Convex invariant sets for discrete-time Lur’e systems

In this paper, a method to estimate the domain of attraction of a class of discrete-time Lur’e systems is presented. A new notion of invariance, denoted -invariance, is introduced. An algorithm to determinate the largest -invariant set for this class of systems is proposed. Moreover, it is proven that the -invariant sets provided by this algorithm are polyhedral convex sets and constitute an estimation of the domain of attraction of the non-linear system. It is shown that any contractive set for the Lur’e system is contained in the -invariant set obtained applying the results of this paper. Two illustrative examples are given.     

Development of PI training algorithms for neuro-wavelet control on the synchronization of uncertain chaotic systems

This paper investigates a neuro-wavelet control (NWC) system to address the problem of synchronization control of uncertain chaotic systems. In this NWC system, a wavelet neural network (WNN) controller is the principal tracking controller designed to mimic the perfect control law and an auxiliary compensation controller is used to recover the residual approximation error so that the favorable synchronization can be achieved. Moreover, the proportional-integral (PI) training algorithms of the control system are derived from the Lyapunov stability theorem, which are utilized to update the adjustable parameters of WNN controller on-line for further assuring system stability and obtaining a fast convergence. In addition, to relax the requirement of unknown uncertainty bound, a bound estimation law is derived to estimate the uncertainty bound. Finally, some numerical simulations are presented to illustrate the effectiveness of the proposed control strategy. The simulation results demonstrate that the proposed NWC with PI training algorithms can synchronize the chaotic systems more accurately than the other control strategies.     

Motion synchronization of dual-cylinder pneumatic servo systems with integration of adaptive robust control and cross-coupling approach

We investigate motion synchronization of dual-cylinder pneumatic servo systems and develop an adaptive robust synchronization controller. The proposed controller incorporates the cross-coupling technology into the integrated direct/indirect adaptive robust control （DIARC） architecture by feeding back the coupled position errors, which are formed by the trajectory tracking errors of two cylinders and the synchronization error between them. The controller employs an online recursive least squares estimation algorithm to obtain accurate estimates of model parameters for reducing the extent of parametric uncertainties, and uses a robust control law to attenuate the effects of parameter estimation errors, unmodeled dynamics, and disturbances. Therefore, asymptotic convergence to zero of both trajectory tracking and synchronization errors can be guaranteed. Experimental results verify the effectiveness of the proposed controller.     

有界丢包网络环境下不确定系统的预测控制

研究了有界丢包网络环境下的多包不确定系统的鲁棒预测控制．首先在构建无限时域性能代价函数时,不同于传统预测控制方法,只考虑成功数据传输序列,并由此提出了两种鲁棒预测控制方法：将无限时域控制作用参数化为一个状态反馈控制律;或参数化为一个自由控制作用接一个状态反馈控制律．与传统方法一样,采用性能代价函数作为Ｌｙａｐｕｎｏｖ函数证明了系统的闭环稳定性．仿真实例验证了此方法的有效性．     

Delay distribution based robust H∞ control of networked control systems with uncertainties

Network induced delay in networked control systems (NCS) is inherently non‐uniformly distributed and behaves with multifractal nature. However, such network characteristics have not been well considered in NCS analysis and synthesis. Making use of the information of the statistical distribution of NCS network induced delay, a delay distribution based stochastic model is adopted to link Quality‐of‐Control and network Quality‐of‐Service for NCS with uncertainties. From this model together with a tighter bounding technology for cross terms, H_∞ NCS analysis is carried out with significantly improved stability results. Furthermore, a memoryless H_∞ controller is designed to stabilize the NCS and to achieve the prescribed disturbance attenuation level. Numerical examples are given to demonstrate the effectiveness of the proposed method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

网络控制系统中动态调度策略与控制器的综合设计

针对CAN网下的网络控制系统（NCS）,提出一种动态闭环调度策略．通过网络监测器周期地在线获取当前的网络服务质量,估计当前可利用的网络带宽等参数,实时地调整控制系统的采样周期以适应网络中信息流的变化。将采用动态闭环调度策略的变采样周期NCS建模为一类具有参数不确定性的离散系统,研究了系统的鲁棒稳定性和控制器的设计方法．仿真结果表明所提出的综合设计方法对改善网络的运行能力和保证系统稳定性是有效的。     

Event‐based distributed robust synchronization control for multiple Euler‐Lagrange systems without relative velocity measurements

This paper focuses on the event‐based distributed robust leaderless synchronization control for multiple Euler‐Lagrange systems with directed communication topology that contains a directed spanning tree. Update frequency of the system is reduced by taking advantages of the event‐triggered approach, which can help extend the service life of the controller. Robust control theory is employed to guarantee the synchronization stability of the networked Euler‐Lagrange systems when unmodeled dynamics occur. The cost on the distributed synchronization protocol design can be saved due to the relaxation of the requirement on relative velocity measurements. Furthermore, our results are more practical because unknown disturbance is taken into consideration. In addition, it can be rigorously analyzed that each agent can exclude the undesired Zeno behavior. Some simulation examples are provided in the end to demonstrate the effectiveness of the proposed event‐based distributed robust control algorithm.     

A generalized function projective synchronization scheme for uncertain chaotic systems subject to input nonlinearities

In this paper, a modified generalized function projective synchronization scheme for a class of master–slave chaotic systems subject to dynamic disturbances and input nonlinearities (dead-zone and sector nonlinearities) is investigated. This synchronization system can be seen as a generalization of many existing projective synchronization schemes (namely the function projective synchronization, the modified projective synchronization and so on), in the sense that the master system has a scaling function matrix and the slave system has a scaling factor matrix. To practically achieve this generalized function synchronization, an adaptive fuzzy variable-structure control system is designed. The fuzzy systems are used to appropriately approximate the uncertain nonlinear functions. A Lyapunov approach is employed to prove the boundedness of all signals of the closed-loop control system as well as the exponential convergence of the synchronization errors to an adjustable region. Simulations results are presented to illustrate the effectiveness of the proposed generalized function PS scheme.     

Fully distributed robust consensus control of multi-agent systems with heterogeneous unknown fractional-order dynamics

This paper investigates the robust consensus control problem of heterogeneous unknown nonlinear fractional-order multi-agent systems (FOMASs) without leader and with multiple leaders of bounded inputs. More specifically, FOMASs with nonidentical unknown coupling nonlinearities and external disturbances are considered in this paper, which takes the first-order MASs as its special case. Based on the σ-modification adaptive control technique, some class of discontinuous robust adaptive control protocols are proposed to solve the leaderless consensus problem and containment consensus problem, respectively. By means of the set-valued maps theory and by artfully choosing Lyapunov function, it is shown that the proposed consensus protocols are user friendly in that they are capable of compensating uncertain coupling nonlinearities, rejecting disturbances, rendering smaller control gains and thus requiring smaller amplitude on the control input while preserving global consensus convergence. All of the proposed robust adaptive consensus protocols are independent of any global and unknown information and thus are fully distributed. Some numerical simulations are provided to validate the correctness of the obtained results.     

H∞ control for linear systems with state saturation nonlinearities

The problem of H_∞ control for a class of linear systems with state saturation nonlinearities is considered in this paper. By introducing a row diagonally dominant matrix with negative diagonal elements and a diagonal matrix with positive elements, the H_∞ control problem is reduced to a matrix inequality feasibility problem that can be solved by the proposed iterative linear matrix inequality algorithm. The effectiveness of the presented method is demonstrated by a numerical example. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Adaptive sliding mode control of chaotic dynamical systems with application to synchronization

We address the problem of control and synchronization of a class of uncertain chaotic systems. Our approach follows techniques of sliding mode control and adaptive estimation law. The adaptive algorithm is constructed based on the sliding mode control to ensure perfect tracking and synchronization in presence of system uncertainty and external disturbance. Stability of the closed-loop system is proved using Lyapunov stability theory. Our theoretical findings are supported by simulation results.     

On robust synchronization of nonlinear systems with application to grid integration of renewable energy sources

Many systems in the natural and physical world often work in unison with similar other systems. This process of simultaneous operation is known as synchronization. In the past few decades, owing to this phenomenon’s importance, extensive research efforts have been made. However, many of the existing results consider the systems are identical and/or linear time-invariant, while practical systems are often nonlinear and nonidentical for various reasons. This observation motivated several recent studies on the synchronization of nonidentical (i.e., heterogeneous) nonlinear systems. This paper summarizes some recent results on the synchronization of heterogeneous nonlinear systems, as developed in the thesis (Ahmed 2016). First, the results on the synchronization of a particular class of robustly stable nonlinear systems are presented. Then, these results are applied to an example model known as Brockett oscillator. Finally, using the Brockett oscillator as a common dynamics, output oscillatory synchronization results are given for heterogeneous nonlinear systems of relative degree 2 or higher. An application example of Brockett oscillator for power-grid synchronization is also presented. Some outlooks are provided regarding future research directions.     

Cooperative adaptive control for synchronization of second‐order systems with unknown nonlinearities

This paper studies synchronization to a desired trajectory for multi‐agent systems with second‐order integrator dynamics and unknown nonlinearities and disturbances. The agents can have different dynamics and the treatment is for directed graphs with fixed communication topologies. The command generator or leader node dynamics is also nonlinear and unknown. Cooperative tracking adaptive controllers are designed based on each node maintaining a neural network parametric approximator and suitably tuning it to guarantee stability and performance. A Lyapunov‐based proof shows the ultimate boundedness of the tracking error. A simulation example with nodes having second‐order Lagrangian dynamics verifies the performance of the cooperative tracking adaptive controller. Copyright © 2010 John Wiley & Sons, Ltd.     

Establishing robust stability of discrete-time systems with time-varying uncertainty: The Gram-SOS approach

This paper addresses the problem of establishing robust asymptotical stability of discrete-time linear systems polynomially affected by time-varying uncertainty confined into a polytope. A linear matrix inequality (LMI) condition for establishing robust asymptotical stability is proposed by introducing a novel approach for establishing the existence of a common homogeneous polynomial Lyapunov function (HPLF). This approach consists, firstly, of introducing a Gram matrix built with respect to the state and parametrized by an arbitrary vector function of the uncertainty, and secondly, of requiring that a transformation of the introduced Gram matrix is a sum of squares (SOS) of matrix polynomials. The approach, hence, is referred to as a Gram-SOS approach. It is shown that the proposed LMI condition is sufficient for any degree of the HPLF candidate, that includes quadratic robust stability as a special case, and that is also necessary for a sufficiently large degree of the HPLF candidate. Numerical examples also show that the proposed LMI condition can outperform alternative ones in terms of conservatism and computational burden.     

Guaranteed cost control of stochastic uncertain systems with slope bounded nonlinearities via the use of dynamic multipliers

This paper presents a new approach to constructive output feedback robust nonlinear guaranteed cost controller design. The approach involves a class of controllers which include copies of the slope bounded nonlinearities occurring in the plant. Dynamic multipliers are introduced to exploit these repeated nonlinearities. The linear part of the controller is synthesized using minimax LQG control theory.     

Robust control of systems with fuzzy representation of uncertainties

In this paper, an approach is proposed to design robust controllers for uncertain systems with the linguistic uncertainties represented by fuzzy sets. With a provided technique, the fuzzy sets are best approximated by intervals (crisp sets). Then the Kharitonovs theorem is applied to construct a robust PID controller for the uncertain plant with time-invariant uncertainties represented by interval models. Also, for the uncertain system with linguistic values of the time-varying uncertainties best approximated by intervals (which are bounded), a robust sliding mode controller is developed to stabilize the uncertain system if the sliding coefficient conditions are satisfied. Moreover, the best approximation intervals are shown to be more related to the possibility distribution of the elements in the universes of discourse of fuzzy sets than the type of membership functions used for fuzzy sets. Examples and simulation results are included to indicate the design approach and the effectiveness of the proposed robust controller.This work is partly supported by the the R.O.C. National Science Council through Grant NSC 90-2213-E-197-002.     

H∞ estimation for discrete-time linear uncertain systems

This paper is concerned with the problem of H_∞ estimation for linear discrete-time systems with time-varying norm-bounded parameter uncertainty in both the state and output matrices. We design an estimator such that the estimation error dynamics is quadratically stable and the induced operator norm of the mapping from noise to estimation error is kept within a prescribed bound for all admissible uncertainties. A Riccati equation approach is proposed to solve the estimation problem and it is shown that the solution is related to two algebraic Riccati equations.     

Application of a multiplier method to uncertain Lur’e-like systems

This paper investigates the conditions under which an abstract matrix multiplier method can be applied to determine guaranteeing cost controls for systems containing nonlinear/uncertain elements via linear matrix inequalities (LMIs). Quadratically constrained uncertainties and nonlinearities are considered, which comprehend the cases of norm-bounded, positive-real and sector-bounded uncertainties/nonlinearities. Both the discrete-time and the continuous-time cases are discussed. Necessary and sufficient conditions are formulated in the case of unstructured uncertainty. The conditions are sufficient in the structured case. The cost guaranteeing controls can be determined by solving LMIs. Numerical examples illustrate the effectiveness of the proposed method.     

Event‐triggered observer‐based robust H∞ control for networked control systems with unknown disturbance

In this article, the event‐triggered robust H_∞ control is studied for a class of uncertain networked control systems (NCSs) subject to unknown state and variable disturbance. First, aiming to decrease the unnecessary transmissions of sampled data, an efficient adaptive event‐triggered scheme (AETS) is presented, which can reflect the full real‐time variation of addressed NCSs and help to reduce the conservativeness. Second, based on the triggered output signals and disturbance model, two effective observers are, respectively, exploited to estimate the state and disturbance, which are further utilized to reject the disturbance and design the controller. By using the overall closed‐loop system and selecting an augmented Lyapunov‐Krasovskii functional, two sufficient conditions on jointly designing the adaptive event scheme, observers, and controller are established via linear matrix inequality forms, which can guarantee the global exponential stability and ensure H_∞ performance. Finally, some simulations and comparisons in a numerical example are provided to demonstrate the effectiveness of the derived results.