Control With Minimal Cost-Per-Symbol Encoding and Quasi-Optimality of Event-Based Encoders

Pearson, Justin; Hespanha, João P.; Liberzon, Daniel

doi:10.1109/tac.2016.2604921

Cited by 53 publications

(58 citation statements)

References 15 publications

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“…which is the uncertainty set of z 1 (t c,1 ) given t s,1 for the differential equationż 1 = λz 1 . By comparing the definitions of the sets Ω(z(t c,1 )|t s,1 ) and Y 1 , we have (42), event-triggering strategy (5), and event-triggering function (43). For the j th Jordan block choose the following sequence of design parameters…”

Section: Extension To the Vector Systemsmentioning

confidence: 99%

The Value of Timing Information in Event-Triggered Control

Khojasteh

Tallapragada

Cortés

et al. 2020

IEEE Trans. Automat. Contr.

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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in the communication channel causes information loss, as it makes the state information available at the controller out of date.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 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. Index TermsData-rate theorem, event-triggered control, control under communication constraints, quantized control I. INTRODUCTIONCyber-physical systems (CPS) are engineering systems that integrate computing, communication, and control. They arise in a wide range of areas such as robotics, energy, civil infrastructure, manufacturing, and transportation [3], [4]. Due to the need for tight integration of different components, requirements and time scales, the modeling, analysis, and design of CPS present new challenges. One key aspect is the presence of finite-rate, digital communication channels in the feedback loop. Data-rate theorems quantify the effect that communication has on stabilization by stating that the communication rate available in the feedback loop should be at least as large as the intrinsic entropy rate of the system (corresponding to the sum of the logarithms of the unstable modes). In this way, the controller can compensate for the expansion of the state occurring during the communication process. Early formulations of data-rate theorems appeared in [5]-[7], followed by the key contributions in [8], [9]. More recent extensions include time-varying rate, Markovian, erasure, additive white and colored Gaussian, and multiplicative noise feedback communication channels [10]-[16], formulations for nonlinear systems [17]-[19], for optimal control [20]-[22], for systems with random parameters [23]-[26], and for switching systems [27]-[29]. Connections with information theory are highlighted in [19], [30]-[33]. Extended surveys of the literature appear in [34], [35] and in the book [36].Another key aspect of CPS to which we pay special attention he...

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Section: Extension To the Vector Systemsmentioning

confidence: 99%

The Value of Timing Information in Event-Triggered Control

Khojasteh

Tallapragada

Cortés

et al. 2020

IEEE Trans. Automat. Contr.

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“…Second, we prove that the symmetric threshold sampling policy (13) in Theorem 1 can be reduced to (15)…”

Section: Proof Of Theoremmentioning

confidence: 98%

“…Under the symmetric threshold sampling policy (13), the MMSE decoding policy in (8) can be expanded as, for τ i ≤ t < τ i+1 ,…”

Section: B Proof Of Corollary 11mentioning

confidence: 99%

Optimal Causal Rate-Constrained Sampling of the Wiener Process

Guo

Kostina

2019

2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Consider the following communication scenario. An encoder observes a stochastic process and causally decides when and what to transmit about it, under a constraint on bits transmitted per second. A decoder uses the received codewords to causally estimate the process in real time. We aim to find the optimal encoding and decoding policies that minimize the end-to-end estimation mean-square error under the rate constraint. For * N. Guo and V. Kostina are with the

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“…Similar ideas seem to extend also to the case of delayed packet arrivals, and are left for future research. ACKNOWLEDGMENT A. Khina thanks M. J. Khojasteh and M. Franceschetti for many stimulating and helpful discussions, and especially for introducing him to event-triggered control and pointing his attention to [9]- [12].…”

Section: E Delayed Arrivals and Acknowledgmentsmentioning

confidence: 99%

Algorithms for optimal control with fixed-rate feedback

Khina

Nakahira

et al. 2017

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

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We consider a discrete-time linear quadratic Gaussian networked control setting where the (full information) observer and controller are separated by a fixed-rate noiseless channel. The minimal rate required to stabilize such a system has been well studied. However, for a given fixed rate, how to quantize the states so as to optimizeperformance is an open question of great theoretical and practical significance. We concentrate on minimizing the control cost for first-order scalar systems. To that end, we use the Lloyd-Max algorithm and leverage properties of logarithmically-concave functions and sequential Bayesian filtering to construct the optimal quantizer that greedily minimizes the cost at every time instant. By connecting the globally optimal scheme to the problem of scalar successive refinement, we argue that its gain over the proposed greedy algorithm is negligible. This is significant since the globally optimal scheme is often computationally intractable. All the results are proven for the more general case of disturbances with logarithmically-concave distributions and rate-limited time-varying noiseless channels. We further extend the framework to event-triggered control by allowing to convey information via an additional "silent symbol", i.e., by avoiding transmitting bits; by constraining the minimal probability of silence we attain a tradeoff between the transmission rate and the control cost for rates below one bit per sample.

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Control With Minimal Cost-Per-Symbol Encoding and Quasi-Optimality of Event-Based Encoders

Cited by 53 publications

References 15 publications

The Value of Timing Information in Event-Triggered Control

The Value of Timing Information in Event-Triggered Control

Optimal Causal Rate-Constrained Sampling of the Wiener Process

Algorithms for optimal control with fixed-rate feedback

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