Online Seminar on Control and Information
Date
Speaker Title and Abstract
2021-03-08
5:30 PM CET
via Zoom
Alexander Pogromsky
(Dynamics and Control Group,
Department of Mechanical Engineering, Eindhoven University of Technology)

Title
Data Rate Limits for the Remote State Estimation Problem
Abstract : The past few decades have witnessed a substantially growing attention to networked control systems and related problems of control and/or state estimation via communication channels with constrained bit-rates.
One of the fundamental concerns in this context is to find a minimal data rate between the communication peers under which remote state estimation is feasible; in other words, the receiver is able to reconstruct the current state of the remote system in the real time regime if and only if data about this state is updated by means of a bit flow whose intensity exceeds that “threshold” rate. Loosely speaking, this communication rate has to exceed the rate at which the system “generates information”, while the latter concept is classically formalized in a form of entropy-like characteristic of the dynamical system at hands. The related mathematical results are usually referred to as Data Rate Theorems. Keeping in mind relevance of communication constraints in modern control engineering, constructive methods to compute or finely estimate those entropy-like characteristics take on crucial not only theoretical but also practical importance.
The primary goal of the talk is to present an approach to a solution of the bit-rate constrained remote observation problem along with the tight estimates of a particular version of the entropy-like characteristic, the so called restoration entropy. The talk will focus on upper and lower estimates of the restoration entropy derived by the second  Lyapunov method.

2021-03-15
5:30 PM CET
Alexander L. Fradkov and Boris R. Andrievskii
(Institute for Problems of Mechanical Engineering of RAS, St. Petersburg, Russia)

Seminar Slides (part I / part II)

Title:
Synchronization and State Estimation of Nonlinear Physical Systems under Communication Constraints
Abstract: An exposition of the results on synchronization and state estimation of nonlinear systems over the limited-band communication channel is given. Relevance of passifiability condition for controlled synchronization of master-slave nonlinear systems for first order and full-order coder/decoder pairs is demonstrated. The algorithm for state estimation of spatially distributed systems based on the local measurements and quantization of the transmitted data is developed, and its limit opportunities are studied. The numerical and experimental results for various physical systems are presented. They  demonstrate practical applicability of the theoretical statements and high efficiency of the proposed estimation and synchronization schemes.

2021-03-22
5:30 PM CET
Raphaël Jungers

(Université Catholique de Louvain)

Title:
Quantized Control of Switched Linear Systems
Abstract: Network Control Systems have found applications in a broad range of areas, like intelligent transportation, remote surgery, IoT, etc. Due to the digital nature of the network, all data must be quantized before transmission, resulting in quantization error that can affect the performance of the observing/controlling scheme. Consequently, a major challenge in the design of such networked systems is to determine the minimal communication data rate required to achieve a given control objective. Despite the increasing attention devoted to quantized control in the last decades, the topic seems to have not received much attention in the case of switched and hybrid systems until very recently. In this work, we study the question of finite data-rate control for the class of switched linear systems, i.e., systems described by a finite set of linear modes, among which the system can switch over time. We focus on both theoretical and practical aspects of this issue: we provide necessary and sufficient conditions, which combine the data rate of the controller and the switching parameters of the system, to achieve stabilization. Moreover, we describe practical implementations of controllers that stabilize the system, and whose data rate can be arbitrarily close to the optimal data rate. Finally, we will present numerical examples and perspectives for future research in this field.

2021-03-29
5:30 PM CET
Luca Schenato (University of Padova, Italy)

Title:
Control over Wireless: An Unfinished Journey
Abstract: The proliferation of large scale smart multi-agent systems, also known as Internet-of-Things, Networked Control Systems, Wireless sensor and actuator networks, Cyber-physical Systems, etc., are the pillars of the so-called fourth industrial revolution referred as Industry 4.0. In particular the need for small, reconfigurable, mobile industrial robots in the foreseen future smart factories calls for a more extensive use of wireless communication not only to collect data for off-line monitoring and predictive maintenance, but also for real-time control in machine-to-machine and human-robot interaction. The interplay between wireless communication and control has created great enthusiasm in both control and communication community in the past 15 years and a wealth of theoretical results have appeared. Nonetheless, wireless communication for control in the industrial realm is still limited, with the notable exception of the process industry and smart building, where control bandwidth requirements are not very high. In this talk I will review some of the fundamental theoretical results obtained in the field of control over wireless, and I will try to suggest some of the reasons for its limited adoption in high-bandwidth applications in industrial scenarios. I will also present our current effort in bridging the gap between theory and practice and I will show preliminary theoretical and experimental results on how off-the-shelf Wi-Fi communication paired with model-based control tools can potentially bridge this gap.

2021-04-12
5:30 PM CET
(Massachusetts Institute of Technology)

Title:
Event-Triggered Stabilization over Digital channels
Abstract: In many cyber-physical systems (CPS), control occurs under communication constraints, where observations are corrupted by noise and subjected to delay. Data-rate theorems represent a cornerstone of CPS theory and have been studied for more than two decades. These theorems essentially state that the minimum communication rate to achieve stabilization is equal to the plant's entropy rate. On the other hand, the need to use distributed resources efficiently in CPS has led to event-triggering control techniques based on the idea of sending information opportunistically between the controller and the plant. After reviewing the basics of the data rate theorems, we illustrate how they are to be modified in the presence of an event-triggered implementation. In the same way that subsequent pauses in spoken language are used to convey information, it is also possible to transmit information in communication networks not only by message content but also with its timing. In this talk, we discuss how event-triggering strategies provide timing information by transmitting in a state-dependent fashion. In fact, the event-triggering paradigm brings a new perspective, leading to insights on the information-theoretic value of timing in communication that can be used for control. We will conclude the talk by discussing some open problems.

2021-04-19
5:30 PM CET
Daniel Liberzon
(University of Illinois at Urbana-Champaign)

Title: Estimation entropy for nonlinear and switched systems
Abstract: In this talk we will discuss estimation entropy for continuous-time nonlinear systems, which is a variant of topological entropy formulated in terms of the number of functions that approximate all system trajectories up to an exponentially decaying error. We will establish an upper bound on the estimation entropy in terms of the sum of the desired convergence rate and the system's expansion rate multiplied by the system dimension, as well as a lower bound. We will describe an iterative procedure that uses quantized and sampled state measurements to generate state estimates that converge to the true state at the desired exponential rate. The average bit rate utilized by this procedure matches the derived upper bound on the estimation entropy, and no other algorithm of this type can perform the same estimation task with bit rates lower than the estimation entropy. As an application of this estimation procedure, we will study the problem of determining, from quantized state measurements, which of two competing models of a dynamical system is the true model. We will show that under a mild assumption of exponential separation of the candidate models, detection always happens in finite time. Recent work on entropy of switched systems will also be discussed.

2021-04-26
5:30 PM CET
Nicolas Garcia (Queen's University)

Title:
Ergodicity and Asymptotic Stationarity of Controlled Stochastic Nonlinear Systems under Information Constraints
Abstract: The presence of real-world scenarios where controllers must make control decisions with quantized or noisy state information has motivated the subfield of control under communication constraints. For stochastic systems, an important problem is to characterize the smallest data rate or channel capacity above which stabilization is possible. This problem has been extensively studied for linear (noiseless and stochastic) systems, with a reoccurring theme being the characterization of the minimum data rate as the log-sum of the unstable eigenvalues. For non-linear stochastic systems, however, the problem has not been extensively studied. In this talk, we present several converse results, in the form of lower bounds necessary for ergodic and AMS (asymptotic mean stationarity) stabilization for discrete-time non-linear stochastic systems. These results were established using a modification of invariance entropy for the case of systems with noise, which will be discussed in detail. For noiseless systems, invariance entropy characterizes the difficulty of rendering a subset of the state space invariant, based on the number of open-loop control sequences required to do so. This idea is applied for the stochastic case, where we relax the control objective to probabilistic invariance. This notion, combined with a volume growth approach, is used to obtain the results. Comparison with information theoretic methods will also be made. Although the talk will mostly focus on systems controlled over noiseless channels, the noisy channel case will be briefly mentioned.

2021-05-03
5:30 PM CET
Photius Stavrou (KTH-Stockholm)

Title:
Structural Solutions via Optimal Reverse-Waterfilling Algorithms in Low-Delay Quantized MMSE State Estimation
Abstract: Tatikonda, Sahai Mitter in their landmark work in 2004, studied the performance analysis and synthesis of a single loop NCS using a stochastic linear plant driven by a Gaussian noise process when the performance criterion is the classical LQG cost. A primary result therein was a control theoretic separation principle between the control and the quantized state estimation (communication) problem that bridges the connection of performance analysis and synthesis of a closed-loop control system with nonanticipative rate distortion theory. Inspired by this result, the last fifteen years many researchers used information theoretic tools to either study performance limitations of a stochastic linear control problem under communication constraints or their low delay quantized MMSE state estimation counterparts. In this presentation, we first give an overview of some relevant results on the performance limitations of closed-loop control systems under information theoretic constraints. Then, we focus on the quantized MMSE state estimation problem of a closed-loop control network to obtain the following new results. (i) We derive strong structural properties on a time-invariant multivariate Gauss-Markov processes that allow to obtain optimally lower bounds on the empirical rates via a reverse-waterfilling algorithm. We also implement an iterative scheme to numerically compute the reverse-waterfilling algorithm and show via simulations that it is computationally much less expensive in addition to being scalable compared to general solvers of the problem like semidefinite programming algorithm.  (ii) We consider the problem of time-invariant partially observable multivariate Gaussian processes and derive a new characterization of the lower bound on the empirical rates and the corresponding optimal realization for jointly Gaussian processes. This characterization is subsequently solved by once again assuming strong structural properties on the partially observable multivariate Gaussian process. The solution reveals a non-trivial reverse-waterfilling algorithm which demonstrates that the distortion allocation at each dimension can be computed by a third-degree polynomial equation.  Subsequently, we present an iterative scheme that solves this structural problem optimally. We corroborate our results with some numerical simulations. A new optimal closed form expression for the lower bound is also provided for scalar Gaussian processes. We note that for both (i), (ii), we briefly explain the corresponding upper bound solutions on the empirical rates and discuss open questions that stem from our results.  If time permits, we will discuss a lower bound on the low delay quantized MMSE state estimation problem with causal side information at the encoder/decoder or only at the decoder which makes sense in that it further improves the LQG cost of control.

2021-05-10
5:30 PM CET
Oron Sabag (Caltech)

Title:
Regret-based Control and Finding the Feedback Capacity of Gaussian channels with Control Methods
Abstract: This talk is planned to have two parts:
First, I will present a channel capacity problem that attracted much attention in information theory that we recently solved using tools from control theory and convex optimization. Consider a communication channel with additive Gaussian noise (AGN) and the channel outputs fed back to the transmitter, that is, a channel with feedback. The channel capacity is the fundamental quantity that characterizes the maximal rate at which a transmitter can convey information to a receiver. When the additive Gaussian noise is white, the feedback capacity is characterized by the well-known formula C = 0.5 \log (1+SNR). However, when the Gaussian noise is not white, i.e., its instances across time are correlated, finding an explicit capacity expression is not trivial due to the memory inherited from the noise process to the optimal channel inputs and outputs distributions. The main result is a closed-form formula for the feedback capacity given by a convex optimization problem in the general case where: the channel noise is generated by any linear state-space (under mild conditions) and a channel that may have multiple inputs and multiple outputs (MIMO).

In the second part, I will talk about regret as a new criterion in classical control and filtering problems. Motivated by learning theory, we utilize regret defined as the costs difference between a practical system to be designed and a superior system that cannot be implemented in practice. The comparative nature of the regret allows one to design systems that minimize their cost with respect to a more adaptive benchmark. In the full-information control setting, our regret compares the linear quadratic regulator (LQR) costs of a causal controller (that has only access to past and current disturbances) and a clairvoyant one (that has also access to future disturbances). In the case of a linear plant, we derive an explicit formula for the optimal regret and derive an explicit regret-optimal controller. Surprisingly, the regret-optimal controller is a sum of the classical $H_2$ control law and an additional controller obtained from a solution to a Nehari problem. This additional controller is the one that enables the regret-optimal controller to maintain as close as possible distance to the performance of the non-causal controller. Simulations demonstrate that the regret-optimal controller interpolates between the $H_2$ and the $H_\infty$ optimal controllers, and generally has $H_2$ and $H_\infty$ costs that are simultaneously close to their optimal values. The regret-optimal controller thus presents itself as a viable option for systems design. Time permitting, I will present a regret-optimal filter for the classical filtering problem.
The material in this talk is based on joint works with Prof. Victoria Kostina and Prof. Babak Hassibi

2021-05-17
5:30 PM CET
Gireeja Ranade (University of California at Berkeley)

Title:
Control of systems with time-varying random parameters
Abstract: This talk aims to understand and quantify the informational bottlenecks imposed by uncertainty in control system models. Control strategies for systems typically depend on a controller's ability to plan. In this talk, we investigate examples where this ability to plan is limited because the system parameters are random and time-varying. We focus on two cases. In the first case, we explore the impact of uncertain actuation. We will first discuss this in the scalar case and then the vector case. We explore an example of a vector system that builds on the intermittent Kalman Filtering problem and where the stability of the system depends not just on the product of the eigenvalues but also their "distribution". If time permits, we may also explore the case of uncertain sensing, which exhibits different behavior. Here we consider a simple-to-state fundamental but long open scalar problem, where for a scalar system the observer sees the system state multiplied by a random variable --- in this case non-linear strategies can unboundedly outperform linear strategies. Here we will discuss how the use of structured neural-networks can help bridge the gap between the best known converse and achievability for this fundamental problem.

2020-05-24

Hamidreza Tavafoghi
(University of California at Berkeley)

Title:
Toward a Unified Approach to Dynamic Decision Problems with Asymmetric Information
Abstract: We study a general class of dynamic multi-agent decision problems with asymmetric information, where agents’ strategy choices and beliefs are interdependent over time (non-classical information structure). We introduce the notion of sufficient information that effectively compresses the agents’ information in a mutually consistent manner. Accordingly, we propose an information state for each agent that is sufficient for decision-making purposes. For dynamic teams, we present a sequential decomposition and formulate a dynamic program to determine a globally optimal policy via backward induction. For dynamic games, we characterize a class of equilibria called Sufficient Information Based Bayesian Nash Equilibrium (SIB-BNE) and provide a sequential decomposition accordingly.

2020-05-31

Maël Le Treust
(CNRS/
Cergy Paris Université)

Title:
Continuous Random Variable Estimation is not Optimal for the Witsenhausen Counterexample
Abstract: Optimal design of distributed decision policies can be a difficult task, illustrated by the famous Witsenhausen counterexample. In this paper we characterize the optimal control designs for the vector-valued setting assuming that it results in an internal state that can be described by a continuous random variable which has a probability density function. More specifically, we provide a genie-aided outer bound that relies on our previous results for empirical coordination problems. This solution turns out to be not optimal in general, since it consists of a time-sharing strategy between two linear schemes of specific power. It follows that the optimal decision strategy for the original scalar Witsenhausen problem must lead to an internal state that cannot be described by a continuous random variable which has a probability density function.

2020-06-07

Nicola Elia
(University of Minnesota)

Title:
Integration of control and information theory: a 20 year personal account
Abstract: In this talk, we present our latest result on the feedback capacity of MIMO ISI channels with Gaussian colored noise. This long-sought result, made possible by the contributions of many researchers over many years, requires a deep integration of information and control theory concepts. This development brings a new insight in the information theory characterization of LTI feedback control systems.   On the other side of the problem space, there are feedback control problems over communication channels. We will review the fading network framework and present a novel MIMO output feedback controller design methodology applied to packet drop networks.

2020-06-14

Charalambos D. Charalambous

(University of Cyprus)

Title: Capacity of discrete-time unstable stochastic dynamical systems: Interaction of Control, Estimation and Information Transmission
Abstract: This talk is focused on the development of Shannon's operational definition of feedback capacity to stochastic dynamical systems, which may correspond to discrete-time (a) unstable stochastic control systems, and (b) unstable communication channels with memory, subject to cost constraints. In such applications of control and communication systems, encoders are randomized strategies, with a dual role, to simultaneously control the output process and to encode information. The dual role is often captured by the interaction of multiple strategies of control, estimation, and information transmission. The concepts are illustrated through the analysis of Gaussian control systems, with complete and partial information, and Gaussian communication channels driven by unstable versus stable noise. In some applications of Gaussian communication channels with memory, it is demonstrated that unstable noise increases feedback as well as nonfeedback capacity, at no expense of additional power allocated to the transmitter, compared to the stable noise.

2020-06-21

Christoph Kawan
(Ludwig Maximilian University of Munich)

Title: Stabilization of nonlinear deterministic systems over digital channels
Abstract: The data-rate theorem for linear systems has been extended in various directions by various groups of researchers. In their 2004 landmark paper, Nair et al. presented an extension to local stabilization of nonlinear deterministic systems around equilibrium points. In this talk, we take a broader perspective and replace the equilibrium by a compact set Lambda, invariant under a constant control input u_0. To analyze the associated local stabilization problem, we impose a hyperbolicity assumption on Lambda, which allows us to describe the dynamics close to Lambda under small time-dependent deviations from the constant input u_0, by using classical tools from hyperbolic dynamical systems. We use this description to derive a lower bound on the smallest average data rate needed for local stabilization to Lambda in terms of classical quantities from the ergodic theory of smooth dynamical systems. In two extremal cases, we are able to prove that our bound is sharp, i.e. equals the data rate limit. A general data-rate theorem, however, is still missing. As a matter of fact, any generalization of our results via similar methods leads to problems that are known to be difficult and are largely unsolved.

Organizers:
Massimo Franceschetti
Christoph Kawan

Alexey Matveev
Serdar Yüksel

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