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This paper is concerned with the privacy-preserving average consensus problem for discrete-time multi-agent systems. The main goal of this paper is to develop a privacy-preserving algorithm that ensures all agents in the network to reach exact average consensus while keeping the initial state of each agent private. To achieve this, a novel two-phase privacy-preserving algorithm is proposed. In the first phase, each agent generates a group of independent random signals and creates a mask signal via local data exchange. In the second phase, all agents execute a standard consensus algorithm. Rigorous analysis shows that each agent can converge to exact average consensus while protecting sensitive information of individuals against internal honest-but-curious nodes and external eavesdroppers. Moreover, the developed algorithm is applied to the distributed load sharing of microgrids. Finally, a simulation example is provided to verify the theoretical results. [ABSTRACT FROM AUTHOR]

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]

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]

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]

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 proposes a cooperative pursuit strategy against a maneuvering target by introducing a cascaded optimization framework for assignment and guidance. The cooperative guidance algorithm, guaranteeing both encirclement and simultaneous attack constraints, is derived by optimizing the normal impact–direction and tangential impact–time control efforts, respectively. Then, by minimizing the performance index identical to the guidance loop, an assignment approach is proposed to allocate the desired impact direction and time for each pursuer. Since the assignment and guidance strategies share a unified optimization tenet in a cascaded manner, the proposed integrated cooperative method proves more efficient than the existing guidance-only methods. Theoretical analysis and numerical simulations are provided to demonstrate its advantages in synergy efficiency. [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 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]

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]

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]

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]

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]

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]

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]

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 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]

Abstract: This paper presents a multivehicle sampling algorithm to generate trajectories for nonuniform coverage of a nonstationary spatiotemporal field characterized by spatial and temporal decorrelation scales that vary in space and time, respectively. The sampling algorithm described in this paper uses a nonlinear coordinate transformation that renders the field locally stationary so that existing multivehicle control algorithms can be used to provide uniform coverage. When transformed back to the original coordinates, the sampling trajectories are concentrated in regions of short spatial and temporal decorrelation scales. For fields with coupled spatial statistics, i.e., the spatial decorrelation scales are functions of both spatial dimensions, the coordinate transformation is implemented numerically, whereas for decoupled spatial statistics, the transformation is expressed analytically. We show that the analytical transformation results in vehicle motion that preserves the vehicle sampling speed (which is a measure of vehicle speed scaled by the ratio of the spatial and temporal decorrelation scales), in the original domain; the sampling speed determines the minimum number of vehicles needed to cover a spatiotemporal domain. Theoretical results are illustrated by numerical simulations. [Copyright &y& Elsevier]

Abstract: This paper considers two discrete time, finite state processes and . In the usual hidden Markov model modulates the values of . However, the values of are then i.i.d. given . In this paper a new model is considered where the Markov chain modulates the transition probabilities of the second, observed chain . This more realistically can represent problems arising in DNA sequencing. Algorithms for all related filters, smoothers and parameter estimations are derived. Versions of the Viterbi algorithms are obtained. [Copyright &y& Elsevier]

Abstract: Using the semi-tensor product method, this paper investigates the algebraic formulation and strategy optimization for a class of evolutionary networked games with “myopic best response adjustment” rule, and presents a number of new results. First, the dynamics of the evolutionary networked game is converted to an algebraic form via the semi-tensor product, and an algorithm is established to construct the algebraic formulation for the game. Second, based on the algebraic form, the dynamical behavior of evolutionary networked games is discussed, and some interesting results are presented. Finally, the strategy optimization problem is considered by adding a pseudo-player to the game, and a free-type control sequence is designed to maximize the average payoff of the pseudo-player. The study of an illustrative example shows that the new results obtained in this paper work very well. [Copyright &y& Elsevier]

Abstract: The paper presents realization theory of discrete-time linear switched systems. We present necessary and sufficient conditions for an input–output map to admit a discrete-time linear switched system realization. In addition, we present a characterization of minimality of discrete-time linear switched systems in terms of reachability and observability. Further, we prove that minimal realizations are unique up to isomorphism. We also discuss algorithms for converting a linear switched system to a minimal one and for constructing a state-space representation from input–output data. The paper uses the theory of rational formal power series in non-commutative variables. [Copyright &y& Elsevier]

Abstract: The control algorithm hierarchy of motion control for over-actuated mechanical systems with a redundant set of effectors and actuators commonly includes three levels. First, a high-level motion control algorithm commands a vector of virtual control efforts (i.e. forces and moments) in order to meet the overall motion control objectives. Second, a control allocation algorithm coordinates the different effectors such that they together produce the desired virtual control efforts, if possible. Third, low-level control algorithms may be used to control each individual effector via its actuators. Control allocation offers the advantage of a modular design where the high-level motion control algorithm can be designed without detailed knowledge about the effectors and actuators. Important issues such as input saturation and rate constraints, actuator and effector fault tolerance, and meeting secondary objectives such as power efficiency and tear-and-wear minimization are handled within the control allocation algorithm. The objective of the present paper is to survey control allocation algorithms, motivated by the rapidly growing range of applications that have expanded from the aerospace and maritime industries, where control allocation has its roots, to automotive, mechatronics, and other industries. The survey classifies the different algorithms according to two main classes based on the use of linear or nonlinear models, respectively. The presence of physical constraints (e.g input saturation and rate constraints), operational constraints and secondary objectives makes optimization-based design a powerful approach. The simplest formulations allow explicit solutions to be computed using numerical linear algebra in combination with some logic and engineering solutions, while the more challenging formulations with nonlinear models or complex constraints and objectives call for iterative numerical optimization procedures. Experiences using the different methods in aerospace, maritime, automotive and other application areas are discussed. The paper ends with some perspectives on new applications and theoretical challenges. [Copyright &y& Elsevier]

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: This paper concerns the problem of designing a modified repetitive-control system for a class of strictly proper plants. Repetitive control involves two types of actions: control and learning; but the insertion of a low-pass filter in a modified repetitive controller, which is employed to guarantee the stability of the system, mixes the two actions together. In this paper, a continuous–discrete two-dimensional model is first constructed. Next, the continuity of repetitive control and Lyapunov stability theory are applied to the model to establish two linear-matrix-inequality (LMI) based sufficient stability conditions, one for the design of the cutoff angular frequency and one for the design of the feedback gains. The features of these conditions are exploited to develop an iterative algorithm that searches for the best combination of the maximum cutoff angular frequency of the low-pass filter and the feedback gains. A numerical example illustrates the design procedure and demonstrates the validity of the method. [Copyright &y& Elsevier]

Abstract: This paper deals with the problem of adaptive suppression of disturbances on Blu-ray disc drives servo-mechanisms. The proposed methodology is intended for enhancing playability of low quality media at higher rotational speeds. One of the main problems in controlling an optical disc drive concerns the control of the radial lens position which assures the disc playback. However, due to the rotary nature of the Blu-ray disc the most important sources of disturbances concern those that present periodic behaviour. The frequency of such disturbances is proportional to the disc speed and inversely depends on the radial lens position, making more difficult the task of the tracking-controller when a high speed playback is required. Here, a new parametric adaptation algorithm is proposed to reject the main narrow-band disturbances without increasing the controller bandwidth. The proposed scheme makes use of the internal model principle and the Youla–Kucera parameterization. The parametric adaptation algorithm together with the robust stability and performance analysis are part of the main contribution of this paper. An experimental-data study illustrates the behaviour of the high speed tracking control. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a novel switched model predictive control (MPC) algorithm for nonlinear continuous-time systems, where we switch between different cost functionals in order to enhance performance. Thus, different performance criteria can be taken into account. In order to ensure stability of the resulting closed-loop system, we consider switching signals which exhibit a certain average dwell-time. When considering switching signals of this type, certain assumptions are common in the switched systems literature in order to ensure stability, like a matching condition for the different Lyapunov functions and the possibility to find Lyapunov functions with an exponential decay rate. In this paper, we show how these assumptions can be satisfied in the MPC context and thus stability of the proposed switched MPC algorithm can be established. [Copyright &y& Elsevier]

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]

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: In this paper, the problem of determining a canonical state-space representation for multivariable systems is revisited. A method is derived to build a canonical state-space representation directly from data generated by a linear time-invariant system. Contrary to the classic construction methods of canonical parameterizations, the technique developed in this paper does not assume the availability of any observability or controllability indices. However, it requires the -matrix of any minimal realization of the system to be non-derogatory. A subspace-based identification algorithm is also introduced to estimate such a canonical state-space parameterization directly from input–output data. [Copyright &y& Elsevier]

Abstract: This paper studies the system transformation using generalized orthonormal basis functions that include the Laguerre basis as a special case. The transformation of the deterministic systems is studied in the literature, which is called the Hambo transform. The aim of the paper is to develop a transformation theory for stochastic systems. The paper establishes the equivalence of continuous and transformed-discrete-time stochastic systems in terms of solutions. The method is applied to the continuous-time system identification problem. It is shown that using the transformed signals the PO-MOESP subspace identification algorithm yields consistent estimates for system matrices. An example is included to illustrate the efficacy of the proposed identification method, and to make a comparison with the method using the Laguerre filter. [Copyright &y& Elsevier]

Abstract: This paper proposes algorithms to coordinate a formation of mobile agents when the agents are not able to measure the relative positions of their neighbors, but only the distances to their respective neighbors. In this sense, less information is available to agents than is normally assumed in formation stabilization or station keeping problems. To control the shape of the formation, the solution advanced in the paper involves subsets of non-neighbor agents cyclically localizing the relative positions of their respective neighbor agents while these are held stationary, and then moving to reduce the value of a cost function which is nonnegative and assumes the zero value precisely when the formation has correct distances. The movement schedule is obtained by a novel vertex-coloring algorithm whose computation time is linear in the number of agents when implemented on the graphs of minimally rigid formations. Since in some formations, it may be that an agent is never allowed to be stationary (e.g. it is a fixed-wing aircraft), or because formations may be required to move as a whole in a certain direction, the results are extended to allow for cyclic localization of agents in this case. The tool used is the Cayley–Menger determinant. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate opacity of discrete event systems. We define two types of opacities: strong opacity and weak opacity. Given a general observation mapping, a language is strongly opaque if all strings in the language are confused with some strings in another language and it is weakly opaque if some strings in the language are confused with some strings in another language. We show that security and privacy of computer systems and communication protocols can be investigated in terms of opacity. In particular, two important properties in security and privacy, namely anonymity and secrecy, can be studied as special cases of opacity. We also show that by properly specifying the languages and the observation mapping, three important properties of discrete event systems, namely observability, diagnosability, and detectability, can all be reformulated as opacity. Thus, opacity has a wide range of applications. Also in this paper we provide algorithms for checking strong opacity and weak opacity for systems described by regular languages and having a generalized projection as the observation mapping. [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 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]

Abstract: The problem addressed in this paper is information theoretic sensor control for recursive Bayesian multi-object state-space estimation using random finite sets. The proposed algorithm is formulated in the framework of partially observed Markov decision processes where the reward function associated with different sensor actions is computed via the Rényi or alpha divergence between the multi-object prior and the multi-object posterior densities. The proposed algorithm in implemented via the sequential Monte Carlo method. The paper then presents a case study where the problem is to localise an unknown number of sources using a controllable moving sensor which provides range-only detections. Four sensor control reward functions are compared in the study and the proposed scheme is found to perform the best. [Copyright &y& Elsevier]

Abstract: The paper considers a sensor network whose sensors observe a common quantity and are affected by arbitrary additive bounded noises with a known upper bound. During the experiment, any sensor can communicate only a finite and given number of bits of information to the decision center. The contributions of the particular sensors, the rules of data encoding, decoding, and fusion, as well as the estimation scheme should be designed to achieve the best overall performance in estimation of the observed quantity by the decision center. An optimal algorithm is obtained that minimizes the maximal feasible error. It is shown that it considerably outperforms the algorithm proposed in recent papers in the area and examined only in the idealized case of noiseless sensors. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we derive formulas for computing graphical derivatives of the (possibly multivalued) solution mapping for convex parametric quadratic programs. Parametric programming has recently received much attention in the control community, however most algorithms are based on the restrictive assumption that the so called critical regions of the solution form a polyhedral subdivision, i.e. the intersection of two critical regions is either empty or a face of both regions. Based on the theoretical results of this paper, we relax this assumption and show how we can efficiently compute all adjacent full dimensional critical regions along a facet of an already discovered critical region. Coupling the proposed approach with the graph traversal paradigm, we obtain very efficient algorithms for the solution of parametric convex quadratic programs. [ABSTRACT FROM AUTHOR]

Abstract: This paper develops a model-free control design algorithm for unknown linear discrete-time systems by using Q-learning, which is a reinforcement learning method based on an actor-critic structure. In model-free design, there is no known dynamical model of the system. Thus, one has no information on the system matrices, but can access the state variables and input variables. The paper derives an iterative solution algorithm for control design that is based on policy iteration. The algorithm is expressed in the form of linear matrix inequalities (LMI) that do not involve the system matrices, but only require data measured from the system state and input. It is shown that, for sufficiently rich enough disturbance, this algorithm converges to the standard control solution obtained using the exact system model. Two numerical examples are given to show the effectiveness in obtaining the control without any using knowledge of the system dynamics matrices, and the examples show that the results converge to the ones obtained with the exact system dynamics matrices. [ABSTRACT FROM AUTHOR]