Stochastic Stability of Event-triggered Anytime Control

We investigate control of a non-linear process when communication and processing capabilities are limited. The sensor communicates with a controller node through an erasure channel which introduces i.i.d. packet dropouts. Processor availability for control is random and, at times, insufficient to calculate plant inputs. To make efficient use of communication and processing resources, the sensor only transmits when the plant state lies outside a bounded target set. Control calculations are triggered by the received data. If a plant state measurement is successfully received and while the processor is available for control, the algorithm recursively calculates a sequence of tentative plant inputs, which are stored in a buffer for potential future use. This safeguards for time-steps when the processor is unavailable for control. We derive sufficient conditions on system parameters for stochastic stability of the closed loop and illustrate performance gains through numerical studies.Comment: IEEE Transactions on Automatic Control, under revie

Performance analysis with network-enhanced complexities: On fading measurements, event-triggered mechanisms, and cyber attacks

Copyright © 2014 Derui Ding et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Nowadays, the real-world systems are usually subject to various complexities such as parameter uncertainties, time-delays, and nonlinear disturbances. For networked systems, especially large-scale systems such as multiagent systems and systems over sensor networks, the complexities are inevitably enhanced in terms of their degrees or intensities because of the usage of the communication networks. Therefore, it would be interesting to (1) examine how this kind of network-enhanced complexities affects the control or filtering performance; and (2) develop some suitable approaches for controller/filter design problems. In this paper, we aim to survey some recent advances on the performance analysis and synthesis with three sorts of fashionable network-enhanced complexities, namely, fading measurements, event-triggered mechanisms, and attack behaviors of adversaries. First, these three kinds of complexities are introduced in detail according to their engineering backgrounds, dynamical characteristic, and modelling techniques. Then, the developments of the performance analysis and synthesis issues for various networked systems are systematically reviewed. Furthermore, some challenges are illustrated by using a thorough literature review and some possible future research directions are highlighted.This work was supported in part by the National Natural Science Foundation of China under Grants 61134009, 61329301, 61203139, 61374127, and 61374010, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Linear control of the Pendubot over packet-drop networks

In this thesis we investigate control across stochastic drop-out channels. We seek optimal linear controllers for mean-square stability that make use of the knowledge of whether a packet is received. We establish a fundamental bound on drop-out probability allowable for stabilization, which in some cases is tight. When tight, a convex optimization provides controller design. The main result is a remote stabilization technique that always achieves this bound via acknowledgement from the actuation receiver. Controller information structure and decentralization issues are considered. The theory is then applied to the inverted pendulum experiment Pendubot. The Pendubot is a nonlinear plant that balances the links of an inverted pendulum via a control torque and optical sensors for position. A control strategy is developed using the stabilization technique derived above together with linearization and discretization of the apparatus. The complete design procedure is documented leading to a successful controller. Included are the encountered hardware issues, software issues in Matlab and C programming, theoretical issues, and experiment results. A mock drop-out network is simulated via C programming. The experiments validate that the theoretical design technique actually works, and that the theoretical bounds on allowable drop-out have significant practical bearing

Information-theoretic approach to the study of control systems

We propose an information-theoretic framework for analyzing control systems based on the close relationship of controllers to communication channels. A communication channel takes an input state and transforms it into an output state. A controller, similarly, takes the initial state of a system to be controlled and transforms it into a target state. In this sense, a controller can be thought of as an actuation channel that acts on inputs to produce desired outputs. In this transformation process, two different control strategies can be adopted: (i) the controller applies an actuation dynamics that is independent of the state of the system to be controlled (open-loop control); or (ii) the controller enacts an actuation dynamics that is based on some information about the state of the controlled system (closed-loop control). Using this communication channel model of control, we provide necessary and sufficient conditions for a system to be perfectly controllable and perfectly observable in terms of information and entropy. In addition, we derive a quantitative trade-off between the amount of information gathered by a closed-loop controller and its relative performance advantage over an open-loop controller in stabilizing a system. This work supplements earlier results [H. Touchette, S. Lloyd, Phys. Rev. Lett. 84, 1156 (2000)] by providing new derivations of the advantage afforded by closed-loop control and by proposing an information-based optimality criterion for control systems. New applications of this approach pertaining to proportional controllers, and the control of chaotic maps are also presented.Comment: 18 pages, 7 eps figure

Stabilization of Linear Systems Over Gaussian Networks

The problem of remotely stabilizing a noisy linear time invariant plant over a Gaussian relay network is addressed. The network is comprised of a sensor node, a group of relay nodes and a remote controller. The sensor and the relay nodes operate subject to an average transmit power constraint and they can cooperate to communicate the observations of the plant's state to the remote controller. The communication links between all nodes are modeled as Gaussian channels. Necessary as well as sufficient conditions for mean-square stabilization over various network topologies are derived. The sufficient conditions are in general obtained using delay-free linear policies and the necessary conditions are obtained using information theoretic tools. Different settings where linear policies are optimal, asymptotically optimal (in certain parameters of the system) and suboptimal have been identified. For the case with noisy multi-dimensional sources controlled over scalar channels, it is shown that linear time varying policies lead to minimum capacity requirements, meeting the fundamental lower bound. For the case with noiseless sources and parallel channels, non-linear policies which meet the lower bound have been identified

Advances in Bosonic Quantum Error Correction with Gottesman-Kitaev-Preskill Codes: Theory, Engineering and Applications

Encoding quantum information into a set of harmonic oscillators is considered a hardware efficient approach to mitigate noise for reliable quantum information processing. Various codes have been proposed to encode a qubit into an oscillator -- including cat codes, binomial codes and Gottesman-Kitaev-Preskill (GKP) codes. These bosonic codes are among the first to reach a break-even point for quantum error correction. Furthermore, GKP states not only enable close-to-optimal quantum communication rates in bosonic channels, but also allow for error correction of an oscillator into many oscillators. This review focuses on the basic working mechanism, performance characterization, and the many applications of GKP codes, with emphasis on recent experimental progress in superconducting circuit architectures and theoretical progress in multimode GKP qubit codes and oscillators-to-oscillators (O2O) codes. We begin with a preliminary continuous-variable formalism needed for bosonic codes. We then proceed to the quantum engineering involved to physically realize GKP states. We take a deep dive into GKP stabilization and preparation in superconducting architectures and examine proposals for realizing GKP states in the optical domain (along with a concise review of GKP realization in trapped-ion platforms). Finally, we present multimode GKP qubits and GKP-O2O codes, examine code performance and discuss applications of GKP codes in quantum information processing tasks such as computing, communication, and sensing.Comment: 77+5 pages, 31 figures. Minor bugs fixed in v2. comments are welcome

On linear encoder-decoder design for multi-sensor state estimation subject to quantization noise and channel erasure

We consider remote state estimation of a scalar stationary linear Gauss-Markov process observed via noisy measurements obtained by two sensors. The sensors can construct a causal linear function of their measurements, which are quantized and transmitted to a decoder (or fusion centre (FC)) over channels which are prone to packet erasures. We design linear encoding and decoding strategies for estimating the state of the linear system that allow improved estimation performance in the presence of packet erasures and quantization errors. To this end, we construct and compare various distributed encoding and decoding methods without any feedback from the FC regarding the channel erasures. We also design various decentralized benchmark methods that either assume perfect feedback from the FC or in addition co-location of the two sensors resulting in a centralized scheme with diversity. These benchmark methods provide various lower bounds for the distributed encoding-decoding schemes designed without feedback. Numerical results indicate i) that optimal decentralized design of the encoders and the decoder in the absence of feedback can provide a remote state estimation performance that is comparable to those achieved by the lower bounds (with feedback) particularly when the sensors are identical and their channels are symmetric, and (ii) a little feedback from the decoder can improve the performance considerably when the channels are asymmetric (i.e. the packet erasure probabilities are unequal)