2,888 research outputs found

    Singularly Perturbed Stochastic Hybrid Systems: Stability and Recurrence via Composite Nonsmooth Foster Functions

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    We introduce new sufficient conditions for verifying stability and recurrence properties in singularly perturbed stochastic hybrid dynamical systems. Specifically, we focus on hybrid systems with deterministic continuous-time dynamics that exhibit multiple time scales and are modeled by constrained differential inclusions, as well as discrete-time dynamics modeled by constrained difference inclusions with random inputs. By assuming regularity and causality of the dynamics and their solutions, respectively, we propose a suitable class of composite nonsmooth Lagrange-Foster and Lyapunov-Foster functions that can certify stability and recurrence using simpler functions related to the slow and fast dynamics of the system. We establish the stability properties with respect to compact sets, while the recurrence properties are studied only for open sets

    Revealing networks from dynamics: an introduction

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    What can we learn from the collective dynamics of a complex network about its interaction topology? Taking the perspective from nonlinear dynamics, we briefly review recent progress on how to infer structural connectivity (direct interactions) from accessing the dynamics of the units. Potential applications range from interaction networks in physics, to chemical and metabolic reactions, protein and gene regulatory networks as well as neural circuits in biology and electric power grids or wireless sensor networks in engineering. Moreover, we briefly mention some standard ways of inferring effective or functional connectivity.Comment: Topical review, 48 pages, 7 figure

    Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems

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    Development of robust dynamical systems and networks such as autonomous aircraft systems capable of accomplishing complex missions faces challenges due to the dynamically evolving uncertainties coming from model uncertainties, necessity to operate in a hostile cluttered urban environment, and the distributed and dynamic nature of the communication and computation resources. Model-based robust design is difficult because of the complexity of the hybrid dynamic models including continuous vehicle dynamics, the discrete models of computations and communications, and the size of the problem. We will overview recent advances in methodology and tools to model, analyze, and design robust autonomous aerospace systems operating in uncertain environment, with stress on efficient uncertainty quantification and robust design using the case studies of the mission including model-based target tracking and search, and trajectory planning in uncertain urban environment. To show that the methodology is generally applicable to uncertain dynamical systems, we will also show examples of application of the new methods to efficient uncertainty quantification of energy usage in buildings, and stability assessment of interconnected power networks

    Estimation and stability of nonlinear control systems under intermittent information with applications to multi-agent robotics

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    This dissertation investigates the role of intermittent information in estimation and control problems and applies the obtained results to multi-agent tasks in robotics. First, we develop a stochastic hybrid model of mobile networks able to capture a large variety of heterogeneous multi-agent problems and phenomena. This model is applied to a case study where a heterogeneous mobile sensor network cooperatively detects and tracks mobile targets based on intermittent observations. When these observations form a satisfactory target trajectory, a mobile sensor is switched to the pursuit mode and deployed to capture the target. The cost of operating the sensors is determined from the geometric properties of the network, environment and probability of target detection. The above case study is motivated by the Marco Polo game played by children in swimming pools. Second, we develop adaptive sampling of targets positions in order to minimize energy consumption, while satisfying performance guarantees such as increased probability of detection over time, and no-escape conditions. A parsimonious predictor-corrector tracking filter, that uses geometrical properties of targets\u27 tracks to estimate their positions using imperfect and intermittent measurements, is presented. It is shown that this filter requires substantially less information and processing power than the Unscented Kalman Filter and Sampling Importance Resampling Particle Filter, while providing comparable estimation performance in the presence of intermittent information. Third, we investigate stability of nonlinear control systems under intermittent information. We replace the traditional periodic paradigm, where the up-to-date information is transmitted and control laws are executed in a periodic fashion, with the event-triggered paradigm. Building on the small gain theorem, we develop input-output triggered control algorithms yielding stable closed-loop systems. In other words, based on the currently available (but outdated) measurements of the outputs and external inputs of a plant, a mechanism triggering when to obtain new measurements and update the control inputs is provided. Depending on the noise environment, the developed algorithm yields stable, asymptotically stable, and Lp-stable (with bias) closed-loop systems. Control loops are modeled as interconnections of hybrid systems for which novel results on Lp-stability are presented. Prediction of a triggering event is achieved by employing Lp-gains over a finite horizon in the small gain theorem. By resorting to convex programming, a method to compute Lp-gains over a finite horizon is devised. Next, we investigate optimal intermittent feedback for nonlinear control systems. Using the currently available measurements from a plant, we develop a methodology that outputs when to update the control law with new measurements such that a given cost function is minimized. Our cost function captures trade-offs between the performance and energy consumption of the control system. The optimization problem is formulated as a Dynamic Programming problem, and Approximate Dynamic Programming is employed to solve it. Instead of advocating a particular approximation architecture for Approximate Dynamic Programming, we formulate properties that successful approximation architectures satisfy. In addition, we consider problems with partially observable states, and propose Particle Filtering to deal with partially observable states and intermittent feedback. Finally, we investigate a decentralized output synchronization problem of heterogeneous linear systems. We develop a self-triggered output broadcasting policy for the interconnected systems. Broadcasting time instants adapt to the current communication topology. For a fixed topology, our broadcasting policy yields global exponential output synchronization, and Lp-stable output synchronization in the presence of disturbances. Employing a converse Lyapunov theorem for impulsive systems, we provide an average dwell time condition that yields disturbance-to-state stable output synchronization in case of switching topology. Our approach is applicable to directed and unbalanced communication topologies.\u2

    Distributed synchronization algorithms for wireless sensor networks

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    The ability to distribute time and frequency among a large population of interacting agents is of interest for diverse disciplines, inasmuch as it enables to carry out complex cooperative tasks. In a wireless sensor network (WSN), time/frequency synchronization allows the implementation of distributed signal processing and coding techniques, and the realization of coordinated access to the shared wireless medium. Large multi-hop WSN\u27s constitute a new regime for network synchronization, as they call for the development of scalable, fully distributed synchronization algorithms. While most of previous research focused on synchronization at the application layer, this thesis considers synchronization at the lowest layers of the communication protocol stack of a WSN, namely the physical and the medium access control (MAC) layer. At the physical layer, the focus is on the compensation of carrier frequency offsets (CFO), while time synchronization is studied for application at the MAC layer. In both cases, the problem of realizing network-wide synchronization is approached by employing distributed clock control algorithms based on the classical concept of coupled phase and frequency locked loops (PLL and FLL). The analysis takes into account communication, signaling and energy consumption constraints arising in the novel context of multi-hop WSN\u27s. In particular, the robustness of the algorithms is checked against packet collision events, infrequent sync updates, and errors introduced by different noise sources, such as transmission delays and clock frequency instabilities. By observing that WSN\u27s allow for greater flexibility in the design of the synchronization network architecture, this work examines also the relative merits of both peer-to-peer (mutually coupled - MC) and hierarchical (master-slave - MS) architectures. With both MC and MS architectures, synchronization accuracy degrades smoothly with the network size, provided that loop parameters are conveniently chosen. In particular, MS topologies guarantee faster synchronization, but they are hindered by higher noise accumulation, while MC topologies allow for an almost uniform error distribution at the price of much slower convergence. For all the considered cases, synchronization algorithms based on adaptive PLL and FLL designs are shown to provide robust and scalable network-wide time and frequency distribution in a WSN
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