FeedNetBack - D03.02 - Control Subject to Transmission Constraints, With Transmission Errors

This is a Deliverable Report for the FeedNetBack project (www.feednetback.eu). It describes the research performed within Work Package 3, Task 3.2 (Control Subject to Transmission Constraints, with Transmission Errors), in the first 36 months of the project. It targets the issue of control subject to transmission constraints with transmission error. This research concerns problems arising from the presence of a noisy communication channel (specified and modeled at the physical layer) within the control loop. The resulting constraints include finite capacities in the transmission of the sensor and/or actuator signals and transmission errors. Our focus is on designing new compression and coding techniques to support networked control in this scenario. This Deliverable extends the analysis provided in the companion Deliverable D03.01, to deal with the effects of noise in communication channel. The quantization schemes described in D03.01, in particular the adaptive ones, might be very sensitive to the presence of even a few errors. Indeed error-correction coding for estimation or control purposes cannot simply exploit classical coding theory and practice, where vanishing error probability is obtained only in the limit of infinite block-length. A first contribution reported in this Deliverable is the construction of families of codes having the any-time property required in this setting, and the analysis of the trade-off between code complexity and performance. Our results consider the binary erasure channel, and can be extended to more general binary-input output-symmetric memoryless channels. The second and third contributions reported in this deliverable deal with the problem of remotely stabilizing linear time invariant (LTI) systems over Gaussian channels. Specifically, in the second contribution we consider a single LTI system which has to be stabilized by remote controller using a network of sensors having average transmit power constraints. We study basic sensor network topologies and provide necessary and sufficient conditions for mean square stabilization. Then in the third contribution, we extend our study to two LTI systems which are to be simultaneously stabilized. In this regard, we study the interesting setups of joint and separate sensing and control. By joint sensing we mean that there exists a common sensor node to simultaneously transmit the sensed state processes of the two plants and by joint control we mean that there is a common controller for both plants. We name these setups as: i) control over multiple-access channel (separate sensors, joint controller setup), ii) control over broadcast channel (common sensor, separate controllers setup), and iii) control over interference channel (separate sensors, separate controllers). We propose to use delay-free linear schemes for these setups and thus obtain sufficient conditions for mean square stabilization. Then, we discuss the joint design of the encoder and the controller. We propose an iterative design procedure for a joint design of the sensor measurement quantization, channel error protection, and controller actuation, with the objective to minimize the expected linear quadratic cost over a finite horizon. Finally, the same as for the noiseless case, we address the issues that arise when not only one plant and one controller are communicating through a channel, but there is a whole network of sensors and actuators. We consider the effects of digital noisy channels on the consensus algorithm, and we present an algorithm which exploits the any-time codes discussed above

Event-Based Control and Estimation with Stochastic Disturbances

This thesis deals with event-based control and estimation strategies, motivated by certain bottlenecks in the control loop. Two kinds of implementation constraints are considered: closing one or several control loops over a data network, and sensors that report measurements only as intervals (e.g. with quantization). The proposed strategies depend critically on _events_, when a data packet is sent or when a change in the measurement signal is received. The value of events is that they communicate new information about stochastic process disturbances. A data network in the control loop imposes constraints on the event timing, modelled as a minimum time between packets. A thresholdbased control strategy is suggested and shown to be optimal for firstorder systems with impulse control. Different ways to find the optimal threshold are investigated for single and multiple control loops sharing one network. The major gain compared to linear time invariant (LTI) control is with a single loop a greatly reduced communication rate, which with multiple loops can be traded for a similarly reduced regulation error. With the bottleneck that sensors report only intervals, both the theoretical and practical control problems become more complex. We focus on the estimation problem, where the optimal solution is known but untractable. Two simplifications are explored to find a realistic state estimator: reformulation to a mixed stochastic/worst case scenario and joint maximum a posteriori estimation. The latter approach is simplified and evaluated experimentally on a moving cart with quantized position measurements controlled by a low-end microcontroller. The examples considered demonstrate that event-based control considerably outperforms LTI control, when the bottleneck addressed is a genuine performance constraint on the latter

Lecture Notes on Network Information Theory

These lecture notes have been converted to a book titled Network Information Theory published recently by Cambridge University Press. This book provides a significantly expanded exposition of the material in the lecture notes as well as problems and bibliographic notes at the end of each chapter. The authors are currently preparing a set of slides based on the book that will be posted in the second half of 2012. More information about the book can be found at http://www.cambridge.org/9781107008731/. The previous (and obsolete) version of the lecture notes can be found at http://arxiv.org/abs/1001.3404v4/

Computational Methods for Nonlinear Optimization Problems: Theory and Applications

This dissertation is motivated by the lack of efficient global optimization techniques for polynomial optimization problems. The objective is twofold. First, a new mathematical foundation for obtaining a global or near-global solution will be developed. Second, several case studies will be conducted on a variety of real-world problems. Global optimization, convex relaxation and distributed computation are at the heart of this PhD dissertation. Some of the specific problems to be addressed in this thesis on both the theory and the application of nonlinear optimization are explained below: Graph theoretic algorithms for low-rank optimization problems: There is a rapidly growing interest in the recovery of an unknown low-rank matrix from limited information and measurements. This problem occurs in many areas of engineering and applied science such as machine learning, control, and computer vision. We develop a graph-theoretic technique in Part I that is able to generate a low-rank solution for a sparse Linear Matrix Inequality (LMI), which is directly applicable to a large set of problems such as low-rank matrix completion with many unknown entries. Our approach finds a solution with a guarantee on its rank, using the recent advances in graph theory. Resource allocation for energy systems: The flows in an electrical grid are described by nonlinear AC power flow equations. Due to the nonlinear interrelation among physical parameters of the network, the feasibility region represented by power flow equations may be nonconvex and disconnected. Since 1962, the nonlinearity of the network constraints has been studied, and various heuristic and local-search algorithms have been proposed in order to perform optimization over an electrical grid [Baldick, 2006; Pandya and Joshi, 2008]. Part II is concerned with finding convex formulations of the power flow equations using semidefinite programming (SDP). The potential of SDP relaxation for problems in power systems has been manifested in [Lavaei and Low, 2012], with further studies conducted in [Lavaei, 2011; Sojoudi and Lavaei, 2012]. A variety of graph-theoretic and algebraic methods are developed in Part II in order to facilitate performing fundamental, yet challenging tasks such as optimal power flow (OPF) problem, security-constrained OPF and the classical power flow problem. Synthesis of distributed control systems: Real-world systems mostly consist of many interconnected subsystems, and designing an optimal controller for them pose several challenges to the field of control theory. The area of distributed control is created to address the challenges arising in the control of these systems. The objective is to design a constrained controller whose structure is specified by a set of permissible interactions between the local controllers with the aim of reducing the computation or communication complexity of the overall controller. It has been long known that the design of an optimal distributed (decentralized) controller is a daunting task because it amounts to an NP-hard optimization problem in general [Witsenhausen, 1968; Tsitsiklis and Athans, 1984]. Part III is devoted to study the potential of the SDP relaxation for the optimal distributed control (ODC) problem Our approach rests on formulating each of different variations of the ODC problem as rank-constrained optimization problems from which SDP relaxations can be derived. As the first contribution, we show that the ODC problem admits a sparse SDP relaxation with solutions of rank at most 3. Since a rank-1 SDP matrix can be mapped back into a globally-optimal controller, the low-rank SDP solution may be deployed to retrieve a near-global controller. Parallel computation for sparse semidefinite programs: While small- to medium-sized semidefinite programs are efficiently solvable by second-order-based interior point methods in polynomial time up to any arbitrary precision [Vandenberghe and Boyd, 1996a], these methods are impractical for solving large-scale SDPs due to computation time and memory issues. In Part IV of this dissertation, a parallel algorithm for solving an arbitrary SDP is introduced based on the alternating direction method of multipliers. The proposed algorithm has a guaranteed convergence under very mild assumptions. Each iteration of this algorithm has a simple closed-form solution, and consists of scalar multiplication and eigenvalue decomposition over matrices whose sizes are not greater than the treewdith of the sparsity graph of the SDP problem. The cheap iterations of the proposed algorithm enable solving real-world large-scale conic optimization problems

Design and Real-World Evaluation of Dependable Wireless Cyber-Physical Systems

The ongoing effort for an efficient, sustainable, and automated interaction between humans, machines, and our environment will make cyber-physical systems (CPS) an integral part of the industry and our daily lives. At their core, CPS integrate computing elements, communication networks, and physical processes that are monitored and controlled through sensors and actuators. New and innovative applications become possible by extending or replacing static and expensive cable-based communication infrastructures with wireless technology. The flexibility of wireless CPS is a key enabler for many envisioned scenarios, such as intelligent factories, smart farming, personalized healthcare systems, autonomous search and rescue, and smart cities. High dependability, efficiency, and adaptivity requirements complement the demand for wireless and low-cost solutions in such applications. For instance, industrial and medical systems should work reliably and predictably with performance guarantees, even if parts of the system fail. Because emerging CPS will feature mobile and battery-driven devices that can execute various tasks, the systems must also quickly adapt to frequently changing conditions. Moreover, as applications become ever more sophisticated, featuring compact embedded devices that are deployed densely and at scale, efficient designs are indispensable to achieve desired operational lifetimes and satisfy high bandwidth demands. Meeting these partly conflicting requirements, however, is challenging due to imperfections of wireless communication and resource constraints along several dimensions, for example, computing, memory, and power constraints of the devices. More precisely, frequent and correlated message losses paired with very limited bandwidth and varying delays for the message exchange significantly complicate the control design. In addition, since communication ranges are limited, messages must be relayed over multiple hops to cover larger distances, such as an entire factory. Although the resulting mesh networks are more robust against interference, efficient communication is a major challenge as wireless imperfections get amplified, and significant coordination effort is needed, especially if the networks are dynamic. CPS combine various research disciplines, which are often investigated in isolation, ignoring their complex interaction. However, to address this interaction and build trust in the proposed solutions, evaluating CPS using real physical systems and wireless networks paired with formal guarantees of a system’s end-to-end behavior is necessary. Existing works that take this step can only satisfy a few of the abovementioned requirements. Most notably, multi-hop communication has only been used to control slow physical processes while providing no guarantees. One of the reasons is that the current communication protocols are not suited for dynamic multi-hop networks. This thesis closes the gap between existing works and the diverse needs of emerging wireless CPS. The contributions address different research directions and are split into two parts. In the first part, we specifically address the shortcomings of existing communication protocols and make the following contributions to provide a solid networking foundation: • We present Mixer, a communication primitive for the reliable many-to-all message exchange in dynamic wireless multi-hop networks. Mixer runs on resource-constrained low-power embedded devices and combines synchronous transmissions and network coding for a highly scalable and topology-agnostic message exchange. As a result, it supports mobile nodes and can serve any possible traffic patterns, for example, to efficiently realize distributed control, as required by emerging CPS applications. • We present Butler, a lightweight and distributed synchronization mechanism with formally guaranteed correctness properties to improve the dependability of synchronous transmissions-based protocols. These protocols require precise time synchronization provided by a specific node. Upon failure of this node, the entire network cannot communicate. Butler removes this single point of failure by quickly synchronizing all nodes in the network without affecting the protocols’ performance. In the second part, we focus on the challenges of integrating communication and various control concepts using classical time-triggered and modern event-based approaches. Based on the design, implementation, and evaluation of the proposed solutions using real systems and networks, we make the following contributions, which in many ways push the boundaries of previous approaches: • We are the first to demonstrate and evaluate fast feedback control over low-power wireless multi-hop networks. Essential for this achievement is a novel co-design and integration of communication and control. Our wireless embedded platform tames the imperfections impairing control, for example, message loss and varying delays, and considers the resulting key properties in the control design. Furthermore, the careful orchestration of control and communication tasks enables real-time operation and makes our system amenable to an end-to-end analysis. Due to this, we can provably guarantee closed-loop stability for physical processes with linear time-invariant dynamics. • We propose control-guided communication, a novel co-design for distributed self-triggered control over wireless multi-hop networks. Self-triggered control can save energy by transmitting data only when needed. However, there are no solutions that bring those savings to multi-hop networks and that can reallocate freed-up resources, for example, to other agents. Our control system informs the communication system of its transmission demands ahead of time so that communication resources can be allocated accordingly. Thus, we can transfer the energy savings from the control to the communication side and achieve an end-to-end benefit. • We present a novel co-design of distributed control and wireless communication that resolves overload situations in which the communication demand exceeds the available bandwidth. As systems scale up, featuring more agents and higher bandwidth demands, the available bandwidth will be quickly exceeded, resulting in overload. While event-triggered control and self-triggered control approaches reduce the communication demand on average, they cannot prevent that potentially all agents want to communicate simultaneously. We address this limitation by dynamically allocating the available bandwidth to the agents with the highest need. Thus, we can formally prove that our co-design guarantees closed-loop stability for physical systems with stochastic linear time-invariant dynamics.:Abstract Acknowledgements List of Abbreviations List of Figures List of Tables 1 Introduction 1.1 Motivation 1.2 Application Requirements 1.3 Challenges 1.4 State of the Art 1.5 Contributions and Road Map 2 Mixer: Efficient Many-to-All Broadcast in Dynamic Wireless Mesh Networks 2.1 Introduction 2.2 Overview 2.3 Design 2.4 Implementation 2.5 Evaluation 2.6 Discussion 2.7 Related Work 3 Butler: Increasing the Availability of Low-Power Wireless Communication Protocols 3.1 Introduction 3.2 Motivation and Background 3.3 Design 3.4 Analysis 3.5 Implementation 3.6 Evaluation 3.7 Related Work 4 Feedback Control Goes Wireless: Guaranteed Stability over Low-Power Multi-Hop Networks 4.1 Introduction 4.2 Related Work 4.3 Problem Setting and Approach 4.4 Wireless Embedded System Design 4.5 Control Design and Analysis 4.6 Experimental Evaluation 4.A Control Details 5 Control-Guided Communication: Efficient Resource Arbitration and Allocation in Multi-Hop Wireless Control Systems 5.1 Introduction 5.2 Problem Setting 5.3 Co-Design Approach 5.4 Wireless Communication System Design 5.5 Self-Triggered Control Design 5.6 Experimental Evaluation 6 Scaling Beyond Bandwidth Limitations: Wireless Control With Stability Guarantees Under Overload 6.1 Introduction 6.2 Problem and Related Work 6.3 Overview of Co-Design Approach 6.4 Predictive Triggering and Control System 6.5 Adaptive Communication System 6.6 Integration and Stability Analysis 6.7 Testbed Experiments 6.A Proof of Theorem 4 6.B Usage of the Network Bandwidth for Control 7 Conclusion and Outlook 7.1 Contributions 7.2 Future Directions Bibliography List of Publication