132 research outputs found

    Stabilizing a System with an Unbounded Random Gain Using Only Finitely Many Bits

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    We study the stabilization of an unpredictable linear control system where the controller must act based on a rate-limited observation of the state. More precisely, we consider the system X_(n+1) = A_n X_n +W_n –U_n, where the A_n's are drawn independently at random at each time n from a known distribution with unbounded support, and where the controller receives at most R bits about the system state at each time from an encoder. We provide a time-varying achievable strategy to stabilize the system in a second-moment sense with fixed, finite R. While our previous result provided a strategy to stabilize this system using a variable-rate code, this work provides an achievable strategy using a fixed-rate code. The strategy we employ to achieve this is time-varying and takes different actions depending on the value of the state. It proceeds in two modes: a normal mode (or zoom-in), where the realization of A_n is typical, and an emergency mode (or zoom-out), where the realization of A_n is exceptionally large

    Stabilizing a System with an Unbounded Random Gain Using Only Finitely Many Bits

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    We study the stabilization of an unpredictable linear control system where the controller must act based on a rate-limited observation of the state. More precisely, we consider the system X_(n+1) = A_n X_n +W_n –U_n, where the A_n's are drawn independently at random at each time n from a known distribution with unbounded support, and where the controller receives at most R bits about the system state at each time from an encoder. We provide a time-varying achievable strategy to stabilize the system in a second-moment sense with fixed, finite R. While our previous result provided a strategy to stabilize this system using a variable-rate code, this work provides an achievable strategy using a fixed-rate code. The strategy we employ to achieve this is time-varying and takes different actions depending on the value of the state. It proceeds in two modes: a normal mode (or zoom-in), where the realization of A_n is typical, and an emergency mode (or zoom-out), where the realization of A_n is exceptionally large

    Exact minimum number of bits to stabilize a linear system

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    We consider an unstable scalar linear stochastic system, X_(n + 1) = aX_n + Z_n – U_n.; where a ≥ 1 is the system gain, Z_n's are independent random variables with bounded α-th moments, and U_n'S are the control actions that are chosen by a controller who receives a single element of a finite set {1, …, M} as its only information about system state X_i. We show that M = [a] + 1 is necessary and sufficient for ß- moment stability, for any ß < a. Our achievable scheme is a uniform quantizer of the zoom-in / zoom-out type. We analyze its performance using probabilistic arguments. We prove a matching converse using information-theoretic techniques. Our results generalize to vector systems, to systems with dependent Gaussian noise, and to the scenario in which a small fraction of transmitted messages is lost

    Mini-Workshop: Entropy, Information and Control

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    This mini-workshop was motivated by the emerging field of networked control, which combines concepts from the disciplines of control theory, information theory and dynamical systems. Many current approaches to networked control simplify one or more of these three aspects, for instance by assuming no dynamical disturbances, or noiseless communication channels, or linear dynamics. The aim of this meeting was to approach a common understanding of the relevant results and techniques from each discipline in order to study the major, multi-disciplinary problems in networked control

    Exact minimum number of bits to stabilize a linear system

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    We consider an unstable scalar linear stochastic system, X_(n + 1) = aX_n + Z_n – U_n.; where a ≥ 1 is the system gain, Z_n's are independent random variables with bounded α-th moments, and U_n'S are the control actions that are chosen by a controller who receives a single element of a finite set {1, …, M} as its only information about system state X_i. We show that M = [a] + 1 is necessary and sufficient for ß- moment stability, for any ß < a. Our achievable scheme is a uniform quantizer of the zoom-in / zoom-out type. We analyze its performance using probabilistic arguments. We prove a matching converse using information-theoretic techniques. Our results generalize to vector systems, to systems with dependent Gaussian noise, and to the scenario in which a small fraction of transmitted messages is lost
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