Robust H_∞ control for uncertain systems with heterogeneous time-varying delays via static output feedback

This paper is concerned with the problem of robust H∞ control for a novel class of uncertain linear continuous-time systems with heterogeneous time-varying state/input delays and norm-bounded parameter uncertainties.The objective is to design a static output feedback controller such that the closed-loop system is asymptotically stable while satisfying a prescribed H∞ performance level for all admissible uncertainties.By constructing an appropriate Lyapunov-Krasvskii functional,a delay-dependent stability criterion of the closed-loop system is presented with the help of the Jensen integral inequality.From the derived criterion,the solutions to the problem are formulated in terms of linear matrix inequalities and hence are tractable numerically.A simulation example is given to illustrate the effectiveness of the proposed design method.     

Adaptive H∞ synchronization of chaotic systems via linear and nonlinear feedback control

Adaptive H∞ synchronization of chaotic systems via linear and nonlinear feedback control is investigated.The chaotic systems are redesigned by using the generalized Hamiltonian systems and observer approach.Based on Lyapunov’s stability theory,linear and nonlinear feedback control of adaptive H∞ synchronization is established in order to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance on an H∞-norm constraint.Adaptive H∞ synchronization of chaotic systems via three kinds of control is investigated with applications to Lorenz and Chen systems.Numerical simulations are also given to identify theeffectiveness of the theoretical analysis.     

Robust H_∞ observer-based control for synchronization of a class of complex dynamical networks

This paper is concerned with the robust H∞ synchronization problem for a class of complex dynamical networks by applying the observer-based control. The proposed feedback control scheme is developed to ensure the asymptotic stability of the augmented system, to reconstruct the non-measurable state variables of each node and to improve the H∞ performance related to the synchronization error and observation error despite the external disturbance. Based on the Lyapunov stability theory, a synchronization criterion is obtained under which the controlled network can be robustly stabilized onto a desired state with a guaranteed H∞ performance. The controller and the observer gains can be given by the feasible solutions of a set of linear matrix inequalities (LMIs). The effectiveness of the proposed control scheme is demonstrated by a numerical example through simulation.     

L_2-L_∞ learning of dynamic neural networks

This paper proposes an L2 -L∞ learning law as a new learning method for dynamic neural networks with external disturbance. Based on linear matrix inequality (LMI) formulation, the L2-L∞ learning law is presented to not only guarantee asymptotical stability of dynamic neural networks but also reduce the effect of external disturbance to an L2-L∞ induced norm constraint. It is shown that the design of the L2-L∞ learning law for such neural networks can be achieved by solving LMIs, which can be easily facilitated by using some standard numerical packages. A numerical example is presented to demonstrate the validity of the proposed learning law.     

Robust networked H∞ synchronization of nonidentical chaotic Lur＇e systems

We mainly investigate the robust networked H∞synchronization problem of nonidentical chaotic Lur’e systems. In the design of the synchronization scheme, some network characteristics, such as nonuniform sampling, transmissioninduced delays, and data packet dropouts, are considered. The parameters of master–slave chaotic Lur’e systems often allow differences. The sufficient condition in terms of linear matrix inequality(LMI) is obtained to guarantee the dissipative synchronization of nonidentical chaotic Lur’e systems in network environments. A numerical example is given to illustrate the validity of the proposed method.     

Dynamic modeling and H_∞ independent modal space vibration control of laminate plates

In this paper, combining the transfer matrix method and the finite element method, the modified finite element transfer matrix method is presented for high efficient dynamic modeling of laminated plates. Then, by constructing the modal filter and the disturbance force observer, and using the feedback and feedforward approaches, the H ∞ independent modal space control strategy is designed for active vibration control of laminate plates subjected to arbitrary, immeasurable disturbance forces. Compared with or...     

Adaptive synchronization of a hyperchaotic L system based on extended passive control

This paper investigates the adaptive synchronization of hyperchaotic Lü systems based on the method of extended passive control. By combining the feedback control, the extended passive control method with two output variables is developed, which can synchronize hyperchaotic Lü systems asymptotically and globally more easily without knowing the bound of state of the hyperchaotic system. Adaptive laws are introduced to estimate the unknown parameters as well. Simulation results show the effectiveness and flexibility of the proposed control scheme.     

Fault tolerant synchronization of chaotic systems based on T-S fuzzy model with fuzzy sampled-data controller

In this paper the fault tolerant synchronization of two chaotic systems based on fuzzy model and sample data is investigated. The problem of fault tolerant synchronization is formulated to study the global asymptotical stability of the error system with the fuzzy sampled-data controller which contains a state feedback controller and a fault compensator. The synchronization can be achieved no matter whether the fault occurs or not. To investigate the stability of the error system and facilitate the design of the fuzzy sampled-data controller, a Takagi--Sugeno (T--S) fuzzy model is employed to represent the chaotic system dynamics. To acquire the good performance and produce less conservative analysis result, a new parameter-dependent Lyapunov--Krasovksii functional and a relaxed stabilization technique are considered. The stability conditions based on linear matrix inequality are obtained to achieve the fault tolerant synchronization of the chaotic systems. Finally, a numerical simulation is shown to verify the results.     

Disturbance rejection and H∞ pinning control of linear complex dynamical networks

This paper concerns the disturbance rejection problem of a linear complex dynamical network subject to external disturbances.A dynamical network is said to be robust to disturbance,if the H ∞ norm of its transfer function matrix from the disturbance to the performance variable is satisfactorily small.It is shown that the disturbance rejection problem of a dynamical network can be solved by analysing the H ∞ control problem of a set of independent systems whose dimensions are equal to that of a single node.A counter-intuitive result is that the disturbance rejection level of the whole network with a diffusive coupling will never be better than that of an isolated node.To improve this,local feedback injections are applied to a small fraction of the nodes in the network.Some criteria for possible performance improvement are derived in terms of linear matrix inequalities.It is further demonstrated via a simulation example that one can indeed improve the disturbance rejection level of the network by pinning the nodes with higher degrees than pinning those with lower degrees.     

H∞ synchronization of chaotic neural networks with time-varying delays

In this paper,we investigate the problem of H∞ synchronization for chaotic neural networks with time-varying delays.A new model of the networks with disturbances in both master and slave systems is presented.By constructing a suitable Lyapunov–Krasovskii functional and using a reciprocally convex approach,a novel H∞ synchronization criterion for the networks concerned is established in terms of linear matrix inequalities(LMIs)which can be easily solved by various effective optimization algorithms.Two numerical examples are given to illustrate the effectiveness of the proposed method.     

Robust H_∞ control of piecewise-linear chaotic systems with random data loss

<正>This paper studies the problem of robust H_∞control of piecewise-linear chaotic systems with random data loss. The communication links between the plant and the controller are assumed to be imperfect(that is,data loss occurs intermittently,which appears typically in a network environment).The data loss is modelled as a random process which obeys a Bernoulli distribution.In the face of random data loss,a piecewise controller is designed to robustly stabilize the networked system in the sense of mean square and also achieve a prescribed H_∞disturbance attenuation performance based on a piecewise-quadratic Lyapunov function.The required H_∞controllers can be designed by solving a set of linear matrix inequalities(LMIs).Chua's system is provided to illustrate the usefulness and applicability of the developed theoretical results.     

Complete synchronization of double-delayed Rssler systems with uncertain parameters

In this paper,we investigate complete synchronization of double-delayed Rssler systems with uncertain parameters as the master system is in chaotic synchronization.The uncertain parameters can be nonlinearly expressed in the system.The analysis and proof are given by means of the Lyapunov stability theorem.Based on theoretical analysis,some sufficient conditions of complete synchronization are proved.In order to validate the proposed scheme,numerical simulations are performed and the numerical results show that our scheme is very effective.     

Pinning control of complex Lur'e networks

This paper addresses the control problem of a class of complex dynamical networks with each node being a Lur'e system whose nonlinearity satisfies a sector condition, by applying local feedback injections to a small fraction of the nodes. The pinning control problem is reformulated in the framework of the absolute stability theory. It is shown that the global stability of the controlled network can be reduced to the test of a set of linear matrix inequalities, which in turn guarantee the absolute stability of the corresponding Lur'e systems whose dimensions are the same as that of a single node. A circle-type criterion in the frequency domain is further presented for checking the stability of the controlled network graphically. Finally, a network of Chua's oscillators is provided as a simulation example to illustrate the effectiveness of the theoretical results.     

A novel mixed-synchronization phenomenon in coupled Chua’s circuits via non-fragile linear control

Dynamical variables of coupled nonlinear oscillators can exhibit different synchronization patterns depending on the designed coupling scheme.In this paper,a non-fragile linear feedback control strategy with multiplicative controller gain uncertainties is proposed for realizing the mixed-synchronization of Chua’s circuits connected in a drive-response configuration.In particular,in the mixed-synchronization regime,different state variables of the response system can evolve into complete synchronization,anti-synchronization and even amplitude death simultaneously with the drive variables for an appropriate choice of scaling matrix.Using Lyapunov stability theory,we derive some sufficient criteria for achieving global mixed-synchronization.It is shown that the desired non-fragile state feedback controller can be constructed by solving a set of linear matrix inequalities (LMIs).Numerical simulations are also provided to demonstrate the effectiveness of the proposed control approach.     

H∞ consensus control of a class of second-order multi-agent systems without relative velocity measurement

This paper studies consensus control problems for a class of second-order multi-agent systems without relative velocity measurement. Some dynamic neighbour-based rules are adopted for the agents in the presence of external disturbances. A sufficient condition is derived to make all agents achieve consensus while satisfying desired H_∞ performance. Finally, numerical simulations are provided to show the effectiveness of our theoretical results.     

An identifier-actor-optimizer policy learning architecture for optimal control of continuous-time nonlinear systems

An intelligent solution method is proposed to achieve real-time optimal control for continuous-time nonlinear systems using a novel identifier-actor-optimizer(IAO)policy learning architecture.In this IAO-based policy learning approach,a dynamical identifier is developed to approximate the unknown part of system dynamics using deep neural networks(DNNs).Then,an indirect-method-based optimizer is proposed to generate high-quality optimal actions for system control considering both the constraints and performance index.Furthermore,a DNN-based actor is developed to approximate the obtained optimal actions and return good initial guesses to the optimizer.In this way,the traditional optimal control methods and state-of-the-art DNN techniques are combined in the IAO-based optimal policy learning method.Compared to the reinforcement learning algorithms with actor-critic architectures that suffer hard reward design and low computational efficiency,the IAO-based optimal policy learning algorithm enjoys fewer user-defined parameters,higher learning speeds,and steadier convergence properties in solving complex continuous-time optimal control problems(OCPs).Simulation results of three space flight control missions are given to substantiate the effectiveness of this IAO-based policy learning strategy and to illustrate the performance of the developed DNN-based optimal control method for continuous-time OCPs.