of L ₂ perturbations. A more practical model of actuators or control channel failures than outage is adopted, considering partial achievement. The continuous H_∞ control problem is solved via elementary manipulations on linear matrix inequalities and the resulting control systems are robustly stable against plant uncertainties and failures.     

H∞ output tracking fuzzy control for nonlinear systems with time-varying delay

This paper proposes an observer-based output tracking control via virtual desired reference model for a class of nonlinear systems with time-varying delay and disturbance. First, the Takagi–Sugeno fuzzy model represents the nonlinear system with time-varying delay and disturbance. Then we design an observer to estimate immeasurable states and controller to drive the error between estimated state and virtual desired variables (VDVs) to zero such that the overall control output tracking system has H_∞ control performance. Using Lyapunov–Krasovskii functional, we derive sufficient conditions for stability. The advantages of the proposed output control system are (i) systematic approach to derive VDVs for controller design; (ii) relaxes need for real reference model; (iii) drops need for information of equilibrium; (iv) relaxed condition is provided via three-step procedure to find observer and controller gain. We carry out simulation using a continuous stirred tank reactor system where the effectiveness of the proposed controller is demonstrated by satisfactory numerical results.     

H∞ output tracking control of uncertain and disturbed nonlinear systems based on neural network model

The work presented in this paper seeks to address the tracking problem for uncertain continuous nonlinear systems with external disturbances. The objective is to obtain a model that uses a reference-based output feedback tracking control law. The control scheme is based on neural networks and a linear difference inclusion (LDI) model, and a PDC structure and H_∞ performance criterion are used to attenuate external disturbances. The stability of the whole closed-loop model is investigated using the well-known quadratic Lyapunov function. The key principles of the proposed approach are as follows: neural networks are first used to approximate nonlinearities, to enable a nonlinear system to then be represented as a linearised LDI model. An LMI (linear matrix inequality) formula is obtained for uncertain and disturbed linear systems. This formula enables a solution to be obtained through an interior point optimisation method for some nonlinear output tracking control problems. Finally, simulations and comparisons are provided on two practical examples to illustrate the validity and effectiveness of the proposed method.     

Robust containment tracking of uncertain linear multi-agent systems: a non-smooth control approach

This paper addresses the distributed robust containment tracking problem of networked systems with uncertain linear dynamics and multiple controlled leaders. The uncertainty class considered in this paper satisfies some matched conditions. To achieve containment tracking in such a multi-agent system, some distributed controllers consisting of using relative state-based continuous feedback and a non-smooth manoeuvre are developed. By transforming the containment tracking problem into the global robust stabilisation problem of interconnected systems, it is shown that the states of followers will asymptotically converge to a convex hull formed by those of the leaders if the control parameters in the proposed controllers are appropriately selected. It is clearly pointed out that the involved control parameters can be successfully found for solving the containment tracking problem if each follower can be directly or indirectly influenced by at least one leader, and the nominal dynamics of followers are stabilisable. The important issue of how fast containment can be achieved is also addressed. Finally, some numerical simulations are given for illustration.     

Robust adaptive fuzzy control for a class of perturbed pure-feedback nonlinear systems

A new design scheme of direct adaptive fuzzy controller for a class of perturbed pure-feedback nonlinear systems is proposed. The design is based on backstepping and the approximation capability of the first type fuzzy systems. A continuous robust term is adopted to minify the influence of modeling errors or disturbances. By introducing the modified integral-type Lyapunov function, the approach is able to avoid the requirement of the upper bound of the first time derivation of the high frequency control gain. Through theoretical analysis, the closed-loop control system is proven to be semi-globally uniformly ultimately bounded, with tracking error converging to a residual set.     

A new approach to robust reliable H∞ control for uncertain nonlinear systems

This paper focuses on the optimal robust reliable H_∞ control for a class of uncertain nonlinear systems with actuator faults. A new method of annihilating uncertain matrix is proposed. Based on this approach, a new method of disposing of the phenomenon of uncertain matrices multiplication is provided. In accordance with the method, the optimal robust reliable H_∞ control problem for uncertain nonlinear systems is settled by employing state feedback, in terms of linear matrix inequality (LMI). Finally, two illustrative examples are given to show the feasibility and validity of the proposed method.     

Robust adaptive tracking control of MIMO nonlinear systems in the presence of actuator hysteresis

Adaptive tracking control of a class of MIMO nonlinear system preceded by unknown hysteresis is investigated. Based on dynamic surface control, an adaptive robust control law is developed and compensators are designed to mitigate the influences of both the unknown bounded external uncertainties and the unknown Prandtl–Islinskii hysteresis. By adopting the low-pass filters, the explosion of complexity caused by tedious computation of the time derivatives of the virtual control laws is overcome. With the proposed control scheme, the closed-loop system is proved to be semi-globally ultimately bounded by the Lyapunov stability theory, and the output of the controlled system can track the desired trajectories with an arbitrarily small error. Finally, numerical simulations are given to verify the effectiveness of the proposed approach.     

Nonsmooth finite-time control of uncertain second-order nonlinear systems

Nonsmooth finite-time stabilizing control laws have been developed for the double integrator system. The objective of this paper is to further explore the finite-time tracking control problem of a general form of uncertain second-order affine nonlinear system with the new forms of terminal sliding mode (TSM). Discontinuous and continuous finite-time controllers are also developed respectively without the singularity problem. Complete robustness can be acquired with the former, and enhanced robustness compared with the conventional boundary layer method can be expressed as explicit bounded function with the latter. Simulation results on the stabilizing and tracking problems are presented to demonstrate the effectiveness of the control algorithms.     

Robust H ∞ control of uncertain nonlinear switched systems using constructive method

This paper focuses on the problem of robust H _?? control of nonlinear switched systems with parameter uncertainty via the multiple Lyapunov functions (MLFs) approach. The uncertain parameters are assumed to be in a known compact set and are allowed to enter the system nonlinearly. Based on the explicit construction of Lyapunov functions, which avoids solving the Hamilton-Jacobi-Isaacs (HJI) inequalities, sufficient conditions for the solvability of the robust H _?? control problem of cascade nonlinear switched systems are derived under some switching signal. Then, the result is extended to solve the robust H _?? control problem of nonlinear switched systems in strict feedback form. Finally, the effectiveness of the proposed results is illustrated through a simulation example.     

Adaptive H2/H∞ tracking control for a class of uncertain robotic systems

This paper addresses the problem of designing mixed H₂/H_∞ tracking control for a large class of uncertain robotic systems. Nonlinear H_∞ control theory, H₂ control theory and intelligent adaptive control algorithm are combined to construct a hybrid adaptive/robust H₂/H_∞ tracking control scheme. One adaptive neural network system is constructed to approximate the behaviour of uncertain robot dynamics, and the other adaptive control algorithm is designed to estimate the behaviour of the modelled disturbance. Moreover, a robust H_∞ control algorithm is designed to attenuate the effects of the unmodelled disturbance. Only a set of algebraic matrix Riccati-like equations is required to implement the proposed mixed H₂/H_∞ tracking controller, and so an explicit and closed-form solution is obtained. Consequently, the mixed H₂/H_∞ adaptive/robust tracking controller developed here can be analytically computed and easily implemented. Finally, simulations are presented to illustrate the effectiveness of the proposed control algorithm.     

Distributed cooperative H∞ optimal tracking control of MIMO nonlinear multi-agent systems in strict-feedback form via adaptive dynamic programming

The design of distributed cooperative H_∞ optimal controllers for multi-agent systems is a major challenge when the agents’ models are uncertain multi-input and multi-output nonlinear systems in strict-feedback form in the presence of external disturbances. In this paper, first, the distributed cooperative H_∞ optimal tracking problem is transformed into controlling the cooperative tracking error dynamics in affine form. Second, control schemes and online algorithms are proposed via adaptive dynamic programming (ADP) and the theory of zero-sum differential graphical games. The schemes use only one neural network (NN) for each agent instead of three from ADP to reduce computational complexity as well as avoid choosing initial NN weights for stabilising controllers. It is shown that despite not using knowledge of cooperative internal dynamics, the proposed algorithms not only approximate values to Nash equilibrium but also guarantee all signals, such as the NN weight approximation errors and the cooperative tracking errors in the closed-loop system, to be uniformly ultimately bounded. Finally, the effectiveness of the proposed method is shown by simulation results of an application to wheeled mobile multi-robot systems.     

Robust H ∞ fuzzy control of nonlinear systems with multiple time delays

A robustness design of fuzzy control via model-based approach is proposed in this article to overcome the effect of approximation error between multiple time-delay nonlinear systems and Takagi--Sugeno (T-S) fuzzy models. A stability criterion is derived based on Lyapunov's direct method to ensure the stability of nonlinear multiple time-delay systems especially for the resonant and chaotic systems. Positive definite matrices P and R_k of the criterion are obtained by using linear matrix inequality (LMI) optimization algorithms to solve the robust fuzzy control problem. In terms of the control scheme and this criterion, a fuzzy controller is then designed via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear multiple time-delay system and the H ^∞ control performance is achieved at the same time. Finally, two numerical examples of the chaotic and resonant systems are demonstrated to show the concepts of the proposed approach.