Search

This paper considers identification of nonlinear rational systems defined as the ratio of two nonlinear functions of past inputs and outputs. Despite its long history, a globally consistent identification algorithm remains illusive. This paper proposes a globally convergent identification algorithm for such nonlinear rational systems. To the best of our knowledge, this is the first globally convergent algorithm for the nonlinear rational systems. The technique employed is a two-step estimator. Though two-step estimators are known to produce consistent nonlinear least squares estimates if a N consistent estimate can be determined in the first step, how to find such a N consistent estimate in the first step for nonlinear rational systems is nontrivial and is not answered by any two-step estimators. The technical contribution of the paper is to develop a globally consistent estimator for nonlinear rational systems in the first step. This is achieved by involving model transformation, bias analysis, noise variance estimation, and bias compensation in the paper. Two simulation examples and a practical example are provided to verify the good performance of the proposed two-step estimator. [ABSTRACT FROM AUTHOR]

This technical paper presents a distributed continuous-time algorithm to solve multi-agent optimization problem with the team objective being the sum of all local convex objective functions while subject to an equality constraint. The optimal solutions are achieved within fixed time which is independent of the initial conditions of agents. This advantage makes it possible to off-line preassign the settling time according to task requirements. The fixed-time convergence for the proposed algorithm is rigorously proved with the aid of convex optimization and fixed-time Lyapunov theory. Finally, the algorithm is valuated via an example. [ABSTRACT FROM AUTHOR]

In this paper we propose an algorithm to estimate the parameters, including time delay, of continuous time systems based on instrumental variable identification methods. To overcome the multiple local minima of the cost function associated with the estimation of a time delay system, we utilize the useful redundancy technique. Specifically, the cost function is filtered through a set of low-pass filters to improve convexity with the useful redundancy technique exploited to achieve convergence to the global minimum of the optimization problem. Numerical examples are presented to demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

A novel adaptive frequency-domain system identification method for linear time-invariant systems is proposed in this paper. It finds poles for discrete rational atoms with discrete frequency responses. The theoretical foundation, including adaptive decomposition principle and decomposition convergence rate, is established. The algorithm of the adaptive pursuit is also provided in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we extend convergence conditions for the parameter adaptation algorithm, used in discrete-time recursive identification schemes, or in adaptive control. Whereas the classical stability analysis of this algorithm consists in checking the strictly real positiveness of an associated transfer function, we demonstrate that convergence can be obtained even when this condition is not fulfilled, under some assumptions on the algorithm forgetting factors. These results regarding both deterministic and stochastic contexts are obtained by analyzing convergence with a prescribed degree of stability. [ABSTRACT FROM AUTHOR]

This paper derives a recursive prediction error identification method based on the Hammerstein model structure. The convergence properties of the algorithm are analysed by application of Ljung’s associated differential equation method. It is proved that the algorithm can only converge to stable stationary points of the associated ordinary differential equation. General conditions for local convergence to the true parameter vector are given, and the cases with piecewise linear and polynomial nonlinearities are treated in detail. The derived identification method is illustrated in a numerical study that treats identification of a subsystem of a cement mill. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we propose a new methodology to synthesize and implement robust monotonically convergent ILC for lifted systems, with the computational complexity that is linear in the trial length. Starting from the model uncertainty of the local sample to sample LTI or LTV models, and using the randomized algorithm, we compute the bound on the model uncertainty of the ILC system representation in the trial domain (lifted ILC). Based on this computed uncertainty bound, we design weighting matrices of the Norm Optimal ILC, such that the robust monotonic convergence condition is satisfied. Since we compute the uncertainty bound, rather than assuming its value in the trial domain, we reduce the conservatism of the robust design. The linear computational complexity of the algorithms for computation of the uncertainty bound and implementation of the Norm Optimal ILC law, is achieved through exploiting the sequentially semi-separable structure of the lifted system matrices. Therefore the framework proposed in this paper is especially suitable for the LTI and LTV uncertain systems with a large number of samples in the trial. We have performed numerical experiments to demonstrate the robustness and linear computational complexity of the proposed method. [Copyright &y& Elsevier]

Abstract: Skid-steered vehicles, by design, must skid in order to maneuver. The skidding causes the vehicle to behave discontinuously during a maneuver as well as introduces complications to the observation of the vehicle’s state, both of which affect a controller’s performance. This paper addresses estimation of contact state by applying switched system optimization to estimate skidding properties of the skid-steered vehicle. In order to treat the skid-steered vehicle as a switched system, the vehicle’s ground interaction is modeled using Coulomb friction, thereby partitioning the system dynamics into four distinct modes, one for each combination of the forward and back wheel pairs sticking or skidding. Thus, as the vehicle maneuvers, the system propagates over some mode sequence, transitioning between modes over some set of switching times. This paper presents second-order optimization algorithms for estimating these switching times. We emphasize the importance of the second-order algorithm because it exhibits quadratic convergence and because even for relatively simple examples, first-order methods fail to converge on time scales compatible with real-time operation. Furthermore, the paper presents a technique for estimating the mode sequence by optimizing a relaxation of the switched system. [ABSTRACT FROM AUTHOR]

Abstract: In this paper a new parameter-optimal high-order Iterative Learning Control (ILC) algorithms is proposed to extend the work of Owens and Feng [Parameter optimisation in iterative learning control. International Journal of Control 14(11), 1059–1069]. If the original plant is positive, this new algorithm will result in convergent learning where the convergence is monotonic to zero tracking error. If the original plant is not positive, it can be shown that by adding a suitable set of basis functions into the algorithm, the tracking error will again converge monotonically to zero. This provides a considerable improvement to earlier work on parameter-optimal ILC as it opens up the possibility of globally convergent algorithms for any linear plant G. The number of parameters needed to ensure convergence could, however, become large. The paper shows that the use of low-order parameterisations is capable of achieving much of the benefit achieved in the ‘ideal’ case. [Copyright &y& Elsevier]

In this paper we propose a novel algorithm to solve the discrete consensus problem, i.e., the problem of distributing evenly a set of tokens of arbitrary weight among the nodes of a networked system. Tokens are tasks to be executed by the nodes and the proposed distributed algorithm minimizes monotonically the makespan of the assigned tasks. The algorithm is based on gossip -like asynchronous local interactions between the nodes. The convergence time of the proposed algorithm is superior with respect to the state of the art of discrete and quantized consensus by at least a factor O ( n ) in both theoretical and empirical comparisons. [ABSTRACT FROM AUTHOR]

In this paper we propose a fully distributed dual gradient algorithm for minimizing linearly constrained separable convex problems and analyze its rate of convergence. In particular, we prove that under the assumption of strong convexity and Lipschitz continuity of the gradient of the primal objective function we have a global error bound type property for the dual problem. Using this error bound property we devise a fully distributed dual gradient scheme, i.e. a gradient scheme based on a weighted step size, for which we derive global linear rate of convergence for both dual and primal suboptimality and for primal feasibility violation. Numerical simulations are also provided to confirm our theory. [ABSTRACT FROM AUTHOR]

Abstract: This paper studies the identification of finite impulse response (FIR) systems with binary-valued observations. Combining with the stochastic gradient algorithm and statistical property of the system noise, a recursive projection algorithm is proposed to estimate the unknown system parameters. Under some mild conditions on the a priori knowledge of the unknown parameters and inputs, the algorithm is proved to be convergent in the almost sure and mean square sense. Furthermore, the almost sure and mean square convergence rates of estimation errors are also obtained. A numerical example is given to demonstrate the effectiveness of the algorithm and the main results obtained. [Copyright &y& Elsevier]

Abstract: The Prediction Error Method (PEM) is related to an optimization problem built on input/output data collected from the system to be identified. It is often hard to find the global solution of this optimization problem because the corresponding objective function presents local minima and/or the search space is constrained to a nonconvex set. The shape of the cost function, and hence the difficulty in solving the optimization problem, depends directly on the experimental conditions, more specifically on the spectrum of the input/output data collected from the system. Therefore, it seems plausible to improve the convergence to the global minimum by properly choosing the spectrum of the input; in this paper, we address this problem. We present a condition for convergence to the global minimum of the cost function and propose its inclusion in the input design. We present the application of the proposed approach to case studies where the algorithms tend to get trapped in nonglobal minima. [Copyright &y& Elsevier]

Abstract: This paper presents a distributed algorithmic solution, termed Coalition formation and deployment algorithm , to achieve network configurations where agents cluster into coincident groups that are distributed optimally over the environment. The motivation for this problem comes from spatial estimation tasks executed with unreliable sensors. We propose a probabilistic strategy that combines a repeated game governing the formation of coalitions with a spatial motion component governing their location. For a class of probabilistic coalition switching laws, we establish the convergence of the agents to coincident groups of a desired size in finite time and the asymptotic convergence of the overall network to the optimal deployment, both with probability 1. We also investigate the algorithm’s time and communication complexity. Specifically, we upper bound the expected completion time of executions that use the proportional-to-number-of-unmatched-agents coalition switching law under arbitrary and complete communication topologies. We also upper bound the number of messages required per timestep to execute our strategy. The proposed algorithm is robust to agent addition and subtraction. From a coalitional game perspective, the algorithm is novel in that the players’ information is limited to the neighboring clusters. From a motion coordination perspective, the algorithm is novel because it brings together the basic tasks of rendezvous (individual agents into clusters) and deployment (clusters in the environment). Simulations illustrate the correctness, robustness, and complexity results. [Copyright &y& Elsevier]

Abstract: In this paper, we analyze a novel algorithm for 2-D ARMA model parameter estimation in the presence of noise and then develop a fast and efficient blind image restoration algorithm. We show that the novel algorithm can minimize a quadratic convex optimization problem and has a lower computational complexity than the conventional algorithms. As a result, the novel algorithm involves no convergence and local minimum issue. Moreover, the proposed blind image restoration algorithm can overcome the local minimization problem. Computed results confirm that the novel algorithm can more quickly obtain more accurate estimates than the conventional algorithms in the presence of noise. [Copyright &y& Elsevier]

Abstract: DIRECT is a sample-based global optimisation method for Lipschitz continuous functions defined over compact multidimensional domains. This paper adapts the DIRECT method with a modified termination criterion for global extremum seeking control of multivariable dynamical plants. Finite-time semi-global practical convergence is established based on a periodic sampled-data control law, whose sampling period is a parameter which determines the region and accuracy of convergence. A crucial part of the development is dedicated to a robustness analysis of the DIRECT method against bounded additive perturbations on the objective function. Extremum seeking involving multiple units is also considered within the same context as a means to increase the speed of convergence. Numerical examples of global extremum seeking based on DIRECT are presented at the end. [Copyright &y& Elsevier]

Abstract: Gossiping is a distributed process whose purpose is to enable the members of a group of autonomous agents to asymptotically determine in a decentralized manner, the average of the initial values of their scalar gossip variables. This paper analyzes the accelerated gossip algorithms, first proposed in Cao, Spielman, and Yeh (2006), in which local memory is exploited by installing shift-registers at each agent. For the two-register case, the existence of the desired convergence is established under a symmetry assumption by separately studying the convergence in expectation and in mean square. In particular, the optimal rate of convergence in expectation is derived which is faster than that of the standard gossip algorithm, and a sufficient condition on the adjustable parameter for the convergence in mean square is provided. These theoretical results are validated for some classes of networks by comparison with existing empirical data. More general multi-register cases are also discussed. [Copyright &y& Elsevier]

Abstract: The main purpose of this paper is to adapt the so-called Shubert algorithm for extremum seeking control of general dynamic plants. This algorithm is a good representative of the “sampling optimization methods” that achieve global extremum seeking on compact sets in the presence of local extrema. The algorithm applies to Lipschitz mappings; the model of the system is assumed unknown but the knowledge of its Lipschitz constant is assumed. The controller depends on a design parameter, the “waiting time”, and tuning guidelines that relate the design parameter and the region of convergence and accuracy of the algorithm are presented. The analysis shows that semi-global practical convergence (in the initial states) to the global extremum can be achieved in presence of local extrema if compact sets of inputs are considered. Numerical simulations for global optimization in the presence of local extrema are provided to demonstrate the proposed approach. [Copyright &y& Elsevier]

Abstract: Nonlinear stochastic dynamical systems are widely used to model physical processes. In many practical applications, the state variables are defined on a compact set of the state space, i.e., they are bounded or saturated. To estimate the states of systems with saturated variables, the Saturated Particle Filter (SPF) has recently been developed. This filter exploits the structure of the saturated system using a specific importance sampling distribution. In this paper we investigate the asymptotic properties of the filter, in particular its almost sure convergence to the true posterior PDF. Furthermore, an improved SPF is developed that uses a novel resampling procedure to overcome the practical shortcomings of the original SPF. We prove that this new filter also converges almost surely to the true posterior PDF. Both versions of the SPF are presented in easy to implement algorithmic forms. [Copyright &y& Elsevier]

Abstract: The main obstacles for application of Sliding Mode Control are two interconnected phenomena: chattering and high activity of control action. It is well known that the amplitude of chattering is proportional to the magnitude of discontinuous control. These two problems can be handled simultaneously if the magnitude is reduced to a minimal admissible level defined by the conditions for the sliding mode to exist. In this paper an adaptation methodology is developed for searching the minimum possible value of control based on evaluations of the, so-called, equivalent control by a low-pass filter. It is based on direct measurements of the, so-called, equivalent control by a first-order low-pass filter. The application of this methodology to the Super-Twist control enables reducing the control action magnitude to the minimum possible value keeping the property of a finite-time convergence. [Copyright &y& Elsevier]

Abstract: This paper proposes an integral Q-learning for continuous-time (CT) linear time-invariant (LTI) systems, which solves a linear quadratic regulation (LQR) problem in real time for a given system and a value function, without knowledge about the system dynamics and . Here, Q-learning is referred to as a family of reinforcement learning methods which find the optimal policy by interaction with an uncertain environment. In the evolution of the algorithm, we first develop an explorized policy iteration (PI) method which is able to deal with known exploration signals. Then, the integral Q-learning algorithm for CT LTI systems is derived based on this PI and the variants of -functions derived from the singular perturbation of the control input. The proposed Q-learning scheme evaluates the current value function and the improved control policy at the same time, and are proven stable and convergent to the LQ optimal solution, provided that the initial policy is stabilizing. For the proposed algorithms, practical online implementation methods are investigated in terms of persistency of excitation (PE) and explorations. Finally, simulation results are provided for the better comparison and verification of the performance. [Copyright &y& Elsevier]

Abstract: Many iterative approaches in the field of system identification for control have been developed. Although successful implementations have been reported, a solid analysis with respect to the convergence of these iterations has not been established. The aim of this paper is to present a thorough analysis of a specific iterative algorithm that involves nonparametric -norm estimation. The pursued methodology involves a novel frequency domain approach that addresses both additive stochastic disturbances and input normalization. The results of the convergence analysis are twofold: (1) the presence of additive disturbances introduces a bias in the estimation procedure, and (2) the iterative procedure can be interpreted as experiment design for -norm estimation, revealing the value of iterations and limits of accuracy in terms of the Fisher information matrix. The results are confirmed by means of a simulation example. [Copyright &y& Elsevier]

Abstract: We have recently proposed quantized gossip algorithms which solve the consensus and averaging problems on directed graphs with the least restrictive connectivity requirements. In this paper we study the convergence time of these algorithms. To this end, we investigate the shrinking time of the smallest interval that contains all states for the consensus algorithm, and the decay time of a suitable Lyapunov function for the averaging algorithm. The investigation leads us to characterize the convergence time by the hitting time in certain special Markov chains. We simplify the structures of state transition by considering the special case of complete graphs, where every edge can be activated with an equal probability, and derive polynomial upper bounds on convergence time. [Copyright &y& Elsevier]

Abstract: In this paper we establish basic stability results for a class of nonlinear AIMD (additive-increase multiplicative-decrease) algorithms. We consider networks in which the nonlinearity enters through the multiplicative-decrease mechanism. In particular, where the multiplicative-decrease function depends in a nonlinear fashion on the achieved rate. For synchronized deterministic networks, we establish stability and convergence results. For non-synchronized stochastic networks, basic convergence results are also established. In particular, we give conditions for the existence of a unique invariant stationary distribution, and conditions under which time- and ensemble-averages converge to the same unique value (irrespective of initial conditions). [Copyright &y& Elsevier]

Abstract: This paper studies a deployment problem for a group of robots where individual agents operate with outdated information about each other’s locations. Our objective is to understand to what extent outdated information is still useful and at which point it becomes essential to obtain new, up-to-date information. We propose a self-triggered coordination algorithm based on spatial partitioning techniques with uncertain information. We analyze its correctness in synchronous and asynchronous scenarios, and establish the same convergence guarantees that a synchronous algorithm with perfect information at all times would achieve. The technical approach combines computational geometry, set-valued stability analysis, and event-based systems. [Copyright &y& Elsevier]

Abstract: The main contribution of this paper is an algorithm to solve an extended version of the quantized consensus problem over networks represented by Hamiltonian graphs, i.e., graphs containing a Hamiltonian cycle, which we assume to be known in advance. Given a network of agents, we assume that a certain number of tokens should be assigned to the agents, so that the total number of tokens weighted by their sizes is the same for all the agents. The algorithm is proved to converge almost surely to a finite set containing the optimal solution. A worst case study of the expected convergence time is carried out, thus proving the efficiency of the algorithm with respect to other solutions recently presented in the literature. Moreover, the algorithm has a decentralized stop criterion once the convergence set is reached. [Copyright &y& Elsevier]

Abstract: In this paper, the problems of parameter estimation are addressed for systems with scarce measurements. A gradient-based algorithm is derived to estimate the parameters of the input–output representation with scarce measurements, and the convergence properties of the parameter estimation and unavailable output estimation are established using the Kronecker lemma and the deterministic version of the martingale convergence theorem. Finally, an example is provided to demonstrate the effectiveness of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, we study the identification of parametric Hammerstein systems with FIR linear parts. By a proper normalization and a clever characterization, it is shown that the average squared error cost function for identification can be expressed in terms of the inner product between the true but unknown parameter vector and its estimate. Further, the cost function is concave in the inner product and linear in the inner product square. Therefore, the identification of parametric Hammerstein systems with FIR linear parts is a globally convergent problem and has one and only one (local and global) minimum. This implies that the identification of such systems is a linear problem in terms of the inner product square and any local search based identification algorithm converges globally. [Copyright &y& Elsevier]

Abstract: This paper is concerned with asymptotic properties of consensus-type algorithms for networked systems whose topologies switch randomly. The regime-switching process is modeled as a discrete-time Markov chain with a finite state space. The consensus control is achieved by using stochastic approximation methods. In the setup, the regime-switching process (the Markov chain) contains a rate parameter in the transition probability matrix that characterizes how frequently the topology switches. On the other hand, the consensus control algorithm uses a stepsize that defines how fast the network states are updated. Depending on their relative values, three distinct scenarios emerge. Under suitable conditions, we show that when , a continuous-time interpolation of the iterates converges weakly to a system of randomly switching ordinary differential equations modulated by a continuous-time Markov chain. In this case a scaled sequence of tracking errors converges to a system of switching diffusion. When , the network topology is almost non-switching during consensus control transient intervals, and hence the limit dynamic system is simply an autonomous differential equation. When , the Markov chain acts as a fast varying noise, and only its averaged network matrices are relevant, resulting in a limit differential equation that is an average with respect to the stationary measure of the Markov chain. Simulation results are presented to demonstrate these findings. [Copyright &y& Elsevier]

Abstract: In this paper, identification of structured nonlinear systems is considered. Using linear fractional transformations (LFT), the a priori information regarding the structural interconnection is systematically exploited. A parametric approach to the identification problem is investigated, where it is assumed that the linear part of the interconnection is given and the input to the nonlinear part is measurable. An algorithm for the identification of the nonlinear part is proposed. The uniqueness properties of the estimate provided by the algorithm are examined. It is shown that the estimate converges asymptotically to its true value under a certain persistence of excitation condition. Two simulated examples and a real-data example are presented to show the effectiveness of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the convergence of a class of continuous-time nonlinear consensus algorithms for single integrator agents. In the consensus algorithms studied here, the control input of each agent is assumed to be a state-dependent combination of the relative positions of its neighbors in the information flow graph. Using a novel approach based on the smallest order of the nonzero derivative, it is shown that under some mild conditions the convex hull of the agents has a contracting property. A set-valued LaSalle-like approach is subsequently employed to show the convergence of the agents to a common point. The results are shown to be more general than the ones reported in the literature in some cases. An illustrative example demonstrates how the proposed convergence conditions can be verified. [Copyright &y& Elsevier]

Abstract: This paper proposes a model predictive control (MPC) approach to the periodic implementation of the optimal solutions of a class of resource allocation problems in which the allocation requirements and conditions repeat periodically over time. This special class of resource allocation problems includes many practical energy optimization problems such as load scheduling and generation dispatch. The convergence and robustness of the MPC algorithm is proved by invoking results from convex optimization. To illustrate the practical applications of the MPC algorithm, the energy optimization of a water pumping system is studied. [ABSTRACT FROM AUTHOR]

Abstract: The convergence of the iterative identification algorithm for a general Hammerstein system has been an open problem for a long time. In this paper, it is shown that the convergence can be achieved by incorporating a regularization procedure on the nonlinearity in addition to a normalization step on the parameters. [Copyright &y& Elsevier]

Abstract: This paper considers stochastic consensus problems over lossy wireless networks. We first propose a measurement model with a random link gain, additive noise, and Markovian lossy signal reception, which captures uncertain operational conditions of practical networks. For consensus seeking, we apply stochastic approximation and derive a Markovian mode dependent recursive algorithm. Mean square and almost sure (i.e., probability one) convergence analysis is developed via a state space decomposition approach when the coefficient matrix in the algorithm satisfies a zero row and column sum condition. Subsequently, we consider a model with arbitrary random switching and a common stochastic Lyapunov function technique is used to prove convergence. Finally, our method is applied to models with heterogeneous quantizers and packet losses, and convergence results are proved. [Copyright &y& Elsevier]

Abstract: In this paper the extremum seeking algorithm with sinusoidal perturbations has been extended and modified in two ways: (a) the output of the system is corrupted with measurement noise; (b) the amplitudes of the perturbation signals, as well as the gain of the integrator block, are time varying and tend to zero at a pre-specified rate. Convergence to the extremal point, with probability one, has been proved. Also, as a consequence of being able to cope with a stochastic environment, it has been shown how the proposed algorithm can be applied to mobile sensors as a tool for achieving the optimal observation positions. The proposed algorithm has been illustrated through several simulations. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents three novel moving-horizon estimation (MHE) methods for discrete-time partitioned linear systems, i.e., systems decomposed into coupled subsystems with non-overlapping states. The MHE approach is used due to its capability of exploiting physical constraints on states and noise in the estimation process. In the proposed algorithms, each subsystem solves reduced-order MHE problems to estimate its own state and different estimators have different computational complexity, accuracy and transmission requirements among subsystems. In all cases, proper tuning of the design parameters, i.e., the penalties on the states at the beginning of the estimation horizon, guarantees convergence of the estimation error to zero. Numerical simulations demonstrate the viability of the approach. [Copyright &y& Elsevier]

Abstract: In this paper we discuss an online algorithm based on policy iteration for learning the continuous-time (CT) optimal control solution with infinite horizon cost for nonlinear systems with known dynamics. That is, the algorithm learns online in real-time the solution to the optimal control design HJ equation. This method finds in real-time suitable approximations of both the optimal cost and the optimal control policy, while also guaranteeing closed-loop stability. We present an online adaptive algorithm implemented as an actor/critic structure which involves simultaneous continuous-time adaptation of both actor and critic neural networks. We call this ‘synchronous’ policy iteration. A persistence of excitation condition is shown to guarantee convergence of the critic to the actual optimal value function. Novel tuning algorithms are given for both critic and actor networks, with extra nonstandard terms in the actor tuning law being required to guarantee closed-loop dynamical stability. The convergence to the optimal controller is proven, and the stability of the system is also guaranteed. Simulation examples show the effectiveness of the new algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, a novel excitation control is designed for improvement of transient stability of power systems. The control algorithm is based on the adaptive backstepping method in a recursive way without linearizing the system model. Lyapunov function method is applied in designing the controller to ensure the convergence of the power angle, relative speed of the generator and the active electrical power delivered by the generator when a large fault occurs. Compared with the existing nonlinear decentralized control approaches, the proposed controller has no requirement for the bounds of interconnections in the power system. And the new approach does not need the existence of solution of a designed algebraic Riccati equation. Furthermore, the transient stability performance of power systems can also be improved by the designed control approach. The efficacy of the designed controller has been demonstrated in a multimachine power system. Simulation results show transient stability enhancement of a power system in the face of a large sudden fault. [Copyright &y& Elsevier]

Abstract: This paper considers the average consensus problem on a network of digital links, and proposes a set of algorithms based on pairwise “gossip” communications and updates. We study the convergence properties of such algorithms with the goal of answering two design questions, arising from the literature: whether the agents should encode their communication by a deterministic or a randomized quantizer, and whether they should use, and how, exact information regarding their own states in the update. [Copyright &y& Elsevier]

Abstract: Characterizing convergence speed is one of the most important research challenges in the design of distributed consensus algorithms for networked multi-agent systems. In this paper, we consider a group of agents that communicate via a dynamically switching random information network. Each link in the network, which represents the directed/undirected information flow between any ordered/unordered pair of agents, could be subject to failure with a certain probability. Hence we model the information flow using dynamically switching random graphs. We characterize the convergence speed for the distributed discrete-time consensus algorithm over a variety of random networks with arbitrary weights. In particular, we propose the asymptotic and per-step (mean square) convergence factors as measures of the convergence speed and derive the exact value for the per-step (mean square) convergence factor. Numerical examples are also given to illustrate our theoretical results. [Copyright &y& Elsevier]

Abstract: In recent years, there has been a growing interest in developing statistical learning methods to provide approximate solutions to “difficult” control problems. In particular, randomized algorithms have become a very popular tool used for stability and performance analysis as well as for design of control systems. However, as randomized algorithms provide an efficient solution procedure to the “intractable” problems, stochastic methods bring closer to understanding the properties of the real systems. The topic of this paper is the use of stochastic methods in order to solve the problem of control robustness: the case of parametric stochastic uncertainty is considered. Necessary concepts regarding stochastic control theory and stochastic differential equations are introduced. Then a convergence analysis is provided by means of the Chernoff bounds, which guarantees robustness in mean and in probability. As an illustration, the robustness of control performances of example control systems is computed. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate what constitutes the least amount of a priori information on the nonlinearity so that the linear part is identifiable in the non-Gaussian input case. Under the white noise input, three types of a priori information are considered: quadrant information, point information, and monotonic information. In all three cases, identifiability has been established, and the corresponding nonparametric identification algorithms are developed along with their convergence proofs. [Copyright &y& Elsevier]

Abstract: In this paper, an iterative algorithm to solve Hamilton–Jacobi–Bellman–Isaacs (HJBI) equations for a broad class of nonlinear control systems is proposed. By constructing two series of nonnegative functions, we replace the problem of solving an HJBI equation by the problem of solving a sequence of Hamilton–Jacobi–Bellman (HJB) equations whose solutions can be approximated recursively by existing methods. The local convergence of the algorithm and local quadratic rate of convergence of the algorithm are guaranteed and a proof is given. Numerical examples are also provided to demonstrate the effectiveness of the proposed algorithm. A game theoretical interpretation of the algorithm is given. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate what constitutes the least amount of a priori information on the nonlinearity so that the FIR linear part is identifiable in the non-Gaussian input case. Three types of a priori information are considered including quadrant information, point information and locally monotonous information. In all three cases, identifiability has been established and corresponding identification algorithms are developed with their convergence proofs. [Copyright &y& Elsevier]

Abstract: The convergence properties of recently developed recursive subspace identification methods are investigated in this paper. The algorithms operate on the basis of instrumental variable (IV) versions of the propagator method for signal subspace estimation. It is proved that, under suitable conditions on the input signal and the system, the considered recursive subspace identification algorithms converge to a consistent estimate of the propagator and, by extension, to the state-space system matrices. [Copyright &y& Elsevier]

An approach to fault diagnosis for a class of nonlinear systems is proposed in this paper. It is based on a new adaptive estimation algorithm for recursive estimation of the parameters related to faults. This algorithm is designed in a constructive manner through a nontrivial combination of a high gain observer and a recently developed linear adaptive observer, without resort to any linearization. Its global exponential convergence is ensured by an easy-to-check persistent excitation condition. A numerical example is presented for illustration. [Copyright &y& Elsevier]