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We consider the problem of output feedback stabilization in linear systems when the measured outputs and control inputs are subject to event-triggered sampling and dynamic quantization. A new sampling algorithm is proposed for outputs which does not lead to accumulation of sampling times and results in asymptotic stabilization of the system. The approach for output sampling is based on defining an event function that compares the difference between the current output and the most recently transmitted output sample not only with the current value of the output, but also takes into account a certain number of previously transmitted output samples. This allows us to reconstruct the state using an observer with sample-and-hold measurements. The estimated states are used to generate a control input, which is subjected to a different event-triggered sampling routine; hence the sampling times of inputs and outputs are asynchronous. Using Lyapunov-based approach, we prove the asymptotic stabilization of the closed-loop system and show that there exists a minimum inter-sampling time for control inputs and for outputs. To show that these sampling routines are robust with respect to transmission errors, only the quantized (in space) values of outputs and inputs are transmitted to the controller and the plant, respectively. A dynamic quantizer is adopted for this purpose, and an algorithm is proposed to update the range and the centre of the quantizer that results in an asymptotically stable closed-loop system. [ABSTRACT FROM AUTHOR]

This article studies the quantized partial-state feedback stabilization of a class of nonlinear cascaded systems with dynamic uncertainties. Under the assumption that the dynamic uncertainties are input-to-state practically stable, a novel recursive design method is developed for quantized stabilization by taking into account the influence of quantization and using the small-gain theorem. When the dynamic uncertainty is input-to-state stable, asymptotic stabilization can be achieved with the proposed quantized control law. [ABSTRACT FROM AUTHOR]

For a networked control system, we consider the problem of encoder and controller design. We study a discrete-time linear plant with a finite horizon performance cost, comprising a quadratic function of the states and controls, and an additive communication cost. We study separation in design of the encoder and controller, along with related closed-loop properties such as the dual effect and certainty equivalence. The encoder outputs are quantized samples, but our results also apply to two other formats for encoder outputs: real-valued samples at event-triggered times, and real-valued samples over additive noise channels. If the controller and encoder are dynamic, then we show that the performance cost is minimized by a separated design: the controls are updated at each time instant as per a certainty equivalence law, and the encoder is chosen to minimize an aggregate quadratic distortion of the estimation error. This separation is shown to hold even though a dual effect is present in the closed-loop system. We also show that this separated design need not be optimal when the controller or encoder are to be chosen from within restricted classes. [ABSTRACT FROM AUTHOR]

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Constructive nonlinear control design has undergone rapid and significant progress over the last three decades. In this paper, a review of recent results in this important field is presented with a focus on interdisciplinary topics at the interface of control, computing and communications. In particular, it is shown that the nonlinear small-gain theory provides a unified framework for solving problems of quantized feedback stabilization and event-triggered control for nonlinear systems. Some open questions in quantized and networked nonlinear control systems are discussed. [ABSTRACT FROM AUTHOR]

A novel observer-based fault accommodation technique for linear multi-input multi-output sampled-data systems affected by a general class of actuator faults in the presence of quantization errors is addressed in the paper. Only the output signal has been assumed to be available for direct measurement. A simulation study on a three-tank system supports theoretical developments. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper proposes a quantized memory proportional–integral (QMPI) control scheme to study the active power-sharing and frequency regulation (PSFR) issues of island Micro-Grids (MGs) under abnormal asynchronous stochastic cyber attacks (AASCAs). First, AASCAs are considered, which reflected the randomness and asynchrony of the attacks employed by hackers. Second, a novel relaxed condition that depends on the time delay (TD) is constructed, thereby reducing the usual constraint condition. Then, using the reciprocal convex matrix inequality (RCMI), some appropriate integral inequalities are used to process the integral terms to obtain a tighter upper bound. Next, based on Lyapunov–Krasovskii functional (LKF) method, a new QMPI controller under AASCAs is designed to ensure active PSFR in MGs. Finally, two kinds of experiments and simulations are carried out on the improved IEEE 34 bus test system to verify the performance of the control algorithm proposed in this paper. • The island MGs' active PSFR are studied under network communication security. • The TD dependent relaxed condition is constructed, which can effectively improve the performance of the designed control algorithm. • A desired QMPI controller under AASCAs is designed to ensure active PSFR in MGs. • The performance of the designed control algorithm is verified by the improved IEEE 34 bus test system. [ABSTRACT FROM AUTHOR]

This paper investigates quantized feedback control problems for network empowerment ammunition, where the sensors and the controller are connected by a digital communication network with data-rate limitations. Different from the existing ones, a new bit-allocation algorithm on the basis of the singular values of the plant matrix is proposed to encode the plant states. A lower bound on the data rate is presented to ensure stabilization of the unstable plant. It is shown in our results that, the algorithm can be employed for the more general case. An illustrative example is given to demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

SUMMARY Like feedback strategy, coding scheme is an important part of networked control system design as well. On the basis of spherical polar coordinate, a novel coding scheme is proposed for stabilization problem of discrete linear time invariant system subject to packet erasure channel with feedback. The coding scheme uses encoder without access to control inputs. In the case that a decoder does not use control inputs, a definite relation between the quantized data and the corresponding quantization error is established, which helps to analyze the stability of system, and a selective quantization method is adopted, by which finite data rate is obtained. In the case that a decoder uses control inputs, instead of quantizing the system state at each time step as usual, the encoder quantizes the initial state all the time by updating quantizer. Sufficient conditions guaranteeing the system stable are presented for two cases, respectively, and the corresponding design methods for coding schemes are given. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: We study the problem of asymptotically stabilizing a switched linear control system using sampled and quantized measurements of its state. The switching is assumed to be slow enough in the sense of combined dwell time and average dwell time, each individual mode is assumed to be stabilizable, and the available data rate is assumed to be large enough but finite. Our encoding and control strategy is rooted in the one proposed in our earlier work on non-switched systems, and in particular the data-rate bound used here is the data-rate bound from that earlier work maximized over the individual modes. The main technical step that enables the extension to switched systems concerns propagating over-approximations of reachable sets through sampling intervals, during which the switching signal is not known; a novel algorithm is developed for this purpose. Our primary focus is on systems with time-dependent switching (switched systems) but the setting of state-dependent switching (hybrid systems) is also discussed. [Copyright &y& Elsevier]

This paper considers discrete linear systems with multiple distributed sensors that are connected to one controller via channels of finite data rate. Each encoder has access to only one component of the current system output vector. By the proposed boundary function method, a condition expressed in terms of output feedback gain matrix, the parameters of boundary functions, and the channel data rates is given to guarantee the convergence of the state in the case of reliable channels. Then, we extend the result to the case of erasure channels. [ABSTRACT FROM AUTHOR]

Abstract: Quantized control systems design is motivated by the convergence of controls and communications to address modern engineering applications involving the use of information technology. This paper presents an overview of recent developments on the control of linear and nonlinear systems when the control input is subject to quantization or the quantized states or outputs are used as feedback measurements. The co-existence of high-dimensionality, quantization, nonlinearity and uncertainty poses great challenges to quantized control of nonlinear systems and thus calls for new ideas and techniques. The field of quantized nonlinear control is still at its infancy. Preliminary results in our recent work based on input-to-state stability and cyclic-small-gain theorems are reviewed. The open problems in quantized nonlinear control are also outlined. [Copyright &y& Elsevier]

Abstract: The quantized feedback stabilization problem for a class of linear system with nonlinear disturbances is addressed, in which the system and controller are connected via a communication channel. In this case, the effect of quantization errors is studied. A practical quantized scheme is designed such that the transmission error decays to zero exponentially. Meanwhile, a sufficient condition in terms of linear matrix inequality for input-to-state stability (ISS) of the system is presented with regard to the transmission error. Therefore, a quantized stabilization of the system is guaranteed based on the ISS property. A simulation example for the single-link flexible joint robot is presented to demonstrate the effectiveness of the result. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a control law to achieve a rendezvous of autonomous vehicles moving in three-dimensional (3D) space, using minimal data sensing and quantized control. A pre-assigned graph uniquely assigns the pursuer-target pair in a cyclic manner. A quantized control law has been proposed which allows the vehicle to pitch and yaw simultaneously in the required direction and track its target agent. The only measurement required for the proposed control law is the quadrant from which the target vehicle moves out of the field-of-view of the pursuing vehicle. A Lyapunov function is chosen to find a domain for the field-of-view which guarantees rendezvous under the proposed control law. Computer simulations are presented to demonstrate the control law. [Copyright &y& Elsevier]

Abstract: This paper derives performance limitations for disturbance rejection of scalar systems under information constraints subject to either bounded or Gaussian disturbances. Two kinds of disturbance are treated in a unified manner, using appropriate entropies and distortions. It is shown that the achievable performance cannot be improved even if the maximum information constraint is relaxed to an average information constraint. Another observation is that, while the information constraints are weaker than bit-rate or signal-to-noise ratio constraints on the communication channel, the same performance levels are achieved by the best encoder and decoder for disturbance rejection with the information constraints. [Copyright &y& Elsevier]

This paper presents a novel feedback dithering scheme. The dithering circuit feeds the quantization noise through a resonator and a comparator to produce a binary signal for use as a dither input to a quantizer. The outstanding feature of the feedback binary dither is its capacity to eliminate in-band quantization noise while effectively randomizing quantization patterns and linearizing a quantizer. The feedback dither exhibits a consistently high decorrelation performance in either an open-loop or a closed-loop system. The dithering scheme is applied to a bandpass sigma-delta modulator and a multilevel class-D power amplifier to confirm its effectiveness. Simulations indicate significantly improved in-band signal-to-distortion-plus-noise ratios over the conventional ditherings. [ABSTRACT FROM PUBLISHER]

We investigate an industrial case study of a system distributed over a network, namely, a large-scale hydraulic network which underlies a district heating system. The network comprises an arbitrarily large number of components (valves, pipes, and pumps). After introducing the model for this class of networks, we show how to achieve semiglobal practical pressure regulation at designated points of the network by proportional control laws which use local information only. In the analysis, the presence of positivity constraints on the actuators (centrifugal pumps) is explicitly taken into account. Furthermore, motivated by the need of transmitting the values taken by the control laws to the pumps of the network in order to distribute the control effort, we study the pressure regulation problem using quantized controllers. The findings are supported by experimental results. [ABSTRACT FROM AUTHOR]

In this paper, a continuous-time Takagi–Sugeno (T–S) fuzzy system with impulsive effects that are controlled through network is investigated. Network signal-transmission delays and signal-quantization effects are simultaneously considered. The network is with two time-varying additive delays and limited capacity. First, a quantized output-feedback networked control system (NCS) model is established to describe the impulsive NCSs through a channel with limited capacity. Then, based on the Lyapunov–Krasovskii functional approach and a parallel-distributed compensation scheme, a delay-dependent stabilization approach is developed for the impulsive NCSs, which guarantees that the closed-loop system is asymptotically stable. Finally, a simulation example is given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers the problem of finite-time quantized guaranteed cost fuzzy control for continuous-time nonlinear systems. Firstly, the definition on finite-time stability (FTS) for continuous-time nonlinear systems is provided and we give a novel and explicit interpretation for finite-time quantized guaranteed cost control. Secondly, sufficient conditions for the existence of state feedback controller are derived in terms of linear matrix inequities (LMIs), which guarantee the requirements of the provided performance criterion. The related optimization problem is also offered to minimize the guaranteed cost performance bound. Finally, an illustrative example is presented to show the validity of the proposed scheme. [Copyright &y& Elsevier]

Abstract: This paper analyzes the stability of nonlinear systems with quantized feedback in the presence of exogenous disturbances. This paper is an extension of [D. Liberzon, D. Nešić, Input-to-state stabilization of linear systems with quantized state measurements, IEEE Trans. Automat. Control 52 (2007), 413–436] to nonlinear systems. Under appropriate assumptions using a nonlinear modification of the scheme proposed in [D. Liberzon, D. Nešić, Input-to-state stabilization of linear systems with quantized state measurements, IEEE Transactions on Automat. Control 52 (2007), 413–436], it is shown here that it is possible to achieve input-to-state and nonlinear gain stability for nonlinear systems with quantized feedback. [Copyright &y& Elsevier]

Input shaping is an effective method for suppressing motion-induced oscillation in flexible systems. This technique works well on systems with continuously-variable actuation. However, many systems only have a finite number of actuation states. For example, some relay-driven cranes have three actuation states: off, low-speed, and full speed. The discretizing effect of finite-state actuation can reduce the effectiveness of input shaping. This paper investigates the detrimental effects of discretization. The operational effects of finite-state input shaping are evaluated by using experimental results from a human-operated bridge crane, and a 3-D simulation of this crane. [ABSTRACT FROM AUTHOR]

Abstract: The spectral properties of the incidence matrix of the communication graph are exploited to provide solutions to two multi-agent control problems. In particular, we consider the problem of state agreement with quantized communication and the problem of distance-based formation control. In both cases, stabilizing control laws are provided when the communication graph is a tree. It is shown how the relation between tree graphs and the null space of the corresponding incidence matrix encode fundamental properties for these two multi-agent control problems. [Copyright &y& Elsevier]

Abstract: Existing analyses of ‘zooming’ quantisation schemes for bit-rate-limited control systems rely on the encoder and controller being initialised with identical internal states. Due to the quantiser discontinuity and the plant instability, it was not clear if closed-loop stability was possible if the encoder and controller commenced from different initial conditions. In this article, we consider partially observed, unstable linear time-invariant plants, with unbounded and possibly non-Gaussian noise, and propose a modified zooming-like scheme with finite-dimensional internal encoder and controller states that may not initially be identical. Using a stochastic pseudo-norm, we prove that this scheme yields mean-square stability in all closed-loop state variables, not just the plant state, under a sufficient condition involving this initial error, the plant dynamics and the channel data rate. With diminishing initial error, this condition approaches a known universal lower bound on data rates and becomes tight. Furthermore, we show that the scheme automatically corrects itself, in the sense that the errors between the internal states of the encoder and controller tend to zero stochastically with time. This suggests that the policy will maintain stability in the presence of channel errors, for sufficiently low bit error rates. We support these conclusions with simulations. [Copyright &y& Elsevier]

Abstract: We consider closed loop control systems in which feedback laws take values in a discrete set and we study the Zeno phenomenon, i.e. the accumulation of discontinuities with respect to time. The results generalize those obtained in [F. Ceragioli, Finite valued feedback laws and piecewise classical solutions, Nonlinear Analysis 65 (2006) 984–998] for the case where is finite to the case where may be infinite. An application to a quantized control problem is also shown. [Copyright &y& Elsevier]

Abstract: A direct adaptive control framework for linear uncertain systems for using communication channels is developed. Specifically, the control signals are to be quantized and sent over a communication channel to the actuator. The proposed framework is Lyapunov-based and guarantees partial asymptotic stability, that is, Lyapunov stability of the closed-loop system states and attraction with respect to the plant states. The quantizers are logarithmic and characterized by sector-bound conditions, with the conic sectors adjusted at each time instant by the adaptive controller, in conjunction with the system response. Furthermore, we extend the scheme to the case where the logarithmic quantizer has a deadzone around the origin so that only a finite number of quantization levels is required to achieve practical stability. Finally, a numerical example is provided to demonstrate the efficacy of the proposed approach. [Copyright &y& Elsevier]

Abstract: In this paper we consider the classical problem of stabilizing nonlinear systems in the case the control laws take values in a discrete set. First, we present a robust control approach to the problem. Then, we focus on the class of dissipative systems and rephrase classical results available for this class taking into account the constraint on the control values. In this setting, feedback laws are necessarily discontinuous and solutions of the implemented system must be considered in some generalized sense. The relations with the problems of quantized and switching control are discussed. [Copyright &y& Elsevier]

The emerging area of control with limited data rates incorporates ideas from both control and information theory. The data rate constraint introduces quantization into the feedback loop and gives the interconnected system a twofold nature, continuous and symbolic. In this paper, we review the results available in the literature on data-rate-limited control. For linear systems, we show how fundamental tradeoffs between the data rate and control goals, such as stability, mean entry times, and asymptotic state norms, emerge naturally. While many classical tools from both control and information theory can still be used in this context, it turns out that the deepest results necessitate a novel, integrated view of both disciplines. [ABSTRACT FROM AUTHOR]