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 @math , where the @math 's are drawn independently at random at each time @math from a known distribution with unbounded support, and where the controller receives at most @math 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 @math . 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 @math is typical, and an emergency mode (or zoom-out), where the realization of @math is exceptionally large.
We also build on a series of investigations around model unpredictability and multiplicative noise in control systems @cite_1 @cite_19 @cite_10 . In this work, we take a stochastic control approach, which complements the investigations around parameter uncertainty in the robust control literature @cite_12 @cite_18 .
@cite_18 @cite_1 @cite_19 @cite_10 @cite_12
2900806034 2120852651 2739340005 1798863697
Abstract A robust model predictive control (RMPC) approach for linear systems with bounded state-dependent uncertainties is proposed. Such uncertainties can arise from unmodeled non-linearities or external disturbances, for example. By explicitly considering the state dependency of the uncertainty sets in the RMPC approach, it is shown how closed-loop performance can be improved over existing approaches that consider worst-case uncertainty. Being able to handle state-dependent uncertainties is particularly relevant in learning-based MPC where the system model is learned from data and confidence in the model typically varies over the state space. The efficacy of the proposed approach for learning-based RMPC is illustrated with a numerical example, where uncertainty sets are obtained from data using Gaussian Process regression. This paper addresses non-Gaussian statistical modeling of interference as a superposition of a large number of small effects from terminals scatterers distributed in the plane volume according to a Poisson point process. This problem is relevant to multiple access communication systems without power control and radar. Assuming that the signal strength is attenuated over distance r as 1 r m, we show that the interference clutter could be modeled as a spherically symmetric spl alpha -stable noise. A novel approach to stable noise modeling is introduced based on the LePage series representation. This establishes grounds to investigate practical constraints in the system model adopted, such as the finite number of interferers and nonhomogeneous Poisson fields of interferers. In addition, the formulas derived allow us to predict noise statistics in environments with lognormal shadowing and Rayleigh fading. The results obtained are useful for the prediction of noise statistics in a wide range of environments with deterministic and stochastic power propagation laws. Computer simulations are provided to demonstrate the efficiency of the spl alpha -stable noise model in multiuser communication systems. The analysis presented will be important in the performance evaluation of complex communication systems and in the design of efficient interference suppression techniques. This work studies the design of reliable control laws of robotic systems operating in uncertain environments. We introduce a new approach to stochastic policy optimization based on probably approximately correct (PAC) bounds on the expected performance of control policies. An algorithm is constructed which directly minimizes an upper confidence bound on the expected cost of trajectories instead of employing a standard approach based on the expected cost itself. This algorithm thus has built-in robustness to uncertainty, since the bound can be regarded as a certificate for guaranteed future performance. The approach is evaluated on two challenging robot control scenarios in simulation: a car with side slip and a quadrotor navigating through obstacle-ridden environments. We show that the bound accurately predicts future performance and results in improved robustness measured by lower average cost and lower probability of collision. The performance of the technique is studied empirically and compared to several existing policy search algorithms. Abstract This paper describes a new approach for ascertaining the stability of stochastic dynamical systems in their parameter space by examining their time series using topological data analysis (TDA). We illustrate the approach using a nonlinear delayed model that describes the tool oscillations due to self-excited vibrations in turning. Each time series is generated using the Euler-Maruyama method and a corresponding point cloud is obtained using the Takens embedding. The point cloud can then be analyzed using a tool from TDA known as persistent homology. The results of this study show that the described approach can be used for analyzing datasets of delay dynamical systems generated both from numerical simulation and experimental data. The contributions of this paper include presenting for the first time a topological approach for investigating the stability of a class of nonlinear stochastic delay equations, and introducing a new application of TDA to machining processes.