138 research outputs found
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Robust Hybrid Systems for Control, Learning, and Optimization in Networked Dynamical Systems
The deployment of advanced real-time control and optimization strategies in socially-integratedengineering systems could significantly improve our quality of life whilecreating jobs and economic opportunity. However, in cyber-physical systems such assmart grids, transportation networks, healthcare, and robotic systems, there still existseveral challenges that prevent the implementation of intelligent control strategies.These challenges include the existence of limited communication networks, dynamicand stochastic environments, multiple decision makers interacting with the system,and complex hybrid dynamics emerging from the feedback interconnection of physicalprocesses and computational devices.In this dissertation, we study the problem of designing robust control and optimizationalgorithms for cyber-physical systems using the framework of hybrid dynamicalsystems. We propose different theoretical frameworks for the design and analysis offeedback mechanisms that optimize the performance of dynamical systems without requiringan explicit characterization of their mathematical model, i.e., in a model-freeway. The closed-loop system that emerges of the interconnection of the plant with thefeedback mechanism describes, in general, a set-valued hybrid dynamical system. Thesetypes of systems combine continuous-time and discrete-time dynamics, and they usuallylack the uniqueness of solutions property. The framework of set-valued hybriddynamical systems allows us to study many complex dynamical systems that emerge indifferent engineering applications, such as networked multi-agent systems with switching graphs, non-smooth mechanical systems, dynamic pricing mechanisms in transportationsystems, autonomous robots with logic-based controllers, etc. We proposea step-by-step approach to the design of different types of discrete-time, continuous-time,hybrid, and stochastic controllers for different types of applications, extendingand generalizing different results in the literature in the area of extremum seeking control,sampled-data extremization, robust synchronization, and stochastic learning innetworked systems. Our theoretical results are illustrated via different simulations andnumerical examples
Online Optimization of LTI Systems Under Persistent Attacks: Stability, Tracking, and Robustness
We study the stability properties of the interconnection of an LTI dynamical
plant and a feedback controller that generates control signals that are
compromised by a malicious attacker. We consider two classes of controllers: a
static output-feedback controller, and a dynamical gradient-flow controller
that seeks to steer the output of the plant towards the solution of a convex
optimization problem. We analyze the stability of the closed-loop system under
a class of switching attacks that persistently modify the control inputs
generated by the controllers. The stability analysis leverages the framework of
hybrid dynamical systems, Lyapunov-based arguments for switching systems with
unstable modes, and singular perturbation theory. Our results reveal that under
a suitable time-scale separation, the stability of the interconnected system
can be preserved when the attack occurs with "sufficiently low frequency" in
any bounded time interval. We present simulation results in a power-grid
example that corroborate the technical findings
Extremum Seeking Approach for Nonholonomic Systems with Multiple Time Scale Dynamics
In this paper, a class of nonlinear driftless control-affine systems
satisfying the bracket generating condition is considered. A gradient-free
optimization algorithm is developed for the minimization of a cost function
along the trajectories of the controlled system. The algorithm comprises an
approximation scheme with fast oscillating controls for the nonholonomic
dynamics and a model-free extremum seeking component with respect to the output
measurements. Exponential convergence of the trajectories to an arbitrary
neighborhood of the optimal point is established under suitable assumptions on
time scale parameters of the extended system. The proposed algorithm is tested
numerically with the Brockett integrator for different choices of generating
functions.Comment: This is the author's version of the manuscript accepted for
publication in the Proceedings of The 21st IFAC World Congress 2020 (IFAC
2020
Singularly Perturbed Stochastic Hybrid Systems: Stability and Recurrence via Composite Nonsmooth Foster Functions
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
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