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Consider a connected network of agents endowed with local cost functions representing private objectives. Agents seek to find an agreement on some minimizer of the aggregate cost, by means of repeated communications between neighbors. Consensus on the average over the network, usually addressed by gossip algorithms, is a special instance of this problem, corresponding to quadratic private objectives. Consensus on the median, or more generally, consensus on a given quantile, is also a special instance of this problem. In this paper we show that optimizing the aggregate cost function regularized by a total variation (TV) term has appealing properties. First, it can be done very naturally in a distributed way, yielding algorithms that are efficient on numerical simulations. Secondly, the optimum for the regularized cost is shown to be also the optimum for the initial aggregate cost function under assumptions that are simple to state. Finally, these algorithms are robust to unreliable agents that keep injecting some false value in the network. This is remarkable enough, and is not the case, for instance, of gossip algorithms that are entirely ruled by unreliable agents as detailed in the paper. [ABSTRACT FROM PUBLISHER]

The paper presents a system theoretic analysis framework for a network-of-networks, formed from smaller factor networks via graph Cartesian products. We provide a compositional framework for extending the controllability and observability of the factor networks to that of the composite network-of-networks. We then delve into the effectiveness of designing control and estimation algorithms for the composite network via its symmetry and gramian structure. An example demonstrating the usefulness of our results in the context of social networks with a Cartesian product structure is then presented. [ABSTRACT FROM PUBLISHER]

The classical approach to system identification is based on stochastic assumptions about the measurement error, and provides estimates that have random nature. Worst-case identification, on the other hand, only assumes the knowledge of deterministic error bounds, and establishes guaranteed estimates, thus being in principle better suited for the use in control design. However, a main limitation of such deterministic bounds lies in their potential conservatism, thus leading to estimates of restricted use. In this paper, we propose a rapprochement between the stochastic and worst-case system identification viewpoints, which is based on the probabilistic setting of information-based complexity. The main idea in this line of research is to “discard” sets of measure at most $\epsilon$, where $\epsilon$ is a probabilistic accuracy, from the set of deterministic estimates. Therefore, we are decreasing the so-called worst-case radius of information at the expense of a given probabilistic “risk.” In the case of uniformly distributed noise, we derive new computational results, and in particular we compute a trade-off curve, called violation function, which shows how the radius of information decreases as a function of the accuracy. To this end, we construct randomized and deterministic algorithms which provide approximations of this function. We report extensive simulations showing numerical comparisons between the stochastic, worst-case and probabilistic approaches, thus demonstrating the efficacy of the methods proposed in this paper. [ABSTRACT FROM AUTHOR]

This paper deals with the observer problem for dynamical systems in a behavioral context. We are given a dynamical system together with a partition of the system variables into a set of known or measured variables and a set of unknown, to be estimated variables. The observer problem is to find a system that produces an estimate of the unknown variables on the basis of the known or measured variables. For a given plant and partition, we establish a characterization of all error behaviors that can be achieved by interconnecting the plant with some observer. The main result of this paper is a very general, behavioral formulation of an internal model principle for observers. We will show that a nonintrusive observer achieves a stable error behavior if and only if, in addition to a detectability condition on the observer, the observer behavior contains the anti-stabilizable part of the plant behavior. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of exponentially stabilizing periodic orbits in a special class of hybrid models—systems with impulse effects—through control Lyapunov functions. The periodic orbit is assumed to lie in a C^1 submanifold Z that is contained in the zero set of an output function and is invariant under both the continuous and discrete dynamics; the associated restriction dynamics are termed the hybrid zero dynamics. The orbit is furthermore assumed to be exponentially stable within the hybrid zero dynamics. Prior results on the stabilization of such periodic orbits with respect to the full-order dynamics of the system with impulse effects have relied on input-output linearization of the dynamics transverse to the zero dynamics manifold. The principal result of this paper demonstrates that a variant of control Lyapunov functions that enforce rapid exponential convergence to the zero dynamics surface, Z, can be used to achieve exponential stability of the periodic orbit in the full-order dynamics, thereby significantly extending the class of stabilizing controllers. The main result is illustrated on a hybrid model of a bipedal walking robot through simulations and is utilized to experimentally achieve bipedal locomotion via control Lyapunov functions. [ABSTRACT FROM PUBLISHER]

In this paper, the problem of global stabilization of a rather general class of MIMO nonlinear systems is addressed. The systems considered in the paper are invertible, have a trivial zero dynamics and possess a “normal form” in which certain multipliers are functions of the state vector of a special kind. While special structural dependence of such multipliers on the components state vector has been exploited before in the context of achieving stabilization (via full-state feedback, though), the novelty in the approach of this paper is that a peculiar structure is identified which happens to be intimately related to the property of uniform complete observability (thus making the design of observers possible) and to the property of uniform invertibility, relations never established before in the literature. As a result, for this class of MIMO nonlinear systems, a dynamic output feedback law can be designed, yielding semiglobal (and even global, under appropriate assumptions) asymptotic stability. [ABSTRACT FROM PUBLISHER]

This paper studies distributed stochastic approximation algorithms based on broadcast gossip on communication networks represented by digraphs. Weak convergence of these algorithms is proved, and an associated ordinary differential equation (ODE) is formulated connecting convergence points with local objective functions and network properties. Using these results, a methodology is proposed for network design, aimed at achieving the desired asymptotic behavior at consensus. Convergence rate of the algorithm is also analyzed and further improved using an attached stochastic differential equation. Simulation results illustrate the theoretical concepts. [ABSTRACT FROM AUTHOR]

A geometric homogeneity is introduced for evolution equations in a Banach space. Scalability property of solutions of homogeneous evolution equations is proven. Some qualitative characteristics of stability of trivial solution are also provided. In particular, finite-time stability of homogeneous evolution equations is studied. Theoretical results are illustrated on important classes of partial differential equations. [ABSTRACT FROM PUBLISHER]

Impulsive solutions in LTI dynamical systems have received ample attention, but primarily for descriptor systems, i.e., first order Differential Algebraic Equations (DAEs). This paper focuses on the impulsive behavior of higher order dynamical systems and analyzes the causes of impulses in the context of interconnection of one or more dynamical systems. We extend the definition of impulse-controllability to the higher order case. Amongst the various nonequivalent notions of impulse-controllability for first order systems available in the literature, which mostly rely on the input/output structure of the system, our definition, based on a so-called state-map obtained directly from the system equations, generalizes many key first order results to the higher order case. In particular, we show that our higher-order-extension of the definition of impulse controllability generalizes the equivalence between impulse controllability and the ability to eliminate impulses in the closed loop by interconnecting with a suitable controller. This requires an extension of the definition of regularity of interconnection from behaviors involving only smooth trajectories to behaviors on the positive half line involving impulsive-smooth trajectories. [ABSTRACT FROM PUBLISHER]

The problem of output regulation for a class of hybrid linear systems characterized by periodic jumps is considered in this paper. Necessary and sufficient conditions for its solution are provided both in the full information and error feedback case. By a detailed analysis of such conditions, several interesting properties are derived, including the fact that the regulator must contain a (suitably defined) copy of the flow zero dynamics of the plant in addition to the usual copy of the exosystem dynamics, and the fact that the output regulation problem is generically solvable for fat plants (having more inputs than outputs) and generically not solvable for square plants. In addition, semi-classical solutions to the hybrid output regulation problem are introduced and discussed. Such solutions are characterized by the property that the required steady-state input can be generated as a simple linear function of the state of the exosystem (as in the non-hybrid case), although the associated steady-state response has a genuinely hybrid structure. [ABSTRACT FROM PUBLISHER]

The paper deals with the design of sampled-data controllers which preserve the stabilizing performance of a continuous-time backstepping control strategy. This is achieved through matching of the control Lyapunov functions evolutions at the sampling instants. The method is developed for systems in strict-feedback form. The results are discussed and compared with similar strategies through simulated examples. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper deals with controllability of dynamical networks. It is often unfeasible or unnecessary to fully control large-scale networks, which motivates the control of a prescribed subset of agents of the network. This specific form of output control is known under the name target control. We consider target control of a family of linear control systems associated with a network, and provide both a necessary and a sufficient topological condition under which the network is strongly targeted controllable. Furthermore, a leader selection algorithm is presented to compute leader sets achieving target control. [ABSTRACT FROM PUBLISHER]

The paper deals with the classical results of Routh and Hurwitz, Biehler and Kharitonov, concerning the stability of a linear time invariant differential equation. It is shown that these results follow directly from a Schwarz matrix representation of stable systems. [ABSTRACT FROM AUTHOR]

Emerging systems such as smart grids or intelligent transportation systems often require end-user applications to continuously send information to external data aggregators performing monitoring or control tasks. This can result in an undesirable loss of privacy for the users in exchange of the benefits provided by the application. Motivated by this trend, this paper introduces privacy concerns in a system theoretic context, and addresses the problem of releasing filtered signals that respect the privacy of the user data streams. Our approach relies on a formal notion of privacy from the database literature, called differential privacy, which provides strong privacy guarantees against adversaries with arbitrary side information. Methods are developed to approximate a given filter by a differentially private version, so that the distortion introduced by the privacy mechanism is minimized. Two specific scenarios are considered. First, the notion of differential privacy is extended to dynamic systems with many participants contributing independent input signals. Kalman filtering is also discussed in this context, when a released output signal must preserve differential privacy for the measured signals or state trajectories of the individual participants. Second, differentially private mechanisms are described to approximate stable filters when participants contribute to a single event stream, extending previous work on differential privacy under continual observation. [ABSTRACT FROM AUTHOR]

In this paper, we consider the use of a linear periodic controller (LPC) for the control of linear time-invariant (LTI) plants in the decentralized setting. If a plant has an unstable decentralized fixed mode (DFM), it is well known that no decentralized LTI controller can stabilize it, let alone provide good performance. Here we show that, if the plant is centrally controllable and observable and the graph associated with the plant is strongly connected, then even if the plant has an unstable DFM, we can still design a decentralized LPC to provide LQR performance as close to the centralized optimal performance as desired; the proposed controller in each channel consists of a sampler, a zero-order-hold, and a discrete-time linear periodic compensator, which makes it easy to implement. [ABSTRACT FROM AUTHOR]

We consider data fusion for the purpose of smoothing and interpolation based on observation records with missing data. Stochastic processes are generated by linear stochastic models. The paper begins by drawing a connection between time reversal in stochastic systems and all-pass extensions. A particular normalization (choice of basis) between the two time-directions allows the two to share the same orthonormalized state process and simplifies the mathematics of data fusion. In this framework, we derive symmetric and balanced Mayne–Fraser-like formulas that apply simultaneously to continuous-time smoothing and interpolation, providing a definitive unification of these concepts. The absence of data over subintervals requires in general a hybrid filtering approach involving both continuous-time and discrete-time filtering steps. [ABSTRACT FROM PUBLISHER]

This paper proposes an original interval-based method to compute an outer approximation of all invariant sets (such as limit cycles) of a continuous-time nonlinear dynamic system, which are included inside a prior set of the state space. Contrary to all other existing approaches, our method has the following properties: first, it is guaranteed (a solution cannot be lost); second, it is applicable to a large class of systems without any specific assumption such as the knowledge of a Lyapunov function or any partial linearity; and third, there is no need to integrate the system. [ABSTRACT FROM AUTHOR]

The paper deals with the problem of robust output regulation for minimum-phase nonlinear systems in a semiglobal setting. We present a different perspective to the problem of adaptive regulation in which prediction error identification methods, which are routinely used in other control contexts, can be adopted to design robust nonlinear regulators. The proposed control structure combines continuous-time dynamics and “hybrid identifiers”, the latter specifically designed to estimate the actual steady-state control law. The proposed framework encompasses existing frameworks proposed so far in the nonlinear continuous-time literature. [ABSTRACT FROM PUBLISHER]

We present an abstraction and refinement methodology for the automated controller synthesis to enforce general predefined specifications. The designed controllers require quantized (or symbolic) state information only and can be interfaced with the system via a static quantizer. Both features are particularly important with regard to any practical implementation of the designed controllers and, as we prove, are characterized by the existence of a feedback refinement relation between plant and abstraction. Feedback refinement relations are a novel concept introduced in this paper. Our work builds on a general notion of system with set-valued dynamics and possibly non-deterministic quantizers to permit the synthesis of controllers that robustly, and provably, enforce the specification in the presence of various types of uncertainties and disturbances. We identify a class of abstractions that is canonical in a well-defined sense, and provide a method to efficiently compute canonical abstractions. We demonstrate the practicality of our approach on two examples. [ABSTRACT FROM AUTHOR]

In this paper, we address robust static anti-windup compensator design and performance analysis for saturated linear closed loops in the presence of nonlinear probabilistic parameter uncertainties via randomized techniques. The proposed static anti-windup analysis and robust performance synthesis correspond to several optimization goals, ranging from minimization of the nonlinear input/output gain to maximization of the stability region or maximization of the domain of attraction. We also introduce a novel paradigm accounting for uncertainties in the energy of the disturbance inputs. Due to the special structure of linear static anti-windup design, wherein the design variables are decoupled from the Lyapunov certificates, we introduce a significant extension, called scenario with certificates (SwC), of the so-called scenario approach for uncertain optimization problems. This extension is of independent interest for similar robust synthesis problems involving parameter-dependent Lyapunov functions. We demonstrate that the scenario with certificates robust design formulation is appealing because it provides a way to implicitly design the parameter-dependent Lyapunov functions and to remove restrictive assumptions about convexity with respect to the uncertain parameters. Subsequently, to reduce the computational cost, we present a sequential randomized algorithm for iteratively solving this problem. The obtained results are illustrated by numerical examples. [ABSTRACT FROM PUBLISHER]

The use of multivalued controls derived from a special maximally monotone operator are studied in this paper. Starting with a strongly passive linear system (with possible parametric uncertainty and external disturbances) a multivalued control law is derived, ensuring regulation of the output to a desired value. The methodology used falls in a passivity-based control context, where we study how the multivalued control affects the dissipation equation of the closed-loop system, from which we derive its robustness properties. Finally, some numerical examples together with implementation issues are presented to support the main result. [ABSTRACT FROM PUBLISHER]

Event-triggered control (ETC) is a control strategy that is especially suited for applications where communication resources are scarce. By updating and communicating sensor and actuator data only when needed for stability or performance purposes, ETC is capable of reducing the amount of communications, while still retaining a satisfactory closed-loop performance. In this paper, an ETC strategy is proposed by striking a balance between conventional periodic sampled-data control and ETC, leading to so-called periodic event-triggered control (PETC). In PETC, the event-triggering condition is verified periodically and at every sampling time it is decided whether or not to compute and to transmit new measurements and new control signals. The periodic character of the triggering conditions leads to various implementation benefits, including a minimum inter-event time of (at least) the sampling interval of the event-triggering condition. The PETC strategies developed in this paper apply to both static state-feedback and dynamical output-based controllers, as well as to both centralized and decentralized (periodic) event-triggering conditions. To analyze the stability and the \cal L2-gain properties of the resulting PETC systems, three different approaches will be presented based on 1) impulsive systems, 2) piecewise linear systems, and 3) perturbed linear systems. Moreover, the advantages and disadvantages of each of the three approaches will be discussed and the developed theory will be illustrated using a numerical example. [ABSTRACT FROM AUTHOR]

In the recent paper “Input-output finite-time stabilization of linear systems,” (F. Amato ) a sufficient condition for input–output finite-time stability (IO-FTS), when the inputs of the system are \cal L2 signals, has been provided; such condition requires the existence of a feasible solution to an optimization problem involving a certain differential linear matrix inequality (DLMI). Roughly speaking, a system is said to be input–output finite-time stable if, given a class of norm bounded input signals over a specified time interval of length T, the outputs of the system do not exceed an assigned threshold during such time interval. IO-FTS constraints permit to specify quantitative bounds on the controlled variables to be fulfilled during the transient response. In this context, this paper presents several novel contributions. First, by using an approach based on the reachability Gramian theory, we show that the main theorem of F. Amato is actually also a necessary condition for IO-FTS; at the same time we provide an alternative—still necessary and sufficient—condition for IO-FTS, in this case based on the existence of a suitable solution to a differential Lyapunov equality (DLE). We show that the last condition is computationally more efficient; however, the formulation via DLMI allows to solve the problem of the IO finite-time stabilization via output feedback. The effectiveness and computational issues of the two approaches for the analysis and the synthesis, respectively, are discussed in two examples; in particular, our methodology is used in the second example to minimize the maximum displacement and velocity of a building subject to an earthquake of given magnitude. [ABSTRACT FROM AUTHOR]

The problem under consideration in this paper is that of enforcement by supervisory control of a given property on a partially-observed discrete-event system. We present a general methodology that is applicable to a large class of properties previously studied (individually) in the literature. These properties include, but are not restricted to, safety, diagnosability, opacity, detectability, anonymity and attractability. When the given system does not satisfy the considered property, the objective is to synthesize a supervisor that restricts the system's behavior and provably enforces the given property; moreover, it is required that this supervisor be maximally permissive. We consider the general case where the system's events are partitioned into observable and unobservable events, and controllable and uncontrollable events, and we do not make any assumptions about these two partitions; in particular, we do not assume that all controllable events are observable. Our uniform approach first maps the considered property to a suitably-defined information state for the partially-observed system and then develops a supervisor synthesis methodology based on a finite bipartite transition system that embeds all reachable information states and all admissible supervisory control strategies. This transition system is called the All Enforcement Structure (or AES). We present an algorithm for the construction of the AES and discuss its properties. Then we use the AES to develop a synthesis algorithm that constructs a supervisor that is provably property enforcing and maximally permissive. We illustrate the application of our uniform approach to the enforcement of the above-mentioned properties. [ABSTRACT FROM AUTHOR]

This paper deals with systems involving input saturation and quantized control laws, which can be of two types: input quantization case and state quantization case. In both cases, the state feedback control design problem is addressed. Therefore, based on some modified sector conditions and appropriate variable changes, regional (local) uniform ultimate boundedness stabilization problem is tackled. Computational oriented solutions are derived to solve suboptimal convex optimization problems able to give a constructive solution to the design problem of the state feedback gain. [ABSTRACT FROM PUBLISHER]

We first show that the existence, or nonexistence, of a supervisory policy that enforces liveness in an arbitrary Petri net (PN) is not semidecidable. Following this, we show that this is not the case if we restrict our attention to an arbitrary, partially controlled, free-choice Petri net (FCPN). Starting from the observation that the set of initial markings for which there is a supervisory policy that enforces liveness in a free-choice structure is right-closed, we present a string of observations that eventually lead to the conclusion that the existence of a supervisory policy that enforces liveness in an arbitrary FCPN is decidable. The paper concludes with some suggested directions for future research. [ABSTRACT FROM AUTHOR]

Most of the past research on the problem of deadlock avoidance for complex resource allocation systems (RAS) has acknowledged the fact that the computation of the maximally permissive deadlock avoidance policy (DAP) possesses super-polynomial complexity for most RAS classes, and therefore, it has resorted to solutions that trade off maximal permissiveness for computational tractability. In this paper, we distinguish between the off-line and the on-line computation that is required for the effective implementation of the maximally permissive DAP, and we seek to develop representations of this policy that will require minimal on-line computation. The particular representation that we adopt is that of a compact classifier that will effect the underlying dichotomy of the reachable state space into safe and unsafe subspaces. Furthermore, in this first study of the aforementioned problem, we restrict our attention to a particular RAS class that is motivated by an ongoing project of ours called Gadara, and accepts separation of the safe and unsafe subspaces of its instantiations through a set of linear inequalities. Through a series of reductions of the derived classification problem, we are also able to attain extensive reductions in the computational complexity of the off-line task of the construction of the sought classifier. We formally establish completeness and optimality properties for the proposed design procedures. We also offer heuristics that, if necessary, can alleviate the computational effort that is necessary for the construction of the sought classifier. Finally, we demonstrate the efficacy of the developed approaches through a series of computational experiments. To the best of our knowledge, these experiments also establish the ability of the proposed methodology to effectively compute tractable implementations of the maximally permissive DAP for problem instances significantly beyond the capacity of any other approach currently available in the literature. [ABSTRACT FROM AUTHOR]

Blockingness is one of the major obstacles that need to be overcome in the Ramadge-Wonham supervisory synthesis paradigm, especially for large systems. In this paper, we propose an abstraction technique to overcome this difficulty. We first provide details of this abstraction technique, then describe how it can be applied to a supervisor synthesis problem, where plant models are nondeterministic but specifications and supervisors are deterministic. We show that a nonblocking supervisor for an abstraction of a plant under a specification is guaranteed to be a nonblocking supervisor of the original plant under the same specification. The reverse statement is also true, if we impose an additional constraint in the choice of the alphabet of abstraction, i.e., every event, which is either observable or labels a transition to a marker state, is contained in the alphabet of abstraction. [ABSTRACT FROM PUBLISHER]

This paper investigates the consensus problem for multiagent systems, under the assumptions that the agents are homogeneous and described by a single-input positive state-space model, the mutual interactions are cooperative, and the static state-feedback law that each agent adopts to achieve consensus preserves the positivity of the overall system. Necessary conditions for the problem solvability, which allow us to address only the special case when the state matrix is irreducible, are provided. Under the irreducibility assumption, equivalent sets of sufficient conditions are derived. Special conditions either on the system description or on the Laplacian of the communication graph allow us to obtain necessary and sufficient conditions for the problem solvability. Finally, by exploiting some results about robust stability either of positive systems or of polynomials, further sufficient conditions for the problem solvability are derived. Numerical examples illustrate the proposed results. [ABSTRACT FROM AUTHOR]

We investigate how the following properties are related to each other: i) A manifold is “transversally” exponentially stable; ii) the “transverse” linearization along any solution in the manifold is exponentially stable; and iii) there exists a field of positive definite quadratic forms whose restrictions to the directions transversal to the manifold are decreasing along the flow. We illustrate their relevance with the study of exponential incremental stability. Finally, we apply these results to two control design problems, nonlinear observer design and synchronization. In particular, we provide necessary and sufficient conditions for the design of nonlinear observer and of nonlinear synchronizer with exponential convergence property. [ABSTRACT FROM PUBLISHER]

We study a distributed allocation process where, at each time, every player: i) proposes a new bid based on the average utilities produced up to that time, ii) adjusts such allocations based on the inputs received from its neighbors, and iii) generates and allocates new utilities. The average allocations evolve according to a doubly (over time and space) averaging algorithm. We study conditions under which the average allocations reach consensus to any point within a predefined target set even in the presence of adversarial disturbances. Motivations arise in the context of coalitional games with transferable utilities (TU) where the target set is any set of allocations that makes the grand coalition stable. [ABSTRACT FROM AUTHOR]

Nonconvex feasible parameter sets are encountered in set membership identification whenever the regressor vector is affected by bounded uncertainty. This occurs for example when considering standard output error models, or when the available measurements are provided by binary or quantized sensors. In this paper, a unifying framework is proposed to deal with several identification problems involving a nonconvex feasible parameter set and a procedure is proposed for approximating the minimum volume orthotope containing the feasible set. The procedure exploits different relaxations for autoregressive and input parameters, based on the solution of a sequence of linear programming problems. The proposed technique is shown to provide tight bounds in some special cases. Moreover, it is extended to cope with bounds not aligned with the parameter coordinates, in order to obtain polytopic approximations of the feasible set. A number of numerical tests on randomly generated models and data sets demonstrates the accuracy of the computed set approximations. [ABSTRACT FROM AUTHOR]

We develop a complete state-space solution to \cal H2-optimal decentralized control of poset-causal systems with state-feedback. Our solution is based on the exploitation of a key separability property of the problem that enables an efficient computation of the optimal controller by solving a small number of uncoupled standard Riccati equations. Our approach gives important insight into the structure of optimal controllers, such as controller degree bounds that depend on the structure of the poset. A novel element in our state-space characterization of the controller is an intuitive description of the controller as an aggregation of local control laws. [ABSTRACT FROM PUBLISHER]

This paper considers games of incomplete information and studies the evolution of the (not necessarily consistent) perceptions of the players using the framework of hypergames. The focus is on developing methods to modify the players' perception about other players' preferences by incorporating the lessons learned from observing their actions. If players are rational, our first update mechanism, called swap learning, is guaranteed to decrease the mismatch between a player's perception and the true payoff structure of other players. However, this method can lead to inconsistencies in the stability properties of the resulting perception. This motivates the introduction of a second update mechanism, called modified swap learning, that is guaranteed to produce a consistent perception. We also identify a class of hypergames for which modified swap is also guaranteed to decrease the mismatch in a player's perception. We introduce the novel notion of H-digraph as a useful tool to encode the information in a hypergame, and fully characterize how this digraph is affected by changes in the players' beliefs. [ABSTRACT FROM PUBLISHER]

This paper addresses the problem of tracking and rejection of periodic signals for linear multi-input, multi-output systems subject to control saturation. To ensure the periodic tracking/rejection, a modified state-space repetitive control structure is considered. Conditions in a “quasi” linear matrix inequality form are proposed to simultaneously compute a stabilizing state feedback gain and an anti-windup gain. Provided that the references and disturbances belong to a certain admissible set, these gains guarantee that the trajectories of the closed-loop system starting in a certain ellipsoidal set contract to the linearity region of the closed-loop system, where the presence of the repetitive controller ensures the periodic tracking/rejection. [ABSTRACT FROM PUBLISHER]

Finsler's lemma is a classic mathematical result with applications in control and optimization. When the lemma is applied to parameter-dependent LMIs, as such those that arise from problems of robust stability, the extra variables introduced by this lemma also become dependent on this parameter. This technical note presents some sufficient conditions which ensure, without losing generality, that these extra variables can assume a simple functional dependence on the parameters as continuity or even independence. The results allow avoiding an unnecessary use of a more functionally complicated parameter-dependent variable that increases the search computational burden without reducing the conservatism of the solution. [ABSTRACT FROM AUTHOR]

A general framework for analysing robust synchronization in large-scale heterogenous networks is proposed based on the theory of integral quadratic constraints (IQCs). Dynamic agents are represented as linear time-invariant single-input-single-output systems. The agents exchange information according to a sparse dynamical interconnection operator in order to achieve synchronization, where their outputs are steered to the same, possibly time-varying, signal. The main technical hindrance to applying IQCs in this context lies with the presence of the marginally stable dynamics which define the trajectory to which the agents' outputs synchronize. It is shown that by working with conditions defined on modified signal spaces of interest and exploiting the graph structure underlying the connections between the dynamic systems, IQC methods can be applied directly to synchronization analysis without recourse to loop transformations, which may obscure the inherent structural properties of the multi-agent networked systems. Decentralized and scalable conditions for synchronization are proposed within this setting. The IQC framework is demonstrated to unify and generalize some of the existing results in the literature, including certain Nyquist-type consensus certificates for time-delay systems. Moreover, it allows the role of feedback in robustness against uncertainty to be better manifested within the context of synchronization. [ABSTRACT FROM AUTHOR]

Cyber-Physical Systems (CPSs) resulting from the interconnection of computational, communication, and control (cyber) devices with physical processes are wide spreading in our society. In several CPS applications it is crucial to minimize the communication burden, while still providing desirable closed-loop control properties. To this effect, a promising approach is to embrace the recently proposed event-triggered control paradigm, in which the transmission times are chosen based on well-defined events, using state information. However, few general event-triggered control methods guarantee closed-loop improvements over traditional periodic transmission strategies. Here, we provide a new class of event-triggered controllers for linear systems which guarantee better quadratic performance than traditional periodic time-triggered control using the same average transmission rate. In particular, our main results explicitly quantify the obtained performance improvements for quadratic average cost problems. The proposed controllers are inspired by rollout ideas in the context of dynamic programming. [ABSTRACT FROM AUTHOR]

In this technical note, controllability of systems defined on graphs is discussed. We consider the problem of controllability of the network for a family of matrices carrying the structure of an underlying directed graph. A one-to-one correspondence between the set of leaders rendering the network controllable and zero forcing sets is established. To illustrate the proposed results, special cases including path, cycle, and complete graphs are discussed. Moreover, as shown for graphs with a tree structure, the proposed results of the present technical note together with the existing results on the zero forcing sets lead to a minimal leader selection scheme in particular cases. [ABSTRACT FROM PUBLISHER]

This note presents an approach that integrates elements from grammatical inference and game theory to address the problem of supervising finite-state transition systems operating in adversarial, partially known, rule-governed environments. The combined formulation produces controllers which guarantee that a transition system satisfies a task specification in the form of a logical formula, if and only 1) the true model of the environment is in the class of models inferable from positive data presentation (observations), 2) a characteristic sample of the environment's behavior is observed, and 3) the task specification is satisfiable given the capabilities described by the abstractions of the system and its environment. [ABSTRACT FROM AUTHOR]

In this note, we deal with linear systems and we extend to the finite-time setting the concepts of stabilizability and detectability. It will be shown that, similarly to what happens in the classical Lyapunov framework, even in the finite-time context, stabilizability and detectability play a role into the existence of stabilizing dynamical controllers. We prove that a dynamic output feedback controller, which finite-time stabilizes the overall closed-loop system, exists if and only if the open-loop system is finite-time detectable and stabilizable plus a further linear matrix inequality coupling condition. We also show that, in the finite-time context, the equivalence between stabilizability via output feedback and stabilizability via observer-based controllers is no longer true. [ABSTRACT FROM PUBLISHER]

One of the most successful distributed resource allocation algorithms to be deployed in industry is the Additive-Increase Multiplicative-Decrease (AIMD) algorithm of Jain and Chiu. This algorithm already underpins the transport layer of the internet, and is now starting to find application in new areas in the context of Smart Grid and Smart Transportation applications. A distinguishing feature of these latter application areas, when compared with the internet, is the need to modify AIMD to account for lower and upper bounds in the resource allocated to individual agents. Our objective in this note is to demonstrate that the dynamic system arising from AIMD in this extended form has system theoretic properties similar to the classical algorithm. [ABSTRACT FROM PUBLISHER]

The persistence of excitation of signals generated by time-invariant, autonomous, linear, and nonlinear systems is studied using a geometric approach. A rank condition is shown to be equivalent, under certain assumptions, to the persistence of excitation of the solutions of the class of systems considered, both in the discrete-time and in the continuous-time settings. The rank condition is geometric in nature and can be checked a priori, i.e. without knowing explicitly the solutions of the system, for almost periodic systems. The significance of the ideas and tools presented is illustrated by means of simple examples. Applications to model reduction from input–output data and stability analysis of skew-symmetric systems are also discussed. [ABSTRACT FROM PUBLISHER]

A resource allocation mechanism based on matching and bargaining is presented. There are many resource providers and many resource seekers. The resource valuations of the agents are private and are uniformly distributed over a common support. The regulator establishes two bid levels. Each participating agent is randomly paired with a counterpart and the allocations arise out of these bilateral encounters based on agents’ individual bid choices. We show a Bayes Nash equilibrium in dominant strategy when the regulator fixes the strategy for one set of agents. The mechanism has parameters to tune the allocations. [ABSTRACT FROM PUBLISHER]

This technical note is on the model reduction of distributed systems formed by discrete-time, linear time-varying, heterogeneous subsystems interconnected over arbitrary directed graphs and subjected to communication latency. We give two procedures to construct a strongly stable coprime factorization for a strongly stabilizable and strongly detectable system. One of the procedures ensures the contractiveness of the resulting factorization. Then, we apply the structure-preserving balanced truncation method for distributed systems. We illustrate the proposed methods through an example. [ABSTRACT FROM AUTHOR]

It is known that the stability of a Metzler matrix can be characterized in a Routh–Hurwitz-like fashion based on a recursive application of scalar Schur complements [1]. Our objective in this brief note is to show that recently obtained stability conditions are equivalent statements of this result and can be deduced directly therefrom using only elementary results from linear algebra. Implications of this equivalence are also discussed and several examples are given to illustrate potentially interesting system-theoretic applications of this observation. [ABSTRACT FROM AUTHOR]

In this note, we use geometric optimal control to completely solve the problem of minimum-time transitions between thermal equilibrium states of the quantum parametric oscillator, which finds applications in various physical contexts. We discover a new kind of optimal solutions, absent from all the previous treatments of the problem. [ABSTRACT FROM AUTHOR]

Satisficing is a relaxation of maximizing and allows for less risky decision making in the face of uncertainty. We propose two sets of satisficing objectives for the multi-armed bandit problem, where the objective is to achieve reward-based decision-making performance above a given threshold. We show that these new problems are equivalent to various standard multi-armed bandit problems with maximizing objectives and use the equivalence to find bounds on performance. The different objectives can result in qualitatively different behavior; for example, agents explore their options continually in one case and only a finite number of times in another. For the case of Gaussian rewards we show an additional equivalence between the two sets of satisficing objectives that allows algorithms developed for one set to be applied to the other. We then develop variants of the Upper Credible Limit (UCL) algorithm that solve the problems with satisficing objectives and show that these modified UCL algorithms achieve efficient satisficing performance. [ABSTRACT FROM AUTHOR]

In coalitional control the connections among the different parts of a control network evolve dynamically to achieve a trade-off between communication burden and control performance, and the coalition choices are made by selecting the network topology with minimal payoff. This work analyzes how Harsanyi power solutions for games in coalitional control schemes, which generalize the Shapley value in this context, can be used to quantify the value of the communication links under different control topologies. To this end, a game among these links is considered, and the payoff that each link receives is determined by the Harsanyi power solutions, which take into account the communication costs and the predicted infinite-horizon costs for these topologies. The concept of link power measure as a centrality index to configure the communication costs is also introduced. As a result, a more computationally efficient design method with respect to previous works has been proposed. [ABSTRACT FROM PUBLISHER]