and filter design for polytopic continuous‐time Markov jump linear systems with uncertain transition rates

This paper addresses the problems of and full‐order filter design for continuous‐time Markov jump linear systems subject to uncertainties. Different from the available methods in the literature, the main novelty of the proposed approach is the possibility of computing bounds to the and norms of the augmented system composed by the uncertain Markov jump linear system plus the robust filter through Lyapunov matrices depending polynomially on the uncertainties affecting independently the matrices of each operation mode and the transition rate matrix. By means of a suitable representation of the uncertainties, the proposed filter design conditions are expressed in terms of linear matrix inequality relaxations associated with searches on scalar parameters. As an additional flexibility, the conditions can be used to synthesize filters with partial, complete, or null Markov mode availability. Numerical experiments illustrate that the proposed approach is more general and can be less conservative than the available methods. Copyright © 2014 John Wiley & Sons, Ltd.     

Adaptive dynamic programming for tracking design of uncertain nonlinear systems with disturbances and input constraints

In this paper, the tracking controller is designed for uncertain nonlinear systems with external disturbances and input constraints. A discounted nonquadratic function is introduced, which encodes the constrained input into the performance. The key difficulty for tracking control is the requirement of solving the tracking Hamilton‐Jacobi‐Isaacs equation, which is a partial differential equation. It is impossible or extremely difficult to solve analytically even in simple cases. To overcome the difficulty, an online model‐free integral reinforcement learning (IRL) algorithm is proposed to learn online in real time the solution to the tracking Hamilton‐Jacobi‐Isaacs equation without requiring any knowledge of system dynamics. To implement it, critic‐actor‐disturbance neural networks (NNs) are built, and the 3 NNs are updated simultaneously. Stability and convergence analyses are shown by the Lyapunov method. In addition, a robust term is added to the controller to attenuate the effect of NN approximation errors, which leads to the asymptotic stability of the closed‐loop systems. Finally, 2 simulation examples show the effectiveness of the proposed algorithm.     

Adaptive observer for nonlinear fractional‐order systems

In this paper, an adaptive observer is proposed for the joint estimation of states and parameters of a fractional nonlinear system with external perturbations. The convergence of the proposed observer is derived in terms of linear matrix inequalities (LMIs) by using an indirect Lyapunov method.The proposed adaptive observer is also robust against Lipschitz additive nonlinear uncertainty. The performance of the observer is illustrated through some examples including the chaotic Lorenz and Lü's systems. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive output feedback regulation for a class of uncertain feedforward nonlinear systems

In this paper, we solve the problem of global output feedback regulation for uncertain feedforward nonlinear systems. The nonlinear functions, in the class of systems under consideration, are assumed to be dominated by an input‐output function multiplied by an unknown parameter and a linear unmeasured states. Contrarily to the previous works, the interval of the output's power has been expanded from to . A numerical example is provided to illustrate the effectiveness of the proposed design scheme. Copyright © 2016 John Wiley & Sons, Ltd.     

Composite adaptive anti‐disturbance resilient control for Markovian jump systems with partly known transition rate and multiple disturbances

In this paper, the problem of composite adaptive anti‐disturbance resilient control is investigated for Markovian jump systems with partly known transition rate and multiple disturbances. The considered multiple disturbances include two types: one is external disturbance, while the other is an unexpected nonlinear signal which is described as a nonlinear function. Composite adaptive disturbance observers are constructed to estimate these disturbances, and the estimations are applied to feedforward compensation. Then a composite adaptive anti‐disturbance resilient controller is obtained. Furthermore, some sufficient conditions are presented in terms of linear matrix inequalities such that the closed‐loop system is stochastically stable with performance. Finally, a numerical example and an application example are given to illustrate the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

An improved finite frequency approach to robust filter design for LTI systems with polytopic uncertainties

In this paper, the finite frequency robust filtering problem (‐FFRFP), design of a robust filter minimizing the norm from the disturbance input to the estimation error evaluated over a prescribed finite frequency domain, is considered for continuous‐time and discrete‐time linear time‐invariant (LTI) systems with polytopic parameter uncertainties. By means of the generalized Kalman–Yakubovich–Popov (KYP) lemma in combination with a result known as Finsler's lemma, the ‐FFRFP is cast as a linear matrix inequality (LMI) optimization. Examples are given to demonstrate that the proposed condition can achieve improvement over the previous ones in the literature. Copyright © 2012 John Wiley & Sons, Ltd.     

Fault estimation and tolerant control for discrete‐time switched systems with sojourn probabilities

This paper addresses the issue of fault estimation and accommodation for a discrete‐time switched system with actuator faults. Here, we assume that the sojourn probabilities are known a priori. By using the reduced‐order observer method, the sojourn probability approach, and the Lyapunov technique, a fault estimation algorithm is obtained for the considered system. The main objective of this work is to design a dynamic output feedback fault‐tolerant controller based on the obtained fault estimation information such that the closed‐loop discrete‐time switched system with available sojourn probabilities is robustly mean‐square stable and satisfies a prescribed mixed and passivity disturbance attenuation level in the presence of actuator faults. More precisely, a dynamic output feedback fault‐tolerant controller is established in terms of linear matrix inequalities. Finally, numerical examples are provided to illustrate the usefulness and effectiveness of the proposed design technique.     

filtering for switched discrete‐time systems under asynchronous switching: A dwell‐time dependent Lyapunov functional method

In this article, the filtering problem for switched discrete‐time linear systems under asynchronous switching is addressed in the framework of dwell time, where ‘asynchronous switching’ covers more general and practical cases, for example, the switching lags caused by mode identification process are taken into consideration. Firstly, a novel dwell‐time dependent Lyapunov function (DTDLF) is introduced to solve stability and ?₂ gain analysis problems. The main advantage of DTDLF approach is that the derived conditions are all convex in system matrices, so it is convenient to be applied into filter design with performance instead of weighted performance as many other previous results. Thus, on the basis of DTLDF, a dwell‐time dependent filter with time‐varying structure is proposed to achieve the desirable non‐weighted filtering performance. It is notable that the proposed approach can also easily characterize the relationships among filtering performance, dwell time, and asynchronous time. Two examples are provided to validate the theoretical findings in this paper. Copyright © 2014 John Wiley & Sons, Ltd.     

Mixed and passive filtering for linear switched systems with average dwell time

In this paper, a new performance index is proposed for switched systems. The new performance index can be viewed as the mixed weighted and passivity performance. This new performance index covers the weighted performance and the passivity performance as special cases. Based on this new performance index, the weighted filtering problem and the passive filtering problem of linear switched systems with unstable subsystems are solved in a unified framework. The states of the filtering error system constructed by the augmentation technique will be divergent when unstable subsystems are activated. To overcome this problem, a set of mode‐dependent filters of a Luenberger‐like observer type is constructed. The multiple Lyapunov function approach and the average dwell‐time technique are employed to solve the mixed filtering problem. New sufficient conditions for the existence of mixed and passive filters are developed, which ensure the filtering error system to be asymptotically stable with a prescribed mixed and passivity performance index. Moreover, the desired mixed and passive filters can be constructed by solving a set of linear matrix inequalities. Finally, numerical examples are given to demonstrate the applicability and advantage of the obtained results.     

Robust reliable dissipative filtering for Markovian jump nonlinear systems with uncertainties

This paper investigates the problem of robust reliable dissipative filtering for a class of Markovian jump nonlinear systems with uncertainties and time‐varying transition probability matrix described by a polytope. Our main attention is focused on the design of a reliable dissipative filter performance for the filtering error system such that the resulting error system is stochastically stable and strictly dissipative. By introducing a novel augmented Lyapunov–Krasovskii functional, a new set of sufficient conditions is obtained for the existence of reliable dissipative filter design in terms of linear matrix inequalities (LMIs). More precisely, a sufficient LMI condition is derived for reliable dissipative filtering that unifies the conditions for filtering with passivity and H_∞ performances. Moreover, the filter gains are characterized in terms of solution to a set of linear matrix inequalities. Finally, two numerical examples are provided to demonstrate the effectiveness and potential of the proposed design technique. Copyright © 2016 John Wiley & Sons, Ltd.     

2‐matrix‐based finite element linear solver for fast transient thermal analysis of high‐performance ICs

In this article, we propose ²‐based finite element (FE) solver for transient thermal analysis of high‐performance integrated circuits (ICs). ²‐matrix is a special subclass of hierarchical matrix or ‐matrix, which was shown to provide a data‐sparse way to approximate the matrices and their inverses with almost linear space and time complexities. In this work, we show that ²‐based mathematical framework can also be applied to FE‐based transient analysis of thermal parabolic partial differential equations. We show how the thermal matrix can be approximated by ²‐representations with controlled error. Then, we demonstrate that both storage and time complexities of the new solver are bounded by , where N is the matrix size. The method can be applied to any thermal structures for both steady and transient analysis. The numerical results from 3D ICs demonstrate the linear scalability of the proposed method in terms of both memory footprint and CPU time. The comparison with existing product‐quality LU solvers, CSPARSE and UMFPACK, on a number of 3D IC thermal matrices, shows that the new method is much more memory efficient than these methods, which however prevents the demonstration of the potential speedup of the proposed method over those methods. Copyright © 2014 John Wiley & Sons, Ltd.     

A robust output error identifier for continuous‐time systems

This paper shows that the adaptive output error identifier for linear time‐invariant continuous‐time systems proposed by Bestser and Zeheb is robust vis‐à‐vis finite energy measurement noise. More precisely, it is proven that the map from the noise to the estimation error is –stable—provided a tuning parameter is chosen sufficiently large. A procedure to determine the required minimal value of this parameter is also given. If the noise is exponentially vanishing, asymptotic convergence to zero of the prediction error is achieved. Instrumental for the establishment of the results is a suitable decomposition of the error system equations that allows us to strengthen—to strict—the well‐known passivity property of the identifier. The estimator neither requires fast adaptation, a dead‐zone, nor the knowledge of an upperbound on the noise magnitude, which is an essential requirement to prove stability of standard output error identifiers. To robustify the estimator with respect to non‐square integrable (but bounded) noises, a prediction error‐dependent leakage term is added in the integral adaptation. –stability of the modified scheme is established under a technical assumption. A simulated example, which is unstable for the equation error identifier and the output error identifier of Bestser and Zeheb, is used to illustrate the noise insensitivity property of the new scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

Positive invariant set estimation of adaptive controller in the presence of input saturation

For a class of linear dynamical systems with constant unknown parameters, an adaptive control scheme is developed that provides stable adaptation in the presence of input magnitude constraints. Whereas for open‐loop stable systems the results are global, for open‐loop unstable systems, the problem of nonconservative estimation of the nonempty positive invariant set is cast into an LMI framework, which can be efficiently solved numerically via convex optimization. To achieve this, a standard result toward invariant set characterization is appropriately extended to accommodate bounded disturbance and model uncertainties. In addition to closed‐loop stability, performance bounds of the adaptive closed‐loop system are analyzed, and the degradation due to the possible control deficiency is quantified. Simulation examples of aerospace applications are included to illustrate the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

Pressure Rise and Propagation Phenomena Due to Fault Arc in Container with Opened Pipe

This paper describes experimental and analytic studies on pressure rise and propagation phenomena due to high current arcs in a container with opened pipes. The shape of the experimental container was chosen taking into account underground common ducts. First, arcs were ignited in the container with varying diameter D and length L of the opened pipes and at arc currents of 4 kA to 12.5 kA and an arc duration of 0.1 s. Based on measured waveforms, the maximum pressure rise and the pressure oscillation frequency were obtained. It was found that there is a tendency for to increase with decreasing D and increasing L, and that D has a much greater impact on . In addition, the tendencies of with changing D and L can be approximately explained by Helmholtz resonance. Second, a CFD model for the container with opened pipe was developed based on the experimental results, and simulations were performed. The simulation results were found to correspond to the experimental pressure rise.     

A Strategy for the Design of the LCR Filter in a Series Voltage Compensator

In this paper, we propose a strategy for the design of the LCR filter in a series voltage compensator and investigate our method by performing simulations and experiments. In the proposed method, first, the inductance is derived from the ratio of the maximum amplitude of the ripple current to the amplitude of the fundamental current, which is denoted as . Second, the capacitance is derived from the ratio of the ripple voltage to the fundamental voltage. Third, the resistance R is determined from the rate of decrease of the carrier frequency component and the settling time.     

Random adaptive control for cluster synchronization of complex networks with distinct communities

In this paper, we investigate the cluster synchronization for complex networks with time‐varying delayed couplings, stochastic disturbance, and non‐identical nodes in different clusters. Based on randomly occurring controllers, some Bernoulli stochastic variables are introduced to describe the controllers, then, a fraction of nodes in clusters, which have direct connections to the other clusters, is controlled, and the states of the whole dynamical networks can be globally forced to the objective cluster states. Sufficient conditions are derived to guarantee the realization of the mean square cluster synchronization pattern for all initial values by means of Lyapunov stability theory, It differential formula, and LMI approach. Besides, by designing the randomly occurring adaptive update law, some suitable control gains are obtained. Finally, numerical simulations are also given to demonstrate the effectiveness and validity of the main result. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust adaptive output‐feedback control for a class of nonlinear systems with hysteresis compensation controller

In this paper, a robust adaptive output‐feedback dynamic surface control scheme is proposed for a class of single‐input single‐output nonlinear systems preceded by unknown hysteresis with the following features: (1) a hysteresis compensator is designed in the control signal to compensate the hysteresis nonlinearities with only the availability of the output of the control system; (2) by estimating the norm of the unknown parameter vector and the maximum value of the hysteresis density function, the number of the estimated parameters is reduced, which implies that the computational burden is greatly reduced; (3) by introducing the initializing technique, the initial conditions of the state observer and adaptive laws of unknown parameters can be properly chosen, and the arbitrarily small norm of the tracking error is achieved. It is proved that all the signals in the closed‐loop system are ultimately uniformly bounded and can be arbitrarily small. Simulation results show the validity of the proposed scheme.     

Experimental Study of Transformer Residual Flux and the Method of Restraining Inrush Current

Whenever a power transformer in a no‐load condition is manually tripped, a residual flux appears in the transformer core, which causes an inrush current when the transformer is later re‐energized. However, the true nature of residual fluxes has not yet been experimentally elucidated. The authors interpreted the residual flux as representing the ending states of transient phenomena after tripping, and tested this interpretation experimentally. In the authors' interpretation, a three‐phase balanced transient phenomenon of the voltage, current, and core flux occurs immediately after the transformer is tripped at the time t_op0, and it continues until time t_op1. The true nature of the residual flux is the core fluxes , , at t_op1. Furthermore, these residual fluxes as well as the voltages and currents during the transient interval are practically three‐phase balanced, so that they can be expressed as three‐phase balanced equilateral triangular phasors. The core flux values and waveforms cannot be directly measured but they can be digitally generated as the integrals of the voltage waveform. Thus a test of the residual flux under the above interpretation can be performed indirectly by preparing (1) measured voltage waveforms just after transformer tripping, (2) flux waveforms mathematically generated by voltage integration just after tripping, and (3) measured transient inrush current , , , occurring immediately after the transformer is re‐energized at time θcl, and then comparing these three data as characteristics in the 3‐D coordinates of and of . Verification tests were performed utilizing a simulation test circuit in which large numbers of on–off switching tests of a transformer were conducted. The test results clearly indicated that the inrush current reaches its maximum whenever θ_cl is in antiphase with θ_op1 (instead of θ_op0), and reaches its minimum whenever θ_cl is in phase with θ_op1. These test results confirmed the authors' interpretation of the true nature of the transient phenomena and the residual flux after tripping. The test results suggest essential algorithms for inrush current restraining control in order to appropriately restrain inrush current phenomena. Field test results at a 66‐kV wind power station where commercial equipment based on the above described theory and method were in service are also presented.     

Robust neuro‐adaptive cooperative control of multi‐agent port‐controlled Hamiltonian systems

This paper presents the distributed cooperative tracking control of the multi‐agent port‐controlled Hamiltonian (PCH) systems that are networked through a directed graph. Controller is made robust against the parametric uncertainties using neural networks. Dynamics of the the proposed novel neural network tuning law is driven by both the position and the velocity errors owing to the information preserving filtering of the Hamiltonian gradient. In addition, the PCH structure of the closed‐loop system is preserved and the controller achieves the disturbance attenuation objective. Simulations are performed on a group of robotic manipulators to demonstrate the efficacy of the proposed controller. Copyright © 2015 John Wiley & Sons, Ltd.     

A robust adaptive control architecture for disturbance rejection and uncertainty suppression with L ∞ transient and steady‐state performance guarantees

In this paper, a new adaptive control architecture for linear and nonlinear uncertain dynamical systems is developed to address the problem of high‐gain adaptive control. Specifically, the proposed framework involves a new and novel controller architecture involving a modification term in the update law that minimizes an error criterion involving the distance between the weighted regressor vector and the weighted system error states. This modification term allows for fast adaptation without hindering system robustness. In particular, we show that the governing tracking closed‐loop system error equation approximates a Hurwitz linear time‐invariant dynamical system with input–output signals. This key feature of our framework allows for robust stability analysis of the proposed adaptive control law using system theory. We further show that by properly choosing the design parameters in the modification term, we can guarantee a desired bandwidth of the adaptive controller, guaranteed transient closed‐loop performance, and an a priori characterization of the size of the ultimate bound of the closed‐loop system trajectories. Several illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.