Optimum Sampled-Data Systems with Quantized Control Signals

Lewis, James B.; Tou, Julius Τ.

doi:10.1109/tai.1963.5407833

Cited by 36 publications

(10 citation statements)

References 7 publications

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“…Exceptions include the study of optimal stochastic control over communication channels, e.g., [11], [18], [33]- [36], [39]- [41]. The recent paper [40] provides a useful historical review of linear quadratic Gaussian (LQG) control with quantized feedback.…”

Section: A Control Over Data-rate Limited and Noisy Channelsmentioning

confidence: 99%

“…The recent paper [40] provides a useful historical review of linear quadratic Gaussian (LQG) control with quantized feedback. As mentioned in [40], LQG control in the special case of a rate-limited but noiseless feedback link was studied for the first time in the 60'ies, see e.g., [33]- [35]. Later, Fischer [36] characterized the optimal quantizer and controls for this problem in the case of vector-valued state and observation.…”

Section: A Control Over Data-rate Limited and Noisy Channelsmentioning

confidence: 99%

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Iterative Encoder-Controller Design for Feedback Control Over Noisy Channels

Bao

Skoglund

Johansson

2011

IEEE Trans. Automat. Contr.

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Abstract-We study a closed-loop control system with state feedback transmitted over a noisy discrete memoryless channel. With the objective to minimize the expected linear quadratic cost over a finite horizon, we propose a joint design of the sensor measurement quantization, channel error protection, and controller actuation. It is argued that despite that this encoder-controller optimization problem is known to be hard in general, an iterative design procedure can be derived in which the controller is optimized for a fixed encoder, then the encoder is optimized for a fixed controller, etc. Several properties of such a scheme are discussed. For a fixed encoder, we study how to optimize the controller given that full or partial side-information is available at the encoder about the symbols received at the controller. It is shown that the certainty equivalence controller is optimal when the encoder is optimal and has full side-information. For a fixed controller, expressions for the optimal encoder are given and implications are discussed for the special cases when process, sensor, or channel noise is not present. Numerical experiments are carried out to demonstrate the performance obtained by employing the proposed iterative design procedure and to compare it with other relevant schemes.Index Terms-Discrete memoryless channel, joint encoder-controller design, joint source-channel coding, limited information control, quantized feedback control.

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Section: A Control Over Data-rate Limited and Noisy Channelsmentioning

confidence: 99%

Section: A Control Over Data-rate Limited and Noisy Channelsmentioning

confidence: 99%

Iterative Encoder-Controller Design for Feedback Control Over Noisy Channels

Bao

Skoglund

Johansson

2011

IEEE Trans. Automat. Contr.

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“…There is a large literature on jointly optimal quantization for the LQG problem dating back to early 1960s (see, for example, [23] and [13]). References [2,7,17,18,31,38,48], and [57] considered the optimal LQG quantization and control, with various results on the optimality or the lack of optimality of the separation principle.…”

Section: The Linear Quadratic Gaussian (Lqg) Casementioning

confidence: 99%

Design of Information Channels for Optimization and Stabilization in Networked Control

Yüksel

2014

Information and Control in Networks

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In stochastic control, typically a partial observation model/channel is given and one looks for a control policy for optimization or stabilization. Consider a single-agent dynamical system described by the discrete-time equations1)for (Borel measurable) functions f, g, with {w t } being an independent and identically distributed (i.i.d.) system noise process and {v t } an i.i.d. measurement disturbance process, which are independent of x 0 and each other. Here, x t ∈ X, y t ∈ Y, u t ∈ U, where we assume that these spaces are Borel subsets of finite dimensional Euclidean spaces. In (6.2), we can view g as inducing a measurement channel Q, which is a stochastic kernel or a regular conditional probability measure from X to Y in the sense that Q(·|x) is a probability measure on the (Borel) σ -algebra B(Y) on Y for every x ∈ X, and Q(A|·) : ] is a Borel measurable function for every A ∈ B(Y).In networked control systems, the observation channel described above itself is also subject to design. In a more general setting, we can shape the channel input by coding and decoding. This chapter is concerned with design and optimization of such channels.We will consider a controlled Markov model given by (6.1). The observation channel model is described as follows: This system is connected over a noisy channel with a finite capacity to a controller, as shown in Fig. 6.1. The controller has

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“…The measurements z k are quantized by the feedback data compressor and delivered to the controller, while the controller output is quantized by the forward data compressor to produce the quantized control u k which is applied to the plant. The basic design problem is to jointly select control, estimation, and forward and feedback data compression mappings to minimize (3) subject to (1) and (2).…”

Section: Problem Formulationmentioning

confidence: 99%

Quantized control using differential encoding

Fischer¹,

Tinnin

1984

Optim Control Appl Methods

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A vector generalization of differential pulse code modulation is used to provide quantization of control and measurements in a closed-loop control system. Algorithms are developed for the adaptive quantizer and predictor. Explicit expressions are derived for the quantization and estimation errors resulting from the differential encoding. Simulation results are presented which demonstrate that even for very low bit rates the quantized control performance is very close to the performance of the unquantized optimal control solution. KEY WORDS Digital control Linear-quadratic regulators Differential pulse code modulationControl and measurement quantization

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Optimum Sampled-Data Systems with Quantized Control Signals

Cited by 36 publications

References 7 publications

Iterative Encoder-Controller Design for Feedback Control Over Noisy Channels

Iterative Encoder-Controller Design for Feedback Control Over Noisy Channels

Design of Information Channels for Optimization and Stabilization in Networked Control

Quantized control using differential encoding

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