Stabilization and Disturbance Attenuation Over a Gaussian Communication Channel

Freudenberg, J.S.; Middleton, Richard H.; Solo, Victor

doi:10.1109/tac.2010.2040507

Cited by 85 publications

(65 citation statements)

References 13 publications

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“…In the following, we will provide a discussion on the contributions in the literature which are contextually close to our paper. For Gaussian channels, the fact that real-time linear schemes are rate-distortion achieving has been observed earlier in [1] for scalar systems (see also [6] on Gaussian channels regarding relevance to Shannon capacity for multi-dimensional systems). Aside from such results (which involve matching between rate-distortion achieving test channels and capacity achieving source distributions), capacity is known not to be a good measure of information reliability for channels for real-time control and estimation problems [25].…”

Section: A Literature Reviewmentioning

confidence: 83%

Stochastic stability and ergodicity of linear Gaussian systems controlled over discrete channels

Yüksel

2011

IEEE Conference on Decision and Control and European Control Conference

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Abstract-We present necessary and sufficient conditions for stochastic stabilizability of unstable (non-stationary) noisy linear systems over channels with memory with feedback. Stochastic stability notions include recurrence, Birkhoff sample path ergodicity and asymptotic mean stationarity, and the existence of finite second moments. We extend recent results in the literature on noiseless and erasure channels for systems driven by possibly unbounded noise. Our constructive proof uses randomtime state-dependent stochastic drift criteria for stabilization of Markov chains. For asymptotic mean stationarity, it is sufficient that the capacity of a channel is (strictly) greater than the sum of the logarithms of the unstable pole magnitudes for memoryless channels and a class of channels with memory. We also present the tightness of the sufficient condition under a technical condition. We provide sufficiency conditions for the existence of finite average second moments, for such systems driven by unbounded noise, which had not been studied in the literature to our knowledge. Comparison with relevant results in the literature is presented. I. PROBLEM FORMULATIONWe consider a scalar LTI discrete-time system described bywhere x t is the state at time t, u t is the control input, the initial condition x 0 is a second order random variable, and {d t } is a sequence of zero-mean independent, identically distributed (i.i.d.) Gaussian random variables with a finite second moment. It is assumed that |a| ≥ 1 and b = 0:The system is open-loop unstable, but it is stabilizable. This system is connected over a Discrete Memoryless Channel with a finite capacity to a controller, as shown in Figure 1.The channel source consists of state values, taking values in R. The source is quantized: A quantizer Q is represented by a map Q : R → R, characterized by a sequence of nonoverlapping Borel-measurable bins {B i }, such that Q(x) = q i ∈ R if and only if x ∈ B i ; that is, Q(x) = i q i 1 {x∈Bi} . The quantizer outputs are transmitted through a channel, after being subjected to a channel encoder. Definition 1.1: A finite-alphabet channel with memory is characterized by a sequence of finite input alphabets M n+1 , finite output alphabets M ′ n+1 , and a sequence of conditional probability measures P n (q ′ , and a conditional probability mass functionsatisfies the following:The quantizer outputs are transmitted through a noisy channel, hence the receiver has access to noisy versions of the quantizer/coder outputs for each time, which we denote by q ′ ∈ M ′ . The quantizers and controllers are causal such that the quantizer function at time t ≥ 0 is generated using the information vector I The goal of the paper is to identify conditions on the channel under which the controlled process {x t } is stochastically stable in each of the following senses:• {x t } is recurrent: There exists a compact set A such that {x t ∈ A} infinitely often almost surely.• {x t } is asymptotically mean stationary and satisfies the sample path ergodic theorem.2 e...

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Section: A Literature Reviewmentioning

confidence: 83%

Stochastic stability and ergodicity of linear Gaussian systems controlled over discrete channels

Yüksel

2011

IEEE Conference on Decision and Control and European Control Conference

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“…Assumption: To avoid coding computational overflow, it is assumed that T m ≥ sup i∈{1,2,...,n},k∈N+ N ik (β), where N ik (β) = σ ik + γ ik , is the coding computational time associated with the ith coding strategy at the time instant k. Note that for a given coding strategy, sup i∈{1,2,...,n},k∈N+ N ik (β) is known a priori. 2 In the fleet control of AUVs, dynamics of AUVs are described by a kinematic unicycle vehicle model, which represents nonlinear dynamics [13], [14]. One objective of this paper is to study fundamental tradeoffs between duty cycle for feedback channel use and performance in fleets of AUVs.…”

Section: A Definition and Modelmentioning

confidence: 99%

An integration framework for Control/Communication/Computation (3C) co-design with application in fleet control of AUVs

Farhadi

Wit

2011

IEEE Conference on Decision and Control and European Control Conference

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Abstract-In this paper we introduce an integration framework for Control/Communication/Computation (3C) co-design based on the motivating example of fleet control of Autonomous Underwater Vehicles (AUVs). Specifically, we address the problem of almost sure stability of an unstable system with multiple observations over packet erasure channel with emphasize on coding computational complexity. We look at the tradeoff between duty cycle for feedback channel use, coding computational complexity, and performance. We compare coding computational complexity and performance for two cases: a) No feedback channel at all, and b) Feedback channel all the time. It is shown that the strategy of using feedback channel results in a better performance.

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“…If (12) holds, then, from this inequality, there must exist an encoder such that the closed-loop system is stable and POW (s) < P.…”

Section: A Single Encoder and Inequalities For Stabilizabilitymentioning

confidence: 99%

“…Although these results are nice, they rely heavily on various information theoretic techniques, which are unfamiliar to most researchers in control society, and the resulting complex encoding/decoding schemes are difficult to analyze in traditional control terms such as performances and robustness. In [10] and subsequent work [11], [12], an alternative framework for control system analysis and synthesis with data rate constraints has been established for single-input and single-output LTI systems with Gaussian communication channels. A highlight of this framework lies in its simplicity and intimate relationship with modern control theory.…”

Section: Introductionmentioning

confidence: 99%