Quantized Feedback Systems Research Articles

Dynamic output feedback under quantization based on spherical polar coordinate quantizer

AbstractDifferent from uniform quantizer and logarithmic quantizer, this article utilizes a novel quantizer based on spherical polar coordinates for the design problems of quantized feedback systems with dynamic output feedback. This quantizer has a desired relation between the quantized vector and the corresponding quantization error, by which in this article the quantization error is converted to the uncertainty of the systems and stabilization problems of linear systems via dynamic output feedback under quantization can be converted to the corresponding robust control problems. From a practical point of view, we are concerned with quantized feedback control with finite data rate and use the quantizer with finite data rate to design quantized feedback systems. Under the quantizer with finite data rate, a time‐varying bounded quantization region needs to be determined to contain the quantized vector as the system evolves. Under this circumstance, some entries of the quantized vector are not available to the quantizer with finite data rate such that the vector cannot be quantized directly, so we propose a quantization and controller design method to solve this problem.

Limit Cycles in High-Resolution Quantized Feedback Systems

In this paper, the existence of limit cycles in high-resolution quantized feedback systems is examined. It is well known that the relay and the quantized feedback systems exhibit self-oscillations, due to their switching nature. However, the quantizer is a more general nonlinearity as compared to the relay, due to its switching at multiple discrete levels. An extension of periodic switching conditions uncovers the existence of self-oscillations in some systems under high quantization resolution. Multiple limit cycle solutions of switching instants and periods have been found, depending on the initial states of the system. Further analysis on the stability of the limit cycle via the Jacobian of the Poincare map reveals numerical bounds on the quantization step size for a stable limit cycle. Analytical results on the existence of limit cycles in first and second order systems are also presented.

Switched Control for Quantized Feedback Systems: Invariance and Limit Cycle Analysis

We study feedback control for discrete-time linear time-invariant systems in the presence of quantization both in the control action and in the measurement of the controlled variable. While in some application the quantization effects can be neglected, when high-precision control is needed, they have to be explicitly accounted for in control design. In this paper we propose a switched control solution for minimizing the effect of quantization of both the control and controlled variables in the case of a simple integrator with unitary delay, a model that is quite common in the computing systems domain, for example in thread scheduling, clock synchronization, and resource allocation. We show that the switched solution outperforms the one without switching, designed by neglecting quantization, and analyze necessary and sufficient conditions for the controlled system to exhibit periodic solutions in the presence of an additive constant disturbance affecting the control input. Simulation results provide evidence of the effectiveness of the approach.

Optimal Input and Quantization Interval for Quantized Feedback System With Variable Quantizer

Networked control systems (NCSs) have received much attention in the field of robot teleoperation, telesurgery, and other applications. In an NCS, it is important to compress data transmitted over a limited communication network while preserving the data required for control. We address a quantized feedback system in which the output of a plant is quantized with a variable quantization interval. For such a system, we present a novel optimal quantized feedback control. The proposed approach derives not only an optimal input, but also an optimal quantization interval in the quantizer simultaneously using the model predictive control. The approach also satisfies constraints on the state, input, and quantization interval. The effectiveness of the proposed approach is validated through cart-positioning experiments.

Quantized control for networked control systems with packet dropout and unknown disturbances

This paper is concerned with the problem of achieving parameterized input to state stability in mean sense with respect to packet dropout and unknown disturbances for networked control systems with quantized measurements. Similarly to previous literature, the uniform quantizer adopted here holds rectangular quantization regions. However, here we design random lengths of quantization regions according to packet dropout process. The quantization strategy switches between “zooming out” and “zooming in” which holds two modes similarly to Sharon and Liberzon (2012). To deal with packet dropout, the received packet rate at update mode is introduced, which is the main innovation of the paper. Within this setup, we derive a sufficient condition for parameterized input to state stability in mean sense of networked control systems. We also give an illustrative example to show the usefulness of the proposed framework for stability analysis of some classes of quantized feedback systems.

Robust quantized output feedback control for uncertain discrete time‐delay systems with saturation nonlinearity

SummaryThis paper is concerned with robust quantized output feedback control problems for uncertain discrete‐time systems with time‐varying delay and saturation nonlinearity. It is assumed that the quantizer is of the saturating type. A new framework for the local boundedness stabilization of quantized feedback systems is developed. Attention is focused on finding a quantized static output feedback controller such that all trajectories of the resulting closed‐loop system starting from an admissible initial basin converge to a bounded region strictly within the initial basin. A quantized feedback controller is proposed, which comprises output feedback and the exogenous signal parts. Simulation examples are given to illustrate the effectiveness and advantage of the proposed methods. Copyright © 2014 John Wiley & Sons, Ltd.

Model Following Output Feedback Control for Discrete-Valued Input Systems

This paper considers an output feedback control problem for discrete-valued input systems. The proposed controller achieves model following control for networked control systems and embedded devices with low-resolution AD/DA converters. The synthesis problem the authors address is the simultaneous synthesis of the nominal controller and the delta-sigma modulator (where the modulators are called the dynamic quantizers). The proposed approach is based on the invariant set analysis and the LMI technique. First, this paper considers a controller structure for model following control. Second, this paper proposes a controller analysis condition for quantized feedback systems. Third, the authors provide a simultaneous synthesis condition that is recast as a set of matrix inequalities. Finally, to verify the validity of the proposed method, numerical examples are presented and then the contributions related to the existing dynamic quantizer synthesis are clarified.

Synthesis of continuous-time dynamic quantizers for LFT type quantized feedback systems

This paper focuses on analysis and synthesis methods of continuous-time dynamic quantizers for LFT type quantized control systems. Our aim is to propose a numerical optimization design method of multiple (decentralized) quantizers such that a given linear system is optimally approximated by the given linear system with the multiple quantizers. Our method is based on the invariant set analysis and the LMI technique. In addition, we clarify that our proposed method naturally extends to multiobjective control problems similar to linear control. For implementation, this paper presents an analysis condition of the applicable interval of switching process of quantizer. Finally, it is pointed out that the proposed method is helpful through a numerical example.

Energy optimization in multiuser quantized feedback systems

This article explores the effects of quantization of feedback information on energy consumption in multiuser wireless communication systems. In order to optimize the energy consumption of the system, the article concentrates on the amount of transmit energy, the additional energy due to quantization and the probability of power outage. Closed form expressions for such parameters are obtained, where the impact of the number of quantization bits is explicitly outlined. An optimization problem is then formulated to find the optimum number of quantization bits able to minimize the consumption in the energy resources. Simulations demonstrate the good results obtainable with the presented optimization strategy, and provide effective validation of the analytic solution presented in the article.

Synthesis of continuous-time dynamic quantizers for quantized feedback systems

This paper focuses on analysis and synthesis methods of continuous-time dynamic quantizers for quantized feedback systems. Our aim is to find a quantizer such that a given linear system is optimally approximated by the given linear system with the quantizer in terms of invariant set analysis. In the case of minimum phase systems, this paper clarifies that an optimal dynamic quantizer and its performance are parameterized by a design parameter. Otherwise, this paper derives the stable quantizer synthesis condition that can be recast as parameter dependent linear matrix inequalities.

Input-to-State Stability of Differential Inclusions with Applications to Hysteretic and Quantized Feedback Systems

Input-to-state stability (ISS) of a class of differential inclusions is proved. Every system in the class is of Lur'e type: a feedback interconnection of a linear system and a set-valued nonlinearity. Applications of the ISS results, in the context of feedback interconnections with a hysteresis operator or a quantization operator in the feedback path, are developed.

Stability of quantized control systems under dynamic bit assignment

In recent years, there have been several papers characterizing the minimum number of quantization levels required to assure closed-loop stability. This minimum bit rate is usually achieved through time-varying quantization policies. Many networks, however, prefer a constant bit rate configuration, so it is useful to characterize the stability of quantized feedback systems under constant bit rate quantization. This note first derives a lower bound on the number of quantization levels required for closed-loop stability under constant bit rates. We then introduce a novel dynamic bit allocation policy that achieves this bound.

A Symbolic Approach to Performance Analysis of Quantized Feedback Systems: The Scalar Case

When dealing with the control of a large number of interacting systems, the fact that the flow of information has to be limited becomes an essential feature of the control design. The first consequence of the limited information flow constraint is that the signals that the controllers and the systems exchange have to be quantized. Though quantization has already been extensively considered in the control literature, its analysis from the point of view of the information flow demand has been considered only recently. Limiting the information flow between a plant and a controller will necessarily lead to a performance degradation of the feedback loop, and we expect a trade-off between the achievable performance and the amount of information exchange allowed in the loop. Most of the success of modern digital communication theory in the last 50 years is due to the contributions of information theory, which proposed a symbolically based analysis of the communication channel performance. The same goal is much more difficult to reach in digital control theory. This paper proposes an attempt toward this direction. The main contribution of this paper is to provide a complete analysis of the trade-off between performance and information flow in the simple case of the stabilization of a scalar linear system by means of a memoryless quantized feedback map.

Analysis of error propagation and design of filter cutoff frequency in a quantized feedback dc‐restoration system

AbstractIn the regenerative repeater in digital transmission, the low‐frequency component of the transmitted pulse is cut off by the coupling circuits at the input and the output. However, by applying the quantized feedback dc‐restoration circuit in the repeater the digital regenerative transmission with low dc‐balance transmission code can be achieved. In the quantized feedback system, the component lost in the low‐frequency cutoff characteristics of the transmission system is restored by feeding back the low‐frequency component of the pulse regenerated in the repeater to the decision circuit input. Because of this mechanism, however, an error propagation occurs where an error component is fed back to produce a distortion and to enlarge the error, when a decision error is produced in the repeater. This paper derives the state‐transition diagram which approximates the error propagation. By the analysis of the state‐transition diagram, the relation between the filter cutoff frequency and the error propagation characteristics is determined. Furthermore, it is shown by a simulation experiment that the result of the analysis is a good approximation to the error propagation. Based on these results, a design method is presented for the cutoff frequencies of the forward and the feedback low‐pass filters in the quantized feedback system.

Chaos and cooperation in nonlinear pictorial feedback systems 3: Quantized feedback systems

We investigate the behavior of pictorial feedback systems with quantized intensity. These systems are used for numerical experiments to investigate the evolution of chaos and order in pictures. It turns out that chaos experiments with quantized feedback systems may show completely different results compared with those of nonquantized systems. However, the essential properties of the nonquantized system can be restored, in quantized experiments, by addition of noise. We demonstrate a use of the quasi-chaotic behavior of quantized systems, that is, cryptography of pictures.

On the output feedback control of discrete-valued input systems

This paper considers an output feedback control for quantized feedback systems. Our controller focuses on high accuracy control performance for embedded devices with low-resolution AD/DA converters and networked systems with band-limited channels. The synthesis problem we address is the simultaneous synthesis of the nominal controller and the delta-sigma modulator (where the modulators are called the dynamic quantizers). For certain systems, we provide closed form and numerical solutions for the synthesis problem based on the invariant set analysis and the LMI technique. First, this paper proposes a synthesis condition that is recast as a set of matrix inequality conditions. The condition reduces to a tractable numerical optimization problem. Second, a closed form solution of optimal controller for the quantized feedback system is clarified within the invariant set framework. Third, we discuss the controller synthesis conditions which are characterized by the transmission zero property. Finally, to verify the validity of our method, numerical examples are presented and then the contributions related to the existing dynamic quantizer synthesis are clarified.