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In this article, we propose a practicable quantized sampled velocity data coupling protocol for synchronization of a set of harmonic oscillators. The coupling protocol is designed in a quantized way via interconnecting the velocities encoded by a uniform quantizer with a zooming parameter in either a fixed or an adjustable form over a directed communication network. By constructing a suitable norm to measure the convergence of the synchronization errors, we establish sufficient conditions for the networked harmonic oscillators to converge to a bounded neighborhood of the synchronized orbits with a fixed zooming parameter. The oscillators are ensured to achieve synchronization by designing the quantized coupling protocol with an adjustable zooming parameter. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed coupling protocols. [ABSTRACT FROM AUTHOR]

This article focuses on the adaptive synchronization for a class of fractional-order coupled neural networks (FCNNs) with output coupling. The model is new for output coupling item in the FCNNs that treat FCNNs with state coupling as its particular case. Novel adaptive output controllers with logarithm quantization are designed to cope with the stability of the fractional-order error systems for the first attempt, which is also an effective way to synchronize fractional-order complex networks. Based on fractional-order Lyapunov functionals and linear matrix inequalities (LMIs) method, sufficient conditions rather than algebraic conditions are built to realize the synchronization of FCNNs with output coupling. A numerical simulation is put forward to substantiate the applicability of our results. [ABSTRACT FROM AUTHOR]

This article addresses quantized output feedback stabilization under denial-of-service (DoS) attacks. First, assuming that the duration and frequency of DoS attacks are averagely bounded and that an initial bound of the plant state is known, we propose an output encoding scheme that achieves exponential convergence with finite data rates. Next, we show that a suitable state transformation allows us to remove the assumption on the DoS frequency. Finally, we discuss the derivation of state bounds under DoS attacks and obtain sufficient conditions on the bounds of DoS duration and frequency for achieving Lyapunov stability of the closed-loop system. [ABSTRACT FROM AUTHOR]

This note studies the tracking control problem of nonlinear networked and quantized control systems (NQCSs) with communication delays. The communication network is to guarantee the information transmission among the plant, the reference system, and the controller. The communication network also brings about some undesired issues, which lead to nonvanishing network-induced errors and affect the tracking performance. As a result, we first develop a hybrid system model for NQCSs under the network-induced issues. Based on the Lyapunov approach, sufficient conditions are established to guarantee the tracking performance with respect to the nonvanishing network-induced errors. The obtained conditions lead to a tradeoff between the maximally allowable transmission interval and the maximally allowable delay. Furthermore, the existence of Lyapunov functions satisfying the obtained conditions is studied. For specific time-scheduling protocols and quantizers, Lyapunov functions are constructed explicitly. Finally, a numerical example is presented to demonstrate the developed theory. [ABSTRACT FROM AUTHOR]

This paper investigates an adaptive finite-time control (FTC) problem for a class of strict-feedback nonlinear systems with both time-delays and quantized input from a new point of view. First, a new concept, called preassigned finite-time performance function (PFTF), is defined. Then, another novel notion, called practically preassigned finite-time stability (PPFTS), is introduced. With PFTF and PPFTS in hand, a novel sufficient condition of the FTC is given by using the neural network (NN) control and direct adaptive backstepping technique, which is different from the existing results. In addition, a modified barrier function is first introduced in this work. Moreover, this work is first to focus on the FTC for the situation that the time-delay and quantized input simultaneously exist in the nonlinear systems. Finally, simulation results are carried out to illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

We study event-triggered control for stabilization of unstable linear plants over rate-limited communication channels subject to unknown bounded delay. On one hand, the timing of event triggering carries implicit information about the state of the plant. On the other hand, the delay in the communication channel causes information loss, as it makes the state information available at the controller out of date. Combining these two effects, we show a phase transition behavior in the transmission rate required for stabilization using a given event-triggering strategy. For small values of the delay, the timing information carried by the triggering events is substantial, and the system can be stabilized with any positive rate. When the delay exceeds a critical threshold, the timing information alone is not enough to achieve stabilization, and the required rate grows. When the delay equals the inverse of the entropy rate of the plant, the implicit information carried by the triggering events perfectly compensates the loss of information due to the communication delay, and we recover the rate requirement prescribed by the data-rate theorem. We also provide an explicit construction yielding a sufficient rate for stabilization, as well as results for vector systems. Our results do not rely on any a priori probabilistic model for the delay or the initial conditions. [ABSTRACT FROM AUTHOR]

We study a stabilization problem for systems with quantized signals. We propose encoding strategies for three signals: the plant output, the control input, and the estimate of the plant output. A controller generates the estimate of the plant output in addition to the control input and then transmits their quantized data to a plant for control and quantization. We obtain sufficient conditions for local practical stability under bounded disturbances and noise. We first develop an encoding method for general stabilizing gains and then tailor it to deadbeat gains. Finally, we illustrate the proposed encoding methods with numerical simulations. [ABSTRACT FROM AUTHOR]

This paper studies event-based control of nonlinear systems with state quantization. Two configurations of the event-based quantized controller are considered: Quantization after sampling and quantization before sampling. The considered quantizer is assumed to have a finite quantization range. With input-to-state stability (ISS) tools, new event-triggering, and dynamic quantization mechanisms are designed to deal with the interaction of the quantizer and the sampler. For both of the configurations, infinitely fast sampling, and in particular the Zeno phenomenon, is avoided. And the system state asymptotically converges to the origin, if a growth condition is satisfied by the ISS gain of the controlled system. [ABSTRACT FROM AUTHOR]

In this note, a discrete-time modified algebraic Riccati equation (MARE) is investigated. First, the analytic solutions of the homogeneous MARE for controllable single-input systems are explicitly obtained in terms of the system eigenvalues. For anti-Schur systems, the stabilizing, and positive definite solution is proposed. Furthermore, the maximal solution and the solution bound are analyzed for the nonhomogeneous MARE. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of designing time-varying quantizers for the stabilization of switched linear systems with quantized output and switching delays. The detection delays of switches are assumed to be time-varying but bounded, and the dwell time of the switching signal is assumed to be larger than the maximum delay. Given a switching controller, we analyze reachable sets of the closed-loop state by using a common Lyapunov function and then construct a quantizer that guarantees asymptotic stability. A sufficient condition for the existence of such a quantizer is characterized by the maximum switching delay and the dwell time. [ABSTRACT FROM AUTHOR]

Several new expressions for the anytime capacity of Sahai and Mitter are presented for a time-varying rate-limited channel with noiseless output feedback. These follow from a novel parametric characterization obtained in the case of Markov time-varying rate channels, and include an explicit formula for the $r$-bit Markov erasure channel, as well as formulas for memoryless rate processes including Binomial, Poisson, and Geometric distributions. Beside the memoryless erasure channel and the additive white Gaussian noise channel with input power constraint, these are the only cases where the anytime capacity has been computed. At the basis of these results is the study of the threshold function for $m$-th moment stabilization of a scalar linear system controlled over a Markov time-varying digital feedback channel that depends on $m$ and on the channel's parameters. This threshold is shown to be a continuous and strictly decreasing function of $m$ and to have as extreme values the Shannon capacity and the zero-error capacity as $m$ tends to zero and infinity, respectively. Its operational interpretation is that of achievable communication rate, subject to a reliability constraint. [ABSTRACT FROM AUTHOR]

This paper is concerned with optimal communication network-based $H_\infty $ quantized control for a discrete-time neural network with distributed time delay. Control of the neural network (plant) is implemented via a communication network. Both quantization and communication network-induced data packet dropouts are considered simultaneously. It is assumed that the plant state signal is quantized by a logarithmic quantizer before transmission, and communication network-induced packet dropouts can be described by a Bernoulli distributed white sequence. A new approach is developed such that controller design can be reduced to the feasibility of linear matrix inequalities, and a desired optimal control gain can be derived in an explicit expression. It is worth pointing out that some new techniques based on a new sector-like expression of quantization errors, and the singular value decomposition of a matrix are developed and employed in the derivation of main results. An illustrative example is presented to show the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we study a general class of strict feedback nonlinear systems, where the input signal takes quantized values. We consider a stabilization problem for nonlinear uncertain systems via adaptive backstepping approach. The control design is achieved by introducing a hysteretic quantizer to avoid chattering and using backstepping technique. A guideline is derived to select the parameters of the quantizer. The designed controller together with the quantizer ensures the stability of the closed-loop system in the sense of signal boundedness. [ABSTRACT FROM AUTHOR]

The problem of mean-square stabilization of a discrete-time linear dynamical system over a Markov time-varying digital feedback channel is studied. In the scalar case, it is shown that the system can be stabilized if and only if a Markov jump linear system describing the evolution of the estimation error at the decoder is stable —videlicet if and only if the product of the unstable mode of the system and the spectral radius of a second moment matrix that depends only on the Markov feedback rate is less than one. This result generalizes several previous data rate theorems that appeared in the literature, quantifying the amount of instability that can be tolerated when the estimated state is received by the controller over a noise-free digital channel. In the vector case, a necessary condition for stabilizability is derived and a corresponding control scheme is presented, which is tight in some special cases and which strictly improves on a previous result on stability over Markov erasure channels. [ABSTRACT FROM AUTHOR]

We develop a graph-theoretic characterization of controllability and observability of linear systems over finite fields. Specifically, we show that a linear system will be structurally controllable and observable over a finite field if the graph of the system satisfies certain properties, and the size of the field is sufficiently large. We also provide graph-theoretic upper bounds on the controllability and observability indices for structured linear systems (over arbitrary fields). We then use our analysis to design nearest-neighbor rules for multi-agent systems where the state of each agent is constrained to lie in a finite set. We view the discrete states of each agent as elements of a finite field, and employ a linear iterative strategy whereby at each time-step, each agent updates its state to be a linear combination (over the finite field) of its own state and the states of its neighbors. Using our results on structural controllability and observability, we show how a set of leader agents can use this strategy to place all agents into any desired state (within the finite set), and how a set of sink agents can recover the set of initial values held by all of the agents. [ABSTRACT FROM AUTHOR]

In this paper, the quantized H\infty control problem is investigated for a class of nonlinear stochastic time-delay network-based systems with probabilistic data missing. A nonlinear stochastic system with state delays is employed to model the networked control systems where the measured output and the input signals are quantized by two logarithmic quantizers, respectively. Moreover, the data missing phenomena are modeled by introducing a diagonal matrix composed of Bernoulli distributed stochastic variables taking values of 1 and 0, which describes that the data from different sensors may be lost with different missing probabilities. Subsequently, a sufficient condition is first derived in virtue of the method of sector-bounded uncertainties, which guarantees that the closed-loop system is stochastically stable and the controlled output satisfies H\infty performance constraint for all nonzero exogenous disturbances under the zero-initial condition. Then, the sufficient condition is decoupled into some inequalities for the convenience of practical verification. Based on that, quantized H\infty controllers are designed successfully for some special classes of nonlinear stochastic time-delay systems by using Matlab linear matrix inequality toolbox. Finally, a numerical simulation example is exploited to show the effectiveness and applicability of the results derived. [ABSTRACT FROM AUTHOR]

This paper addresses a problem of finding an optimal dynamic quantizer for nonlinear control subject to discrete-valued signal constraints, i.e., to the condition that some signals must take a value on a discrete and countable set at each time instant. The quantizers to be studied are in the form of a nonlinear difference equation which maps continuous-valued signals into discrete-valued ones. They are evaluated by a performance index expressing the difference between the resulting quantized system and the unquantized system, in terms of the input–output relation. In this paper, we present a closed-form solution, which globally minimizes the performance index. This result shows the performance limitation of a general class of dynamic quantizers. In addition to this, some results on the structure and the stability are given in order to clarify the mechanism of the best dynamic quantization in nonlinear control systems. [ABSTRACT FROM PUBLISHER]

Dissensus is a modeling framework for networks of dynamic agents in competition for scarce resources. Originally inspired by biological cell behaviors, it also fits marketing, finance and many other application areas. Competition is often unstable in the sense that strong agents, those having access to large resources, gain more and more resources at the expenses of weak agents. Thus, strong agents duplicate when reaching a critical amount of resources, whereas weak agents die when losing all their resources. To capture all these phenomena we introduce discrete time gossip systems with unstable state dynamics interrupted by discrete events affecting the network topology. Invariancy of states, topologies, and network connectivity are explored. [ABSTRACT FROM AUTHOR]

A data rate theorem for stabilization of a linear, discrete-time, dynamical system with arbitrarily large disturbances, over a rate-limited, time-varying communication channel is presented. Necessary and sufficient conditions for stabilization are derived, their implications and relationships with related results in the literature are discussed. The proof techniques rely on both information-theoretic and control-theoretic tools. [ABSTRACT FROM AUTHOR]

In this paper, we analyze and derive conditions for stability of a feedback system in which the plant and feedback controller are separated by a noiseless finite-rate communication channel. We allow for two deterministic classes of reference inputs to excite the system, and derive sufficient conditions for input-output (IO) stability as a function of the encoding strategy and controller. We first construct an encoder as a quantizer that can have infinite memory and can be time-varying, in that the strategy it follows to allocate a total of R bits to its inputs, is a function of time. This construction of the quantizer leads to the result that the set of allocation strategies that maintains stability for each class of reference signals is convex, allowing the search for the most efficient strategy to ensure stability to be formulated as a convex optimization problem. We then synthesize quantizers and time-varying controllers to minimize the rate required for stability and to track commands. Examples presented in this paper demonstrate how this framework enables computationally efficient methods for simultaneously designing quantizers and controllers for given plants. Furthermore, we observe that our finite memory quantizers that minimize the rate required for stability do not reduce to trivial memoryless bit-allocation strategies. [ABSTRACT FROM AUTHOR]

The purpose of this note is to demonstrate that a unified study of quantization and delay effects in nonlinear control systems is possible by merging the quantized feedback control methodology recently developed by the author and the small-gain approach to the analysis of functional differential equations with disturbances proposed earlier by Teel. We prove that under the action of a robustly stabilizing feedback controller in the presence of quantization and time delays satisfying suitable conditions, solutions of the closed-loop system starting in a given region remain bounded and eventually enter a smaller region. We present several versions of this result and show how it enables global asymptotic stabilization via a dynamic quantization strategy. [ABSTRACT FROM AUTHOR]

Abstract-This paper studies state quantization schemes for feedback stabilization of control systems with limited information. The focus is on designing the least destabilizing quantizer subject to a given information constraint. We explore several ways of mea- suring the destabilizing effect of a quantizer on the closed-loop system, including (but not limited to) the worst-case quantization error. In each case, we show how quantizer design can be naturally reduced to a version of the so-called multicenter problem from locational optimization. Algorithms for obtaining solutions to such problems, all in terms of suitable Voronoi quantizers, are discussed. In particular, an iterative solver is developed for a novel weighted multicenter problem which most accurately represents the least destabilizing quantizer design. A simulation study is also presented. [ABSTRACT FROM AUTHOR]