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The problem of transforming a single-input single-output nonlinear discrete-time state equations into the extended observer form is studied in this paper. Unlike previous solutions which compute the injection terms from the input–output equations, in this paper the computations utilize directly the given state equations. An algorithm is given to find step-by-step the necessary transformation by computing backward-shifts of functions computed in previous step. It is shown that the integrability conditions presented in the algorithm are necessary and sufficient for solvability of the problem. Various examples have been studied to demonstrate the usefulness of the algorithm. [ABSTRACT FROM AUTHOR]

This paper considers the problem of online optimization where the objective function is time-varying. In particular, we extend coordinate descent type algorithms to the online case, where the objective function varies after a finite number of iterations of the algorithm. Instead of solving the problem exactly at each time step, we only apply a finite number of iterations at each time step. Commonly used notions of regret are used to measure the performance of the online algorithm. Moreover, coordinate descent algorithms with different updating rules are considered, including both deterministic and stochastic rules that are developed in the literature of classical offline optimization. A thorough regret analysis is given for each case. Finally, numerical simulations are provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

The sequential stabilizing spline (SSS) algorithm is a remarkable algorithm for identifying linear dynamical systems. It can guarantee the stability of an estimated model by polishing the maximum modulus roots of an equation. Therefore, the root structure of an equation plays an important role in the SSS algorithm. Although the traditional power iterative method can be applied to approximate the extremal eigenvalues which have the largest modulus, it has two limitations: (1) the extremal eigenvalues must be real numbers, and (2) the structures of the extremal eigenvalues should be known a priori. In this paper, a novel power iterative method is proposed to approximate the extremal eigenvalues. Compared with the traditional power iterative method, the method in this paper can (1) determine the types of the extremal eigenvalues without prior knowledge of the matrix; (2) approximate the true values of the extremal eigenvalues regardless of their type; (3) become a worthy addition to SSS algorithm and gradient descent algorithm. Simulation examples demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we propose novel data-driven optimal dynamic controller design frameworks, via both state-feedback and output-feedback, for solving optimal output regulation problems of linear discrete-time systems subject to unknown dynamics and unmeasurable disturbances using reinforcement learning (RL). Fundamentally different from existing research on optimal output regulation problems and RL, the proposed procedures can determine both the optimal control gain and the optimal dynamic compensator simultaneously instead of presetting a non-optimal dynamic compensator. Moreover, we present incremental dataset-based RL algorithms to learn the optimal dynamic controllers that do not require the measurements of the external disturbance and the exostate during learning, which is of great practical importance. Besides, we show that the proposed incremental dataset-based learning methods are more robust to a class of measurement noises with arbitrary magnitudes than routine RL algorithms. Comprehensive simulation results validate the efficacy of our methodologies. [ABSTRACT FROM AUTHOR]

Abstract This paper aims to establish explicit relationships between the controllability degree of a network, that is, the control energy required to move the network between different states, and its graphical structure and edge weights. As it is extremely challenging to accomplish this task for general networks, we focus on the case where the network controllability Gramian is a diagonal matrix. The main technical contributions of the paper are (i) to derive necessary and sufficient graphical conditions for networks to feature a diagonal controllability Gramian, and (ii) to propose a constructive algorithm to design network topologies and weights so as to generate stable and controllable networks with pre-specified diagonal Gramians. The proposed network design algorithm allows for individual assignment of how each node responds to external stimuli, so as to selectively enforce robustness to external disturbances. While relying on the simplifying assumption of a diagonal controllability Gramian, our analysis reveals novel and counterintuitive controllability properties of complex networks. For instance, we identify a class of continuous-time networks where the control energy is independent of their cardinality and number of control nodes (thus disproving existing results based on numerical controllability studies), discuss their stability margin, and show that the energy required to control a node can be made independent of its graphical distance from the control nodes. These results complement and formally support, or challenge, a series of conjectures based on numerical studies in the field of complex networks. [ABSTRACT FROM AUTHOR]

Abstract This paper deals with an optimization problem over a network of agents, where the cost function is the sum of the individual (possibly nonsmooth) objectives of the agents and the constraint set is the intersection of local constraints. Most existing methods employing subgradient and consensus steps for solving this problem require the weight matrix associated with the network to be column stochastic or even doubly stochastic, conditions that can be hard to arrange in directed networks. Moreover, known convergence analyses for distributed subgradient methods vary depending on whether the problem is unconstrained or constrained, and whether the local constraint sets are identical or nonidentical and compact. The main goals of this paper are: (i) removing the common column stochasticity requirement; (ii) relaxing the compactness assumption, and (iii) providing a unified convergence analysis. Specifically, assuming the communication graph to be fixed and strongly connected and the weight matrix to (only) be row stochastic, a distributed projected subgradient algorithm and a variation of this algorithm are presented to solve the problem for cost functions that are convex and Lipschitz continuous. The key component of the algorithms is to adjust the subgradient of each agent by an estimate of its corresponding entry in the normalized left Perron eigenvector of the weight matrix. These estimates are obtained locally from an augmented consensus iteration using the same row stochastic weight matrix and requiring very limited global information about the network. Moreover, based on a regularity assumption on the local constraint sets, a unified analysis is given that can be applied to both unconstrained and constrained problems and without assuming compactness of the constraint sets or an interior point in their intersection. Further, we also establish an upper bound on the absolute objective error evaluated at each agent's available local estimate under a nonincreasing step size sequence. This bound allows us to analyze the convergence rate of both algorithms. [ABSTRACT FROM AUTHOR]

This paper investigates the prescribed-time distributed Nash equilibrium seeking (DNES) problem for multi-agent noncooperation games. Based on the distributed motion-planning method and the gradient search, a class of prescribed-time DNES algorithms are developed for first and second-order multi-agent systems, respectively. They may ensure each player' s action converges to the Nash equilibrium (NE) point at a prescribed settling time in advance. Further, for the case when the velocity information of each agent is not available, an observer-based prescribed-time DNES algorithm is extended. Compared with existing works, the convergence time of proposed prescribed-time DNES algorithms in this paper can be assigned in advance by users according to task requirements. Besides, the designed DNES algorithms are sampled without continuous measurements, which means players can update their actions at each sampling moment to avoid the increasing cost brought by continuous information interaction among players. Finally, the effectiveness of algorithms proposed in this paper is verified by some numerical simulations. [ABSTRACT FROM AUTHOR]

This paper studies the problem of resilient cluster consensus for discrete-time high-order multi-agent systems in the presence of malicious adversaries. Based on a decomposition form of the system matrices, a high-order resilient cluster consensus algorithm is proposed. Necessary and sufficient conditions for the normal agents to reach resilient cluster consensus despite the influence of the malicious adversaries are provided. In contrast to the existing results, the proposed algorithm is suitable for general high-order multi-agent systems and can reduce the network redundancy needed to tolerate the same number of malicious adversaries. Two examples are simulated to validate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a randomized parallel algorithm is proposed to solve the distributed optimal consensus problem of multi-agent systems. Involving both the transient response and the final consensus state, the problem is described as a constrained non-separable optimization problem. Inspired by the randomized Jacobi proximal alternating direction method of multipliers, the proposed algorithm makes it possible for only a fraction of agents to solve their private subproblems in parallel at each iteration, which greatly saves computational resources and enhances running efficiency. The convergence analysis of the algorithm gives fully distributed convergence conditions. A trade-off between the convergence speed and resource savings is then obtained, where the convergence rate is estimated to be at least O 1 t . Furthermore, the algorithm can be accelerated to enjoy a convergence rate of O 1 t 2 by adaptively adjusting the auxiliary parameters properly. Numerical simulations demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper studies the distributed resource allocation problem with nonsmooth local cost functions subject to the coupled equality and inequality constraints. In particular, each local cost function is expressed as the sum of a differentiable function and two nonsmooth functions. By using the operator splitting and primal–dual method, a continuous-time distributed proximal algorithm is developed, which can be applied to more general local cost functions that are convex but not necessarily smooth. In addition, the proposed algorithm is fully distributed in the sense that the gain parameter can be determined locally and does not require any global information of the network. By applying Lyapunov stability analysis and convex optimization theory, it is shown that the decision variables of all the agents converge to an optimal solution. Finally, a simulation example is carried out to demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the problem of multi-dimensional consensus subject to the internal agent dynamics constraint and external non-cooperative malicious attacks. We propose a secure discrete-time multi-dimensional consensus algorithm (SMCA), where two-hop information is utilized to check the integrity of neighboring agents' information. Furthermore, we derive a necessary and sufficient condition for all normal agents to achieve consensus exponentially under SMCA. For the boundary-case attacks under SMCA, we first cast the problem as an equivalent problem of multi-dimensional consensus with nonuniform time-delays, and then obtain the analytical expression of the attacks' effects on the final state and convergence rate. Compared with the existing works, SMCA can achieve multi-dimensional consensus for all normal agents with local dynamics even when the number of compromised agents is unknown. Finally, extensive simulations demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper addresses the robust consensus tracking problem for a class of uncertain nonlinear fractional-order multi-agent systems (FOMASs) under general directed topologies. More specifically, FOMASs in the presence of heterogeneous unknown nonlinearities and external disturbances are considered in this paper, which include the second-order MASs as its special cases. First, we design two distributed saturated observers to overcome the deficiency of the traditional tracking control strategies. Second, when there exists a dynamics leader with unknown and bounded state trajectory, a discontinuous observer-based distributed controller with σ -modification adaptive schemes is presented to guarantee the tracking error converges to zero asymptotically. Next, a continuous observer-based distributed controller is further proposed, under which the consensus tracking error is uniformly ultimately bounded (UUB) and can be reduced as small as desired. A neural network (NN), whose weights are tuned online, is used in the designed controllers to approximate the unknown nonlinearities. Motivated by the σ -modification adaptive method, all the proposed adaptation algorithms require only local information and allow for robust even in the presence of heterogeneous unknown disturbances and fractional-order dynamics. Finally, the simulation results validate the efficacy of our proposed method. [ABSTRACT FROM AUTHOR]

This paper studied distributed estimation of the bounds on algebraic connectivity for a directed graph (i.e., digraph). As is well known, the main challenge of the underlying problem is how to enable local awareness of an entity otherwise prone to global information, in the presence of communication topology. More specifically, we introduce a novel state-dependent approach to estimate the bounds on algebraic connectivity with mild requirement on topology and communication effort. Compared with existing results, the proposed algorithm does not estimate eigenvalues or eigenvectors directly, rather it exploits their implications on the consensus procedure, and achieves a tradeoff between estimation accuracy and topological/communication requirement, and its convergence can be expected in a finite time. Simulation results verified the performance of the proposed strategy. [ABSTRACT FROM AUTHOR]

In this paper, entirely new discrete-time variants of the super-twisting algorithm are presented. The development of these discrete-time equivalents is based on certain criteria, e.g., the approximation of the continuous-time super-twisting algorithm as the discretization time tends to zero. In contrast to the classical explicit Euler discretized super-twisting dynamics, the proposed schemes are exact in the sense that in the unperturbed case, the controllers ensure local convergence to the origin. Oscillations of the system states caused by the discrete-time implementation of the super-twisting algorithm are avoided. The superiority of the developed control laws is demonstrated in simulation examples as well as in a real-world application. These examples reveal that the standard accuracy of the homogeneous second-order sliding mode is preserved and, in contrast to the explicit Euler discretized algorithm, in the presence of exact discrete measurements, the precision of the controlled variable is insensitive to oversized control gains. [ABSTRACT FROM AUTHOR]

This paper presents a primal–dual interior-point (pdip) optimization algorithm for solving extreme-scale model predictive control (mpc) problems with linear dynamics, polytopic constraints, and quadratic/linear costs which are all invariant under the symmetric-group. We show that exploiting symmetry can reduce the computational and memory burden of extreme-scale or fast-paced applications of mpc. Our algorithm transforms the original inputs, states, and constraints of the mpc problem into a symmetric domain. The premise of our algorithm is that the numerical linear algebra used to solve the optimization problem has lower computational and memory complexity in the transformed domain. We demonstrate our algorithm for a heating, ventilation, and air-conditioning (hvac) numerical example. We show that, for our largest hvac control problem, our symmetry exploiting the pdip algorithm reduces the computation-time from minutes to seconds in comparison with the baseline pdip algorithm. Furthermore, we show that the presented symmetry exploiting pdip algorithm outperforms a state-of-the-art symmetry exploiting optimization algorithm. [ABSTRACT FROM AUTHOR]

For a group of networked agents, f -consensus means reaching consensus upon the value of a desired function, f , of the initial state of the individual agents. This paper shows how one can often convert a given f -consensus problem into a suitable distributed convex optimization (DCO) problem, which can be readily solved with existing DCO algorithms in the literature. A computational advantage may then accrue. Particular classes of f -consensus problems shown to be solvable with this approach include weighted power mean consensus, and k th smallest value or k th order statistic consensus (which includes max/min consensus and median consensus as special cases). [ABSTRACT FROM AUTHOR]

Solving large-scale Stein equations with high-ranked coefficient and constant terms is relatively difficult since the solution is no longer numerically low-ranked and its storage and outputting are nontrivial. This paper presents a factorized squared Smith method (FSS) that consists of banded and low-ranked parts to overcome this obstacle when the coefficient and the constant matrices are banded-plus-low-ranked. The deflation process as well as the partial truncation and compression are presented to control the growth of the columns of the low-ranked factors, effectively reducing the complexity of the FSS method. The convergence of the banded and the low-ranked parts is established and the banded part is shown being always numerically banded under some assumptions. The residual computation as well as the termination condition have been redesigned. Numerical examples indicate that for large-scale problems, the proposed FSS algorithm outperforms the Smith method with hierarchical HODLR structured toolkit on CPU time. [ABSTRACT FROM AUTHOR]

In this paper, a general framework is proposed for the analysis and characterization of observability and diagnosability of finite state systems. Observability corresponds to the reconstruction of the system’s discrete state, while diagnosability corresponds to the possibility of determining the past occurrence of some particular states, for example faulty states. A unifying framework is proposed where observability and diagnosability properties are defined with respect to a critical set, i.e. a set of discrete states representing a set of faults, or more generally a set of interest. These properties are characterized and the involved conditions provide an estimation of the delay required for the detection of a critical state, of the precision of the delay estimation and of the duration of a possible initial transient where the diagnosis is not possible or not required. Our framework makes it possible to precisely compare some of the observability and diagnosability notions existing in the literature with the ones introduced in our paper, and this comparison is presented. [ABSTRACT FROM AUTHOR]

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]

In this paper, we study a variance minimization problem in an infinite stage discrete time Markov decision process (MDP), regardless of the mean performance. For the Markov chain under the variance criterion, since the value of the cost function at the current stage will be affected by future actions, this problem is not a standard MDP and the traditional MDP theory is not applicable. In this paper, we convert the variance minimization problem into a standard MDP by introducing a concept called pseudo variance. Then we derive a variance difference formula that quantifies the difference of variances of Markov systems under any two policies. With the difference formula, the correlation of the variance cost function at different stages can be decoupled through a nonnegative term. A necessary condition of the optimal policy is obtained. It is also proved that the optimal policy with the minimal variance can be found in the deterministic policy space. Furthermore, we propose an efficient iterative algorithm to reduce the variance of Markov systems. We prove that this algorithm can converge to a local optimum. Finally, a numerical experiment is conducted to demonstrate the efficiency of our algorithm compared with the gradient-based method widely adopted in the literature. [ABSTRACT FROM AUTHOR]

The paper is concerned with the stability of an uncertain system with quantization by using super-twisting controller. Both uniform and logarithmic quantization schemes are considered. Our main discovery is that the trajectories are always bounded with static uniform quantization scheme and are globally finite-time stable with logarithmic quantization scheme. Furthermore, a dynamic uniform quantization scheme is proposed to eliminate quantization errors. Simulation examples are given to shown the effectiveness of the proposed design approach. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the secure state estimation problem of cyber–physical systems (CPSs) under sparse sensor attacks. First, a novel algorithm, which uses a switched gradient descent technique to harness the intrinsic combinatorial complexity of the secure state estimation problem, is proposed to estimate the state. The computational complexity is reduced through improving the convergence rate, reducing the number of candidates to be searched, reducing the search times, and reducing the computing resources consumed by each incorrect candidate selection simultaneously. Second, based on the proposed switched gradient descent algorithm, an observer-based algorithm is proposed to efficiently update the state estimation while new measurements are available. Compared with the existing methods, the computational complexity is reduced greatly without introducing any constraint except the basic observability assumption by adopting the proposed algorithms. [ABSTRACT FROM AUTHOR]

Abstract Second- and higher-order sliding mode techniques are able to avoid the chattering effect associated with first-order sliding. The super-twisting algorithm is one of the most popular second-order sliding mode techniques. Existing modifications of the super-twisting algorithm allow for improved disturbance rejection capability. In this paper, we introduce a new class of generalizations of the super-twisting algorithm that are able to keep the main advantages of standard super-twisting while rejecting disturbances bounded in forms for which the existing algorithms may be not directly applicable. Our results thus broaden the applicability of second-order sliding-mode techniques. We give conditions for stability and finite-time convergence, and provide a complete design framework based on given disturbance bounds. [ABSTRACT FROM AUTHOR]

Abstract Distributed optimization is of essential importance in networked systems. Most of the existing distributed algorithms either assume the information exchange over undirected graphs, or require that the underlying directed network topology provides a doubly stochastic weight matrix to the agents. In this brief paper, a distributed subgradient-based algorithm is proposed to solve nonsmooth convex optimization problems. The algorithm applies to directed graphs without using a doubly stochastic weight matrix. Moreover, the algorithm is a distributed generalization and improvement of the quasi-monotone subgradient algorithm. An O (1 ∕ k) convergence rate is achieved. The effectiveness of our algorithm is also illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

Abstract The main contribution of this paper is a new submap joining based approach for solving large-scale Simultaneous Localization and Mapping (SLAM) problems. Each local submap is independently built using the local information through solving a small-scale SLAM; the joining of submaps mainly involves solving linear least squares and performing nonlinear coordinate transformations. Through approximating the local submap information as the state estimate and its corresponding information matrix, judiciously selecting the submap coordinate frames, and approximating the joining of a large number of submaps by joining only two maps at a time, either sequentially or in a more efficient Divide and Conquer manner, the nonlinear optimization process involved in most of the existing submap joining approaches is avoided. Thus the proposed submap joining algorithm does not require initial guess or iterations since linear least squares problems have closed-form solutions. The proposed Linear SLAM technique is applicable to feature-based SLAM, pose graph SLAM and D-SLAM, in both two and three dimensions, and does not require any assumption on the character of the covariance matrices. Simulations and experiments are performed to evaluate the proposed Linear SLAM algorithm. Results using publicly available datasets in 2D and 3D show that Linear SLAM produces results that are very close to the best solutions that can be obtained using full nonlinear optimization algorithm started from an accurate initial guess. The C/C++ and MATLAB source codes of Linear SLAM are available on OpenSLAM. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the identification of FIR (finite impulse response) systems whose output observations are subject to both the binary-valued quantization and the event-triggered scheme. Based on the a priori information of the unknown parameters and the statistical property of the system noise, a recursive stochastic-approximation-type identification algorithm is proposed. Under a class of persistently exciting inputs, the algorithm is proved to be strongly convergent and the convergence rate of the estimation error is also established, where the corresponding event-triggering conditions are provided. Moreover, the communication rate is discussed. A numerical example is included to verify the effectiveness of the results obtained. [ABSTRACT FROM AUTHOR]

Abstract This paper considers fault tolerant control for parallel interconnected asynchronous sequential machines (ASMs) governed by a single corrective controller with output feedback. The control objective is to diagnose unauthorized state transitions and to recover the normal input/output behavior of the closed-loop system in an asynchronous mechanism. The existence condition and design algorithm for a fault tolerant controller is addressed in the framework of corrective control. The proposed scheme is efficient in that it does not require complete modeling of parallel composition nor output bursts in the feedback channel. An illustrative example is provided to demonstrate the procedure of controller synthesis. [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]

This paper considers a multiple stopping time problem for a Markov chain observed in noise, where a decision maker chooses at most L stopping times to maximize a cumulative objective. We formulate the problem as a Partially Observed Markov Decision Process (POMDP) and derive structural results for the optimal multiple stopping policy. The main results are as follows: (i) The optimal multiple stopping policy is shown to be characterized by threshold curves Γ l , for l = 1 , … , L , in the unit simplex of Bayesian Posteriors. (ii) The stopping sets S l (defined by the threshold curves Γ l ) are shown to exhibit the following nested structure S l − 1 ⊂ S l . (iii) The optimal cumulative reward is shown to be monotone with respect to the copositive ordering of the transition matrix. (iv) A stochastic gradient algorithm is provided for estimating linear threshold policies by exploiting the structural results. These linear threshold policies approximate the threshold curves Γ l , and share the monotone structure of the optimal multiple stopping policy. (v) Application of the multiple stopping framework to interactively schedule advertisements in live online social media. It is shown that advertisement scheduling using multiple stopping performs significantly better than currently used methods. [ABSTRACT FROM AUTHOR]

In this paper, we develop two zonotope-based set-membership estimation algorithms for identification of time-varying parameters in linear static models, where both additive and multiplicative uncertainties are treated explicitly. The two recursive algorithms can be differentiated by their ways of processing the data and required computations. The first algorithm, which is referred to as Cone And Zonotope Intersection (CAZI), requires solving linear programming problems at each iteration. The second algorithm, referred to as the Polyhedron And Zonotope Intersection (PAZI), involves linear programming as well as an optimization subject to linear matrix inequalities (LMIs). Both algorithms are capable of providing tight overbounds of the feasible solution set (FSS) in an application to health monitoring of marine engines. Furthermore, PAZI algorithm applied to mini-batches of measurement data leads itself to further analysis of the relation between the estimation results at different iterations. In addition, an example of identifying time-varying parameters is also reported. [ABSTRACT FROM AUTHOR]

This paper addresses the classical problem of determining the set of possible states of a linear discrete-time SISO system subject to bounded disturbances, from measurements corrupted by bounded noise. These so-called uncertainty sets evolve with time as new measurements become available. We present two theorems which give a complete description of the relationship between uncertainty sets at two successive time instants, and this yields an efficient algorithm for recursively updating uncertainty sets. Numerical simulations demonstrate performance improvements over existing exact methods. [ABSTRACT FROM AUTHOR]

This brief paper provides a comparison of methods for enclosing a given zonotope within another of lower complexity, commonly called order reduction . These techniques are essential for maintaining efficiency in recursive computations with zonotopes and are widely used in set-based estimation, hybrid systems verification, and fault detection. We first review existing methods and provide a new theoretical analysis of the method recently introduced by Scott et al. (2016). We then compare methods in terms of computational cost and overestimation error, and investigate the effects of zonotope dimension, initial order, and reduced order on these metrics. These results provide valuable guidance for the design of robust estimation and control algorithms that more effectively balance accuracy with computational cost. [ABSTRACT FROM AUTHOR]

This paper investigates the distributed receding horizon control (RHC) problem of a vehicle platoon with nonlinear dynamics and subject to system constraints, where each vehicle can communicate with its immediate predecessor and follower. A novel optimization problem and detailed distributed RHC algorithm are designed in order to keep a platoon formation, and further to ensure neighbor γ -gain stability (which is a new notion proposed in this paper and generalizes the string stability). The sufficient conditions on ensuring closed-loop stability and neighbor γ -gain stability are established, respectively. Finally, simulation studies are provided to verify the theoretical results. It is shown that it is possible to achieve certain control performance (i.e., γ -gain stability) and keep a formation simultaneously for the nonlinear vehicle platoon using distributed RHC. [ABSTRACT FROM AUTHOR]

This paper investigates the distributed finite-time consensus tracking problem for a group of autonomous agents modeled by multiple non-identical second-order nonlinear systems. First, a class of distributed finite-time protocols are proposed based on the relative position and relative velocity measurements. By providing a topology-dependent Lyapunov function, it is shown that distributed consensus tracking can be achieved in finite time under the condition that the nonlinear errors between the leader and the followers are bounded. Then, a new class of observer-based algorithms are designed to solve the finite-time consensus tracking problem without using relative velocity measurements. The main contribution of this paper is that, by computing the value of the Lyapunov function at the initial point, the finite settling time can be theoretically estimated for second-order multi-agent systems with the proposed control protocols. Finally, the effectiveness of the analytical results is illustrated by an application in low-Earth-orbit spacecraft formation flying. [ABSTRACT FROM AUTHOR]

Ordinal optimization (OO) is a widely-studied technique for optimizing discrete-event dynamic systems (DEDS). It evaluates the performance of the system designs in a finite set by sampling and aims to correctly make ordinal comparison of the designs. A well-known method in OO is the optimal computing budget allocation (OCBA). It builds the optimality conditions for the number of samples allocated to each design, and the sample allocation that satisfies the optimality conditions is shown to asymptotically maximize the probability of correct selection for the best design. In this paper, we investigate two popular OCBA algorithms. With known variances for samples of each design, we characterize their convergence rates with respect to different performance measures. We first demonstrate that the two OCBA algorithms achieve the optimal convergence rate under measures of probability of correct selection and expected opportunity cost. It fills the void of convergence analysis for OCBA algorithms. Next, we extend our analysis to the measure of cumulative regret, a main measure studied in the field of machine learning. We show that with minor modification, the two OCBA algorithms can reach the optimal convergence rate under cumulative regret. It indicates the potential of broader use of algorithms designed based on the OCBA optimality conditions. [ABSTRACT FROM AUTHOR]

This paper investigates the resilient consensus problem of high-order networks under malicious attacks. The main difficulty lies in the collusion among attacks against the attack detection and isolation. To overcome such difficulty, a novel attack isolation strategy is developed, based on which, a control algorithm is provided to achieve resilient consensus. A new notion of (r , s) - isolability is introduced to present sufficient conditions for attack isolation. Finally, the effectiveness of the proposed approach is demonstrated by simulation studies. [ABSTRACT FROM AUTHOR]

This paper deals with the replay attack detection problem for a class of cyber–physical systems. A dynamic encryption–decryption scheme is proposed with the purpose of detecting the replay attacks launched by the malicious adversary. First, a new attack model is established to describe the periodic replay attacks that are generated by making use of a series of recorded past measurements. Then, the stealthiness is discussed for the proposed replay attack scheme against the χ 2 detector. Subsequently, on basis of the established model, a dynamic encryption–decryption scheme is developed without sacrificing any system performance, guaranteeing 100% detection probability in the occurrence of attacks. Finally, a simulation example is provided to firstly verify the stealthiness of the proposed replay attack and secondly demonstrate the effectiveness of the exploited dynamic encryption–decryption detection algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach to solve linear and nonlinear model predictive control (MPC) problems that requires small memory footprint and throughput and is particularly suitable when the model and/or controller parameters change at runtime. The contributions of the paper include: (i) a formulation of the nonlinear MPC problem as a bounded-variable nonlinear least-squares (BVNLS) problem, demonstrating that the use of an appropriate solver can outperform industry-standard solvers; (i i) an easily-implementable library-free BVNLS solver with a novel proof of global convergence; (i i i) a matrix-free method for computing the products of vectors and Jacobians, required by BVNLS; (i v) an efficient method for updating sparse QR factors when using active-set methods to solve sparse BVNLS problems. Thanks to explicitly parameterizing the optimization algorithm in terms of the model and MPC tuning parameters, the resulting approach is inherently and immediately adaptive to any changes in the MPC formulation. The same algorithmic framework can cope with linear, nonlinear, and adaptive MPC variants based on a broad class of prediction models and sum-of-squares cost functions. [ABSTRACT FROM AUTHOR]

This paper presents a method for calculating the smoothed state distribution for Jump Markov Linear Systems. More specifically, the paper details a novel two-filter smoother that provides closed-form expressions for the smoothed hybrid state distribution. This distribution can be expressed as a Gaussian mixture with a known, but exponentially increasing, number of Gaussian components as the time index increases. This is accompanied by exponential growth in memory and computational requirements, which rapidly becomes intractable. To ameliorate this, we limit the number of allowed mixture terms by employing a Gaussian likelihood mixture reduction strategy, which results in a computationally tractable, but approximate smoothed distribution. The approximation error can be balanced against computational complexity in order to provide an accurate and practical smoothing algorithm that compares favourably to existing state-of-the-art approaches. [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 study randomized methods for feedback design of uncertain systems. The first contribution is to derive the sample complexity of various constrained control problems. In particular, we show the key role played by the binomial distribution and related tail inequalities, and compute the sample complexity. This contribution significantly improves the existing results by reducing the number of required samples in the randomized algorithm. These results are then applied to the analysis of worst-case performance and design with robust optimization. The second contribution of the paper is to introduce a general class of sequential algorithms, denoted as Sequential Probabilistic Validation (SPV). In these sequential algorithms, at each iteration, a candidate solution is probabilistically validated, and corrected if necessary, to meet the required specifications. The results we derive provide the sample complexity which guarantees that the solutions obtained with SPV algorithms meet some pre-specified probabilistic accuracy and confidence. The performance of these algorithms is illustrated and compared with other existing methods using a numerical example dealing with robust system identification. [ABSTRACT FROM AUTHOR]

The coverage control problem for mobile sensor networks with limited communication ranges is addressed in this paper. The goal of the problem is to minimize a coverage cost function which indicates the largest arrival time from the mobile sensor network to the points on a circle. Different input constraints are imposed on the sensors with first-order dynamics due to their different movement capabilities. To deal with this problem, low gain feedback is utilized to develop a distributed coverage control law for each sensor and an upper bound on the low gain is also provided. It is shown that networked mobile sensors can be driven to the configuration minimizing the coverage cost function as long as their communication ranges exceed a threshold and network connectivity of the sensors does not need to be preserved during the coverage task. Finally, a numerical example is given to illustrate the effectiveness of the proposed coverage control law. [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]

The traditional secondary frequency control of power systems restores nominal frequency by steering Area Control Errors (ACEs) to zero. Existing methods are a form of integral control with the characteristic that large control gain coefficients introduce an overshoot and small ones result in a slow convergence to a steady state. In order to deal with the large frequency deviation problem, which is the main concern of the power system integrated with a large number of renewable energy, a faster convergence is critical. In this paper, we propose a secondary frequency control method named Power-Imbalance Allocation Control (PIAC) to restore the nominal frequency with a minimized control cost, in which a coordinator estimates the power imbalance and dispatches the control inputs to the controllers after solving an economic power dispatch problem. The power imbalance estimation converges exponentially in PIAC, both overshoots and large frequency deviations are avoided. In addition, when PIAC is implemented in a multi-area controlled network, the controllers of an area are independent of the disturbance of the neighbor areas, which allows an asynchronous control in the multi-area network. A Lyapunov stability analysis shows that PIAC is locally asymptotically stable and simulation results illustrate that it effectively eliminates the drawback of the traditional integral control based methods. [ABSTRACT FROM AUTHOR]

This paper proposes a novel clock synchronization algorithm for wireless sensor networks (WSNs). The algorithm is derived using a fast finite-time average consensus idea, and is fully distributed , meaning that each node relies only on its local clock readings and reading announcements from its neighbours. For networks with an acyclic graph, the algorithm converges in only d iterations for clock rate synchronization and another d iterations for clock offset synchronization, where d is the graph diameter. The algorithm enjoys low computational and communicational complexities and robustness against transmission adversaries. Each node can execute the algorithm asynchronously without the need for global coordination. Due to its fast convergence, the algorithm is most suitable for large-scale WSNs. For WSNs with a cyclic graph, a fast distributed depth-first-search (DFS) algorithm can be applied first to form a spanning tree before applying the proposed synchronization algorithm. [ABSTRACT FROM AUTHOR]

In this paper, distance-based formation control laws for the multi-agent systems are proposed when the reference velocity is unknown to the followers. Especially, not only the shape but the orientation of formation is also controlled. Each agent measures only the relative positions of neighbors with respect to their own local coordinate system. The local coordinate systems in each agent are not aligned and unknown to the other agents; thus the control laws are completely decentralized. Using the measured local information, the unknown reference velocity is estimated by applying an adaptive method. The shape and orientation of formation are controlled based on the estimated reference velocity. The stability and convergence of the system are analyzed mathematically and verified through numerical simulation. [ABSTRACT FROM AUTHOR]

Many recently developed data-driven fault estimation methods are restricted to minimum-phase systems so that their practical applications are limited. In this paper, the data-driven fault estimation for non-minimum phase (NMP) systems is studied, for which the main difficulty is that the unstable zeros of an NMP system will result in a growing fault-estimation error. To deal with this problem, the inverse of an NMP system is equivalently formulated as a mixed causal and anti-causal system, and the proposed fault estimator is the sum of a stable causal filter and a stable anti-causal filter. The proposed fault estimator is shown to be asymptotically unbiased and its performance is demonstrated by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper investigates consensus problems for a first-order nonlinear multi-agent system with unknown non-identical parameters when quantized measurements are available. We explore the utility of edge Laplacian for designing adaptive consensus protocol with quantized state information. A tree structure plays an important role in designing adaptive control with quantized information. Then, all agents achieve consensus mainly based on tree edges information. The proposed protocol has the advantage of using an equivalent simpler graph to avoid the redundant edge information in the cycle structure of the graph. Furthermore, when the multi-agent systems have unknown identical control directions, a Nussbaum-type item is used in the protocol for each agent to seek control direction adaptively and cooperatively. Finally, simulation examples are given to illustrate the effectiveness of the proposed method in this article. [ABSTRACT FROM AUTHOR]

This paper redefines the observability matrix and defines the observability index for Boolean networks (BNs). In the new definition, a BN is observable if and only if the observability matrix is of full rank. The observability matrix is calculated by a simple algorithm and is applied to the problem of distinguishability of partitions. A partition of the state space is said to be distinguishable if any two distinct subsets are distinguishable, and the finest distinguishable partition (FDP) is finer than any other distinguishable partition. A necessary and sufficient condition is proposed for checking the distinguishability of any given partition, and an algorithm is proposed for calculating the FDP. The proposed results are illustrated by examples. [ABSTRACT FROM AUTHOR]