Non-coherence in estimation and control

Ranade, Gireeja; Sahai, Anant

doi:10.1109/allerton.2013.6736523

Cited by 16 publications

(10 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note that even in the presence of noisy information about the control direction it is possible to stabilize the system for certain growth rates α. This parallels the result in [14].…”

Section: B Partial Side-informationsupporting

confidence: 78%

“…Surprisingly, the two-step observability result is quite fragile. We know from the arguments in [14] that even a slight continuous uncertainty regarding θ n renders the estimation problem impossible. The error is not shrinking with time.…”

Section: A Spinning Observer: the Estimation Casementioning

confidence: 99%

“…This section draws heavily upon our earlier Allerton paper [14] but helps make the ideas above more concrete. Consider a simple scalar control system with perfect state-observation , so as to stabilize the system.…”

Section: A Scalar Example and Semi-deterministic Storymentioning

confidence: 99%

“…with a continuous density, and X[0] ∼ N (0, 1). We know from [14] that a finite number of bits of side-information regarding the system parameter C[n] do not help us estimate the system or decrease the growth rate of the error by more than a subexponential factor. Side-information is useless in this estimation problem.…”

Section: A Scalar Example and Semi-deterministic Storymentioning

confidence: 99%

See 3 more Smart Citations

Side-information in control and estimation

Ramnarayan

Ranade

Sahai

2014

2014 IEEE International Symposium on Information Theory

Self Cite

View full text Add to dashboard Cite

Abstract-As in portfolio theory, we can think of the value of side-information in a control system as the change in the "growth rate" due to side-information. A scalar counterexample (motivated by carry-free deterministic models) shows the value of side-information for control does not exactly parallel the value of side-information for portfolios. Mutual-information does not seem to be a bound here.The concept is further explored through a spinning vector control system that is re-oriented at each time so that the control or observation direction is partially unknown. The value of sideinformation can be calculated in this setup and it behaves quite differently in a control vs. estimation context. A second example considers the problem of vector control over a (scalar) erasure channel, the dual problem to the estimation problem of intermittent Kalman Filtering. The value of information here is measured through the change in the critical packet-drop probability for the system. While non-causal side-information regarding the packet arrivals does not affect the critical probability for the estimation problem, we find that it can generically be very valuable for the control problem -it seems to change the scaling behavior for the control counterpart to what would be considered the "high SNR limit" in communication problems. I. INTRODUCTIONParameter uncertainty has a long history in control theory -the very idea of robust control is about dealing with it. Recently, the advent of networked control systems has made stochastic uncertainty models more relevant. There is now a real need to have a theory capable of dealing with sideinformation in control. As just one example, control theorists are interested in knowing how networked control systems behave with or without acknowledgements of dropped packets since this is relevant for choosing among practical protocols like TCP vs. UDP [1]. Acknowledgements are a kind of sideinformation about control channel state, but as of now, there is no theoretical guidance for how to think about it in a principled way.Fortunately, such things have long been studied in information theory in the context of unknown fading channels [2]. Medard in [3] examines the effect of imperfect channel knowledge on capacity, and Lapidoth and Shamai quantify the degradation in performance due to channel-state estimation errors by the receiver [4]. Pradhan et al. show that the duality between source and channel coding in fact extends to the case with side-information under certain conditions [5]: this is particularly interesting given the well-known parallel between source coding and portfolio theory, which we will connect to here. Further, Kotagiri and Laneman [6] study the impact of non-causal knowledge of the state in a multiple-access setting. There are many more interesting results as well, but space precludes any serious discussion here.

show abstract

“…Note that even in the presence of noisy information about the control direction it is possible to stabilize the system for certain growth rates α. This parallels the result in [14].…”

Section: B Partial Side-informationsupporting

confidence: 78%

Section: A Spinning Observer: the Estimation Casementioning

confidence: 99%

Section: A Scalar Example and Semi-deterministic Storymentioning

confidence: 99%

Section: A Scalar Example and Semi-deterministic Storymentioning

confidence: 99%

See 2 more Smart Citations

Side-information in control and estimation

Ramnarayan

Ranade

Sahai

2014

2014 IEEE International Symposium on Information Theory

Self Cite

View full text Add to dashboard Cite

show abstract

“…For the first three coordinates of the diagonalized system (19) which are stable the state estimationŝ at the controller simply constructs as follows: s =Ãŝ(t) +Bũ(t) starting fromŝ(0). The unstable mode of the system is as followṡ…”

Section: Event-triggered Designmentioning

confidence: 99%

Event-triggered stabilization of disturbed linear systems over digital channels

Khojasteh

Hedayatpour

Cortés

et al. 2018

2018 52nd Annual Conference on Information Sciences and Systems (CISS)

View full text Add to dashboard Cite

We present an event-triggered control strategy for stabilizing a scalar, continuous-time, time-invariant, linear system over a digital communication channel having bounded delay, and in the presence of bounded system disturbance. We propose an encoding-decoding scheme, and determine lower bounds on the packet size and on the information transmission rate which are sufficient for stabilization. We show that for small values of the delay, the timing information implicit in the triggering events is enough to stabilize the system with any positive rate. In contrast, when the delay increases beyond a critical threshold, the timing information alone is not enough to stabilize the system and the transmission rate begins to increase. Finally, large values of the delay require transmission rates higher than what prescribed by the classic data-rate theorem. The results are numerically validated using a linearized model of an inverted pendulum.Index Terms-Control under communication constraints, event-triggered control, quantized control I. INTRODUCTION Networked control systems (NCS) [1], where the feedback loop is closed over a communication channel, are a fundamental component of cyber-physical systems (CPS) [2], [3]. In this context, data-rate theorems state that the minimum communication rate to achieve stabilization is equal to the entropy rate of the system, expressed by the sum of the logarithms of the unstable modes. Early examples of datarate theorems appeared in [4], [5]. Key later contributions appeared in [6] and [7]. These works consider a "bit-pipe" communication channel, capable of noiseless transmission of a finite number of bits per unit time evolution of the system. Extensions to noisy communication channels are considered in [8]-[12]. Stabilization over time-varying bit-pipe channels, including the erasure channel as a special case, are studied in [13], [14]. Additional formulations include stabilization of systems with random open loop gains over bit-pipe channels [15], stabilization of switched linear systems [16], systems with uncertain parameters [15], [17], multiplicative noise [18], [19], optimal control [20]-[23], and stabilization using event-triggered strategies [24]-[29].This paper focuses on the case of stabilization using eventtriggered communication strategies. In this context, a key observation made in [30] is that if there is no delay in the communication process, there are no system disturbances, and the controller has knowledge of the triggering strategy, then it is possible to stabilize the system with any positive

show abstract

Introduction

2023

Control Over Communication Networks

View full text Add to dashboard Cite

Non-coherence in estimation and control

Cited by 16 publications

References 25 publications

Side-information in control and estimation

Side-information in control and estimation

Event-triggered stabilization of disturbed linear systems over digital channels

Introduction

Contact Info

Product

Resources

About