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

Autonomous Identification and Tracking of Thermoclines

All data acquired from oceanic water features is hard and crucial work. It's hard due to the difficulty to obtain the same data given the unfavourable conditions.It requires, therefore, equipment that are reliable in the measurements of the desired characteristics and robust equipment, that is to say, equipment that are capable to withstand unfavorable and variable conditions in spatial and temporal terms. Due to these same spatial and temporal changes, the traditional methods do not prove to be the most adequate, because these methods do not have sufficient capacity to sample measurements of the dynamic characteristics of oceanographic processes.Thus, to obtain such measurements the use of the autonomous robotic systems proves to be important. With these systems, it is ensured a faster, more efficient and systematic sampling and is not subject to human error. The data acquisition is then a crucial work to understand how oceanographic process happens and varies in time and space. This work proposes an implementation of an algorithm to perform the tracking of the thermocline, from the stratification model of the oceanic water.This model is a parametric model. This work will also take into account the capacity to perform measurements with a sampling capable of adapting the depth control of the underwater vehicle.The stratification of the oceanic water happens when exists different features between different layers. One of these layers is the thermocline. At this layer, the water temperature decreases rapidly with increasing depth. The characterization of the thermocline is so important to marine biology, given the high concentration of phytoplankton in this level, as for acoustic communications equipments or military services, given the special characteristics of speed sound in this level.The model of this stratification will be used to aid in the thermocline's tracking process. This model will serve as a basis for the algorithm to adapt the control in order to carry out the tracking with the greatest success, in real time. This algorithm will focus on the variations in the vertical temperature gradient.The algorithm responsible detect and track of the thermocline will be run on a profiler. The profiler is a vehicle that moves along the vertical axis. However, when subject to tides, the natural process in aquatic environments drifts along the horizontal axis. A set of sensors capable of measuring the water temperature and the depth at which the vehicle is below water shall be placed in this vehicle. These sensors will be important to calculate the vertical gradient

Robust controllers design for unknown error and exosystem: a hybid optimization and output regulation approach

This thesis addresses the problem of robustness in control in two main topics: linear output regulation when no knowledge is assumed of the modes of the exosystem, and hybrid gradient-free optimization. A framework is presented for the solution of the first problem, in which asymptotic regulation is achieved in case of a persistence of excitation condition. The stability properties of the closed-loop system are proved under a small-gain argument with no minimum phase assumption. The second part of the thesis addresses, and proposes, a solution to the gradientfree optimization problem, solved by a discrete-time direct search algorithm. The algorithm is shown to convergence to the set of minima of a particular class of non convex functions. It is, then, applied considering it coupled with a continuous-time dynamical system. A hybrid controller is developed in order to guarantee convergence to the set of minima and stability of the interconnection of the two systems. Almost global asymptotic is proven for the proposed hybrid controller. Shown to not be robust to any bounded measurement noise, a robust solution is also proposed. The aim of this thesis is to lay the ground for a solution of the output regulation problem in case the error is unknown, but a proxy optimization function is available. A controller embedding the characteristics of the two proposed approaches, as a main solution to the aforementioned problem, will be the focus of future studies

Advancements in Real-Time Simulation of Power and Energy Systems

Modern power and energy systems are characterized by the wide integration of distributed generation, storage and electric vehicles, adoption of ICT solutions, and interconnection of different energy carriers and consumer engagement, posing new challenges and creating new opportunities. Advanced testing and validation methods are needed to efficiently validate power equipment and controls in the contemporary complex environment and support the transition to a cleaner and sustainable energy system. Real-time hardware-in-the-loop (HIL) simulation has proven to be an effective method for validating and de-risking power system equipment in highly realistic, flexible, and repeatable conditions. Controller hardware-in-the-loop (CHIL) and power hardware-in-the-loop (PHIL) are the two main HIL simulation methods used in industry and academia that contribute to system-level testing enhancement by exploiting the flexibility of digital simulations in testing actual controllers and power equipment. This book addresses recent advances in real-time HIL simulation in several domains (also in new and promising areas), including technique improvements to promote its wider use. It is composed of 14 papers dealing with advances in HIL testing of power electronic converters, power system protection, modeling for real-time digital simulation, co-simulation, geographically distributed HIL, and multiphysics HIL, among other topics

The Optimal Steady-State Control Problem

Many engineering systems -- including electrical power networks, chemical processing plants, and communication networks -- have a well-defined notion of an "optimal'" steady-state operating point. This optimal operating point is often defined mathematically as the solution of a constrained optimization problem that seeks to minimize the monetary cost of distributing electricity, maximize the profit of chemical production, or minimize the communication latency between agents in a network. Optimal steady-state regulation is obviously of crucial importance in such systems. This thesis is concerned with the optimal steady-state control problem, the problem of designing a controller to continuously and automatically regulate a dynamical system to an optimal operating point that minimizes cost while satisfying equipment constraints and other engineering requirements, even as this optimal operating point changes with time. An optimal steady-state controller must simultaneously solve the optimization problem and force the plant to track its solution. This thesis makes two primary contributions. The first is a general problem definition and controller architecture for optimal steady-state control for nonlinear systems subject to time-varying exogenous inputs. We leverage output regulation theory to define the problem and provide necessary and sufficient conditions on any optimal steady-state controller. Regarding our controller architecture, the typical controller in the output regulation literature consists of two components: an internal model and a stabilizer. Inspired by this division, we propose that a typical optimal steady-state controller should consist of three pieces: an optimality model, an internal model, and a stabilizer. We show that our design framework encompasses many existing controllers from the literature. The second contribution of this thesis is a complete constructive solution to an important special case of optimal steady-state control: the linear-convex case, when the plant is an uncertain linear time-invariant system subject to constant exogenous inputs and the optimization problem is convex. We explore the requirements on the plant and optimization problem that allow for optimal regulation even in the presence of parametric uncertainty, and we explore methods for stabilizer design using tools from robust control theory. We illustrate the linear-convex theory on several examples. We first demonstrate the use of the small-gain theorem for stability analysis when a PI stabilizer is employed; we then show that we can use the solution to the H-infinity control problem to synthesize a stabilizer when the PI controller fails. Furthermore, we apply our theory to the design of controllers for the optimal frequency regulation problem in power systems and show that our methods recover standard designs from the literature