# Showing papers in "IEEE Transactions on Automatic Control in 2015"

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TL;DR: In this paper, the authors present a new class of event triggering mechanisms for event-triggered control systems characterized by the introduction of an internal dynamic variable, which motivates the proposed name of dynamic event triggering mechanism.

Abstract: In this technical note, we present a new class of event triggering mechanisms for event-triggered control systems. This class is characterized by the introduction of an internal dynamic variable, which motivates the proposed name of dynamic event triggering mechanism. The stability of the resulting closed-loop system is proved and the influence of design parameters on the decay rate of the Lyapunov function is discussed. For linear systems, we establish a lower bound on the inter-execution time as a function of the parameters. The influence of these parameters on a quadratic integral performance index is also studied. Some simulation results are provided for illustration of the theoretical claims.

579 citations

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TL;DR: A distributed adaptive consensus protocol is designed to achieve leader-follower consensus in the presence of a leader with a zero input for any communication graph containing a directed spanning tree with the leader as the root node.

Abstract: This technical note addresses the distributed consensus protocol design problem for multi-agent systems with general linear dynamics and directed communication graphs. Existing works usually design consensus protocols using the smallest real part of the nonzero eigenvalues of the Laplacian matrix associated with the communication graph, which however is global information. In this technical note, based on only the agent dynamics and the relative states of neighboring agents, a distributed adaptive consensus protocol is designed to achieve leader-follower consensus in the presence of a leader with a zero input for any communication graph containing a directed spanning tree with the leader as the root node. The proposed adaptive protocol is independent of any global information of the communication graph and thereby is fully distributed. Extensions to the case with multiple leaders are further studied.

567 citations

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TL;DR: A new integral inequality is presented, called a free-matrix-based integral inequality, that further reduces the conservativeness in those methods used to derive delay-dependent criteria for the stability analysis of time-varying-delay systems.

Abstract: The free-weighting matrix and integral-inequality methods are widely used to derive delay-dependent criteria for the stability analysis of time-varying-delay systems because they avoid both the use of a model transformation and the technique of bounding cross terms. This technical note presents a new integral inequality, called a free-matrix-based integral inequality, that further reduces the conservativeness in those methods. It includes well-known integral inequalities as special cases. Using it to investigate the stability of systems with time-varying delays yields less conservative delay-dependent stability criteria, which are given in terms of linear matrix inequalities. Two numerical examples demonstrate the effectiveness and superiority of the method.

530 citations

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TL;DR: A framework for the event-triggered stabilization of nonlinear systems using hybrid systems tools that is general enough to encompass most of the existing event- Triggered control techniques, and derives two new event-triggering conditions which may further enlarge the inter-event times.

Abstract: Event-triggered control consists of closing the feedback loop whenever a predefined state-dependent criterion is satisfied. This paradigm is especially well suited for embedded systems and networked control systems since it is able to reduce the amount of communication and computation resources needed for control, compared to the traditional periodic implementation. In this paper, we propose a framework for the event-triggered stabilization of nonlinear systems using hybrid systems tools, that is general enough to encompass most of the existing event-triggered control techniques, which we revisit and generalize. We also derive two new event-triggering conditions which may further enlarge the inter-event times compared to the available policies in the literature as illustrated by two physical examples. These novel techniques exemplify the relevance of introducing additional variables for the design of the triggering law. The proposed approach as well as the new event-triggering strategies are flexible and we believe that they can be used to address other event-based control problems.

441 citations

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TL;DR: This paper finds the optimal algorithm parameters that minimize the convergence factor of the ADMM iterates in the context of ℓ2-regularized minimization and constrained quadratic programming.

Abstract: The alternating direction method of multipliers (ADMM) has emerged as a powerful technique for large-scale structured optimization. Despite many recent results on the convergence properties of ADMM, a quantitative characterization of the impact of the algorithm parameters on the convergence times of the method is still lacking. In this paper we find the optimal algorithm parameters that minimize the convergence factor of the ADMM iterates in the context of l2-regularized minimization and constrained quadratic programming. Numerical examples show that our parameter selection rules significantly outperform existing alternatives in the literature.

433 citations

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TL;DR: This paper analyzes networked control systems in the presence of denial-of-service (DoS) attacks, namely attacks that prevent transmissions over the network, to characterize frequency and duration of the DoS attacks under which input-to-state stability (ISS) of the closed-loop system can be preserved.

Abstract: The issue of cyber-security has become ever more prevalent in the analysis and design of networked systems. In this paper, we analyze networked control systems in the presence of denial-of-service (DoS) attacks, namely attacks that prevent transmissions over the network. We characterize frequency and duration of the DoS attacks under which input-to-state stability (ISS) of the closed-loop system can be preserved. To achieve ISS, a suitable scheduling of the transmission times is determined. It is shown that the considered framework is flexible enough so as to allow the designer to choose from several implementation options that can be used for trading-off performance versus communication resources. Examples are given to substantiate the analysis.

393 citations

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TL;DR: The problem of second-order leader-following consensus by a novel distributed event-triggered sampling scheme in which agents exchange information via a limited communication medium is studied and it is shown that the inter-event intervals are lower bounded by a strictly positive constant, which excludes the Zeno-behavior before the consensus is achieved.

Abstract: In this note, the problem of second-order leader-following consensus by a novel distributed event-triggered sampling scheme in which agents exchange information via a limited communication medium is studied. Event-based distributed sampling rules are designed, where each agent decides when to measure its own state value and requests its neighbor agents broadcast their state values across the network when a locally-computed measurement error exceeds a state-dependent threshold. For the case of fixed topology, a necessary and sufficient condition is established. For the case of switching topology, a sufficient condition is obtained under the assumption that the time-varying directed graph is uniformly jointly connected. It is shown that the inter-event intervals are lower bounded by a strictly positive constant, which excludes the Zeno-behavior before the consensus is achieved. Numerical simulation examples are provided to demonstrate the correctness of theoretical results.

391 citations

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TL;DR: It is proved that a global optimum of OPF can be obtained by solving a second-order cone program, under a mild condition after shrinking the OPF feasible set slightly, for radial power networks.

Abstract: The optimal power flow (OPF) problem determines a network operating point that minimizes a certain objective such as generation cost or power loss. It is nonconvex. We prove that a global optimum of OPF can be obtained by solving a second-order cone program, under a mild condition after shrinking the OPF feasible set slightly, for radial power networks. The condition can be checked a priori, and holds for the IEEE 13, 34, 37, 123-bus networks and two real-world networks.

369 citations

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TL;DR: This technical note investigates how an attacker should schedule its Denial-of-Service (DoS) attacks to degrade the system performance.

Abstract: Security of Cyber-Physical Systems (CPS) has gained increasing attention in recent years. Most existing works mainly investigate the system performance given some attacking patterns. In this technical note, we investigate how an attacker should schedule its Denial-of-Service (DoS) attacks to degrade the system performance. Specifically, we consider the scenario where a sensor sends its data to a remote estimator through a wireless channel, while an energy-constrained attacker decides whether to jam the channel at each sampling time. We construct optimal attack schedules to maximize the expected average estimation error at the remote estimator. We also provide the optimal attack schedules when a special intrusion detection system (IDS) at the estimator is given. We further discuss the optimal attack schedules when the sensor has energy constraint. Numerical examples are presented to demonstrate the effectiveness of the proposed optimal attack schedules.

299 citations

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TL;DR: It is shown that continuous communication between neighboring agents can be avoided and the Zeno-behavior of triggering time sequences is excluded and a numerical example is presented to illustrate the effectiveness of the obtained theoretical results.

Abstract: The event-based control strategy is an effective methodology for tackling the distributed control of multi-agent systems with limited on-board resources. This technical note focuses on event-based leader-following consensus for multi-agent systems described by general linear models and subject to input time delay between controller and actuator. For each agent, the controller updates are event-based and only triggered at its own event times. A necessary condition and two sufficient conditions on leader-following consensus are presented, respectively. It is shown that continuous communication between neighboring agents can be avoided and the Zeno-behavior of triggering time sequences is excluded. A numerical example is presented to illustrate the effectiveness of the obtained theoretical results.

283 citations

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TL;DR: In this technical note, the problem of switching stabilization for slowly switched linear systems is investigated and sufficient condition of stabilization for switched systems with all stable subsystems under MDADT switching is given.

Abstract: In this technical note, the problem of switching stabilization for slowly switched linear systems is investigated. In particular, the considered systems can be composed of all unstable subsystems. Based on the invariant subspace theory, the switching signal with mode-dependent average dwell time (MDADT) property is designed to exponentially stabilize the underlying system. Furthermore, sufficient condition of stabilization for switched systems with all stable subsystems under MDADT switching is also given. The correctness and effectiveness of the proposed approaches are illustrated by a numerical example.

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TL;DR: This paper investigates the problems of two-dimensional (2-D) dissipative control and filtering for a linear discrete-time Roesser model and proposes new designs of 2-D (Q, S, R)-α-dissipative filters of observer form and general form using a linear matrix inequality (LMI) approach.

Abstract: This paper investigates the problems of two-dimensional (2-D) dissipative control and filtering for a linear discrete-time Roesser model. First, a novel sufficient condition is proposed such that the discrete-time Roesser system is asymptotically stable and 2-D $(Q,S,R)\hbox{-} \alpha$ -dissipative. Special cases, such as 2-D passivity performance and 2-D $H_{\infty} $ performance, and feedback interconnected systems are also discussed. Based on this condition, new 2-D $(Q,S,R)\hbox{-} \alpha$ -dissipative state-feedback and output-feedback control problems are defined and solved for a discrete-time Roesser model. The design problems of 2-D $(Q,S,R)\hbox{-} \alpha$ -dissipative filters of observer form and general form are also considered using a linear matrix inequality (LMI) approach. Two examples are given to illustrate the effectiveness and potential of the proposed design techniques.

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TL;DR: A game-theoretic framework is formulated and it is proved that the optimal strategies for both sides constitute a Nash equilibrium of a zero-sum game.

Abstract: We consider security issues in remote state estimation of Cyber-Physical Systems (CPS). A sensor node communicates with a remote estimator through a wireless channel which may be jammed by an external attacker. With energy constraints for both the sensor and the attacker, the interactive decision making process of when to send and when to attack is studied. We formulate a game-theoretic framework and prove that the optimal strategies for both sides constitute a Nash equilibrium of a zero-sum game. To tackle the computation complexity issues, we present a constraint-relaxed problem and provide corresponding solutions using Markov chain theory.

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TL;DR: This technical note is concerned with the stability analysis of discrete linear systems with time-varying delays and the consideration of a new inequality which is less conservative than the celebrated Jensen inequality employed in the context of discrete-time delay systems.

Abstract: This technical note is concerned with the stability analysis of discrete linear systems with time-varying delays. The novelty of the technical note comes from the consideration of a new inequality which is less conservative than the celebrated Jensen inequality employed in the context of discrete-time delay systems. This inequality is a discrete-time counterpart of the Wirtinger-based integral inequality that was recently employed for the improved analysis of continuous-tine systems with delays. However, differently from the continuous-time case, the proof of the new inequality is not based on the Wirtinger inequality. The method is also combined with an efficient representation of the improved reciprocally convex combination inequality in order to reduce the conservatism induced by the LMIs optimization setup. The effectiveness of the proposed result is illustrated by some classical examples from the literature.

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Selex ES

^{1}TL;DR: Novel theoretical results, limitedly to linear systems, on the guaranteed stability of the Hybrid CMCI filters under collective observability and network connectivity are proved.

Abstract: This note addresses Distributed State Estimation (DSE) over sensor networks. Two existing consensus approaches for DSE, i.e., consensus on information (CI) and consensus on measurements (CM), are combined to provide a novel class of hybrid consensus filters (named Hybrid CMCI) which enjoy the complementary benefits of CM and CI. Novel theoretical results, limitedly to linear systems, on the guaranteed stability of the Hybrid CMCI filters under collective observability and network connectivity are proved. Finally, the effectiveness of the proposed class of consensus filters is evaluated on a target tracking case study with both linear and nonlinear sensors.

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TL;DR: It is proved that infinitely fast sampling can be avoided if the system is input-to-state stabilizable with the sampling error as the external input and the corresponding ISS gain is locally Lipschitz.

Abstract: This paper presents a new approach to event-triggered control for nonlinear uncertain systems by using the notion of input-to-state stability (ISS) and the nonlinear small-gain theorem. The contribution of this paper is threefold. First, it is proved that infinitely fast sampling can be avoided if the system is input-to-state stabilizable with the sampling error as the external input and the corresponding ISS gain is locally Lipschitz. No assumption on the existence of known ISS-Lyapunov functions is made in the discussions. Moreover, the forward completeness problem with event-triggered control is studied systematically by using ISS small-gain arguments. Second, the proposed approach gives rise to a new self-triggered sampling strategy for a class of nonlinear systems subject to external disturbances. If an upper bound of the external disturbance is known, then the closed-loop system can be designed to be robust to the external disturbance, and moreover, the system state globally asymptotically converges to the origin if the external disturbance decays to zero. Third, a new design method is developed for event-triggered control of nonlinear uncertain systems in the strict-feedback form. It is particularly shown that the ISS gain with the sampling error as the input can be designed to satisfy the proposed condition for event-triggered control and self-triggered control.

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TL;DR: This technical note presents a second-order multi-agent network for distributed optimization with a sum of convex objective functions subject to bound constraints that is capable of solving more general constrained distributed optimization problems.

Abstract: This technical note presents a second-order multi-agent network for distributed optimization with a sum of convex objective functions subject to bound constraints. In the multi-agent network, the agents connect each others locally as an undirected graph and know only their own objectives and constraints. The multi-agent network is proved to be able to reach consensus to the optimal solution under mild assumptions. Moreover, the consensus of the multi-agent network is converted to the convergence of a dynamical system, which is proved using the Lyapunov method. Compared with existing multi-agent networks for optimization, the second-order multi-agent network herein is capable of solving more general constrained distributed optimization problems. Simulation results on two numerical examples are presented to substantiate the performance and characteristics of the multi-agent network.

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TL;DR: In this paper, synchronization for linearly coupled networks is investigated by pinning a simple aperiodically intermittent controller, which is described by continuous-time ordinary differential equations, and sufficient conditions to guarantee global synchronization are presented.

Abstract: In this note, synchronization for linearly coupled network is investigated by pinning a simple aperiodically intermittent controller. Nodes' dynamical behaviors in the network are described by continuous-time ordinary differential equations. Some sufficient conditions to guarantee global synchronization are presented. Furthermore, an adaptive algorithm is designed for the pinning control gain and its validity is also proved rigorously. Finally, numerical simulations are given to demonstrate the correctness of obtained results.

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TL;DR: It has been proved that with the proposed “Zeno-free” algorithm the agent group can achieve consensus asymptotically and more energy can be saved using the proposed algorithm in practical multi-agent systems.

Abstract: In this technical note, a self-triggered consensus algorithm for multi-agent systems has been proposed. Each agent receives the state information of its neighbors and computes the average state of its neighborhood. Based on this average state the event trigger is designed to determine when the agent updates its control input and transmits the average state to its neighbors. By specifying a strictly positive minimal inter-event time for each agent, Zeno behavior can be avoided. Then by solving quadratic equations related to the event condition, the self-triggered consensus algorithm is developed by directly computing the event time instants with a set of iterative procedures. It has been proved that with the proposed “Zeno-free” algorithm the agent group can achieve consensus asymptotically. Compared with the existing works, the proposed algorithm is simpler in formulation and computation. Moreover, it has been showed that agents need less time to achieve consensus with considerable reduction of the number of triggering events, controller updates and information transmission. As a result, more energy can be saved using the proposed algorithm in practical multi-agent systems.

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TL;DR: After a rigorous definition of controlled NEGs, some control problems, including controllability, stabilization, and network consensus, are considered, and some verifiable conditions are presented.

Abstract: Consider a networked evolutionary game (NEG). According to its strategy updating rule, a fundamental evolutionary equation (FEE) for each node is proposed, which is based on local information. Using FEEs, the network strategy profile dynamics (SPD) is expressed as a $k$ -valued (deterministic or probabilistic) logical dynamic system. The SPD is then used to analyze the network dynamic behaviors, such as the fixed points, the cycles, and the basins of attractions, etc. Particularly, when the homogeneous networked games are considered, a necessary and sufficient condition is presented to verify when a stationary stable profile exists. Then the equivalence of two NEGs is investigated. Finally, after a rigorous definition of controlled NEGs, some control problems, including controllability, stabilization, and network consensus, are considered, and some verifiable conditions are presented. Examples with various games are presented to illustrate the theoretical results. The basic tool for this approach is the semi-tensor product (STP) of matrices, which is a generalization of the conventional matrix product.

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TL;DR: Convergence to the configuration of minimum losses and feasible voltages is proved analytically for both a synchronous and an asynchronous version of the algorithm, where agents update their state independently one from the other.

Abstract: We consider the problem of exploiting the microgenerators dispersed in the power distribution network in order to provide distributed reactive power compensation for power losses minimization and voltage regulation. In the proposed strategy, microgenerators are smart agents that can measure their phasorial voltage, share these data with the other agents on a cyber layer, and adjust the amount of reactive power injected into the grid, according to a feedback control law that descends from duality-based methods applied to the optimal reactive power flow problem. Convergence to the configuration of minimum losses and feasible voltages is proved analytically for both a synchronous and an asynchronous version of the algorithm, where agents update their state independently one from the other. Simulations are provided in order to illustrate the performance and the robustness of the algorithm, and the innovative feedback nature of such strategy is discussed.

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TL;DR: In this article, a distributed algorithm for solving a linear algebraic equation of the form $Ax = b$ assuming the equation has at least one solution is described, where each agent recursively updates its estimate by utilizing the current estimates generated by each of its neighbors.

Abstract: A distributed algorithm is described for solving a linear algebraic equation of the form $Ax = b$ assuming the equation has at least one solution. The equation is simultaneously solved by $m$ agents assuming each agent knows only a subset of the rows of the partitioned matrix $[\matrix{A & b}]$ , the current estimates of the equation's solution generated by its neighbors, and nothing more. Each agent recursively updates its estimate by utilizing the current estimates generated by each of its neighbors. Neighbor relations are characterized by a time-dependent directed graph $\BBN(t)$ whose vertices correspond to agents and whose arcs depict neighbor relations. It is shown that for any matrix $A$ for which the equation has a solution and any sequence of “repeatedly jointly strongly connected graphs” $\BBN(t)$ , $t = 1, 2, \ldots$ , the algorithm causes all agents' estimates to converge exponentially fast to the same solution to $Ax = b$ . It is also shown that, under mild assumptions, the neighbor graph sequence must actually be repeatedly jointly strongly connected if exponential convergence is to be assured. A worst case convergence rate bound is derived for the case when $Ax = b$ has a unique solution. It is demonstrated that with minor modification, the algorithm can track the solution to $Ax = b$ , even if $A$ and $b$ are changing with time, provided the rates of change of $A$ and $b$ are sufficiently small. It is also shown that in the absence of communication delays, exponential convergence to a solution occurs even if the times at which each agent updates its estimates are not synchronized with the update times of its neighbors. A modification of the algorithm is outlined which enables it to obtain a least squares solution to $Ax = b$ in a distributed manner, even if $Ax = b$ does not have a solution.

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TL;DR: The distributed filtering problem is investigated for a class of discrete time-varying systems with an event-based communication mechanism, where a novel matrix simplification technique is developed to handle the challenges resulting from the sparseness of the sensor network topology and filter structure preserving issues.

Abstract: In this technical note, the distributed filtering problem is investigated for a class of discrete time-varying systems with an event-based communication mechanism. Each intelligent sensor node transmits the data to its neighbors only when the local innovation violates a predetermined Send-on-Delta (SoD) data transmission condition. The aim of the proposed problem is to construct a distributed filter for each sensor node subject to sporadic communications over wireless networks. In terms of an event indicator variable, the triggering information is utilized so as to reduce the conservatism in the filter analysis. An upper bound for the filtering error covariance is obtained in form of Riccati-like difference equations by utilizing the inductive method. Subsequently, such an upper bound is minimized by appropriately designing the filter parameters iteratively, where a novel matrix simplification technique is developed to handle the challenges resulting from the sparseness of the sensor network topology and filter structure preserving issues. The effectiveness of the proposed strategy is illustrated by a numerical simulation.

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TL;DR: In this article, a distributed control for automated demand response that can be used by grid operators as ancillary service for maintaining demand-supply balance is proposed, motivated by the need for decentralized decision making, and the need to avoid synchronization that can lead to large and detrimental spikes in demand.

Abstract: Renewable energy sources such as wind and solar power have a high degree of unpredictability and time-variation, which makes balancing demand and supply challenging. One possible way to address this challenge is to harness the inherent flexibility in demand of many types of loads. Introduced in this paper is a technique for decentralized control for automated demand response that can be used by grid operators as ancillary service for maintaining demand-supply balance. A randomized control architecture is proposed, motivated by the need for decentralized decision making, and the need to avoid synchronization that can lead to large and detrimental spikes in demand. An aggregate model for a large number of loads is then developed by examining the mean field limit. A key innovation is a linear time-invariant (LTI) system approximation of the aggregate nonlinear model, with a scalar signal as the input and a measure of the aggregate demand as the output. This makes the approximation particularly convenient for control design at the grid level.

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TL;DR: Finite time stability analysis for the augmented system is presented by means of Lyapunov stability theorems, which shows that the system output is regulated to zero in finite time even in the presence of mismatched disturbances.

Abstract: In this technical note, the problem of finite-time output regulation control for a class of disturbed system under mismatching condition is investigated via a composite control design manner. The composite controller is developed by using a finite time control technique and a finite time disturbance observer (FTDO). A key idea is to design virtual control laws based on estimation values of the disturbances and the ith (1 ≤ i ≤ n - 1 where n is the order of the system) order derivative of disturbances. Finite time stability analysis for the augmented system is presented by means of Lyapunov stability theorems, which shows that the system output is regulated to zero in finite time even in the presence of mismatched disturbances. A motion control application demonstrates the effectiveness and attractive properties of the proposed method.

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TL;DR: A robust constrained control scheme is developed for MIMO nonlinear systems based on backstepping control techniques and the disturbance estimate of the SMDO, and the first-order sliding mode differentiator introduced to compute the derivatives of virtual control laws is introduced.

Abstract: In this note, a robust constrained control scheme is proposed for multi-input and multi-output (MIMO) cascade nonlinear systems with unknown external disturbance and input saturation. To efficiently observe unknown external disturbance, a novel sliding mode disturbance observer (SMDO) with finite time convergence performance is presented. A robust constrained control scheme is developed for MIMO nonlinear systems based on backstepping control techniques and the disturbance estimate of the SMDO. With the first-order sliding mode differentiator introduced to compute the derivatives of virtual control laws, the computational burden in backstepping control is reduced for a MIMO cascade nonlinear system. Numerical simulation results are presented to show the effectiveness of the proposed robust constrained control scheme.

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TL;DR: With the proposed systematization of the Unscented Kalman Filter theory, the symmetric sets of sigma points in the literature are formally justified, and the proposed SRUKF has improved computational properties when compared to state-of-the-art methods.

Abstract: In this paper, we propose a systematization of the (discrete-time) Unscented Kalman Filter (UKF) theory. We gather all available UKF variants in the literature, present corrections to theoretical inconsistencies, and provide a tool for the construction of new UKF's in a consistent way. This systematization is done, mainly, by revisiting the concepts of Sigma-Representation, Unscented Transformation (UT), Scaled Unscented Transformation (SUT), UKF, and Square-Root Unscented Kalman Filter (SRUKF). Inconsistencies are related to 1) matching the order of the transformed covariance and cross-covariance matrices of both the UT and the SUT; 2) multiple UKF definitions; 3) issue with some reduced sets of sigma points described in the literature; 4) the conservativeness of the SUT; 5) the scaling effect of the SUT on both its transformed covariance and cross-covariance matrices; and 6) possibly ill-conditioned results in SRUKF's. With the proposed systematization, the symmetric sets of sigma points in the literature are formally justified, and we are able to provide new consistent variations for UKF's, such as the Scaled SRUKF's and the UKF's composed by the minimum number of sigma points. Furthermore, our proposed SRUKF has improved computational properties when compared to state-of-the-art methods.

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TL;DR: A significant class of signed graphs is identified for which the linear dynamics are however predictable and many analogies with positive dynamical systems are shown, including those of adjacency matrices that are eventually positive.

Abstract: For communities of agents which are not necessarily cooperating, distributed processes of opinion forming are naturally represented by signed graphs, with positive edges representing friendly and cooperative interactions and negative edges the corresponding antagonistic counterpart. Unlike for nonnegative graphs, the outcome of a dynamical system evolving on a signed graph is not obvious and it is in general difficult to characterize, even when the dynamics are linear. In this paper, we identify a significant class of signed graphs for which the linear dynamics are however predictable and show many analogies with positive dynamical systems. These cases correspond to adjacency matrices that are eventually positive, for which the Perron–Frobenius property still holds and implies the existence of an invariant cone contained inside the positive orthant. As examples of applications, we determine cases in which it is possible to anticipate or impose unanimity of opinion in decision/voting processes even in presence of stubborn agents, and show how it is possible to extend the PageRank algorithm to include negative links.

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TL;DR: In this article, a novel method of global adaptive dynamic programming (ADP) for the adaptive optimal control of nonlinear polynomial systems is presented, which consists of relaxing the problem of solving the Hamilton-Jacobi-Bellman (HJB) equation to an optimization problem, which is solved via a new policy iteration method.

Abstract: This paper presents a novel method of global adaptive dynamic programming (ADP) for the adaptive optimal control of nonlinear polynomial systems. The strategy consists of relaxing the problem of solving the Hamilton-Jacobi-Bellman (HJB) equation to an optimization problem, which is solved via a new policy iteration method. The proposed method distinguishes from previously known nonlinear ADP methods in that the neural network approximation is avoided, giving rise to significant computational improvement. Instead of semiglobally or locally stabilizing, the resultant control policy is globally stabilizing for a general class of nonlinear polynomial systems. Furthermore, in the absence of the a priori knowledge of the system dynamics, an online learning method is devised to implement the proposed policy iteration technique by generalizing the current ADP theory. Finally, three numerical examples are provided to validate the effectiveness of the proposed method.

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TL;DR: The model transformation technique is first employed to simplify the addressed problem, and the stochastic analysis in combination with the completing squares method are carried out to obtain necessary and sufficient conditions of an auxiliary index which is closely related to the finite-horizon H∞ performance.

Abstract: This technical note deals with the ${\cal H}_{\infty}$ control problem for a class of discrete time-varying nonlinear systems with both randomly occurring nonlinearities and fading measurements over a finite-horizon. The system measurements are transmitted through fading channels described by a modified stochastic Rice fading model. The purpose of the addressed problem is to design a set of time-varying controllers such that, in the presence of channel fading and randomly occurring nonlinearities, the ${\cal H}_{\infty}$ performance is guaranteed over a given finite-horizon. The model transformation technique is first employed to simplify the addressed problem, and then the stochastic analysis in combination with the completing squares method are carried out to obtain necessary and sufficient conditions of an auxiliary index which is closely related to the finite-horizon ${\cal H}_{\infty}$ performance. Moreover, the time-varying controller parameters are characterized via solving coupled backward recursive Riccati difference equations (RDEs). A simulation example is utilized to illustrate the usefulness of the proposed controller design scheme.