512 research outputs found
<i>H</i><sub>2</sub> and mixed <i>H</i><sub>2</sub>/<i>H</i><sub>∞</sub> Stabilization and Disturbance Attenuation for Differential Linear Repetitive Processes
Repetitive processes are a distinct class of two-dimensional systems (i.e., information propagation in two independent directions) of both systems theoretic and applications interest. A systems theory for them cannot be obtained by direct extension of existing techniques from standard (termed 1-D here) or, in many cases, two-dimensional (2-D) systems theory. Here, we give new results towards the development of such a theory in H2 and mixed H2/H∞ settings. These results are for the sub-class of so-called differential linear repetitive processes and focus on the fundamental problems of stabilization and disturbance attenuation
Robustness of networked systems to unintended interactions with application to engineered genetic circuits
A networked dynamical system is composed of subsystems interconnected through
prescribed interactions. In many engineering applications, however, one
subsystem can also affect others through "unintended" interactions that can
significantly hamper the intended network's behavior. Although unintended
interactions can be modeled as disturbance inputs to the subsystems, these
disturbances depend on the network's states. As a consequence, a disturbance
attenuation property of each isolated subsystem is, alone, insufficient to
ensure that the network behavior is robust to unintended interactions. In this
paper, we provide sufficient conditions on subsystem dynamics and interaction
maps, such that the network's behavior is robust to unintended interactions.
These conditions require that each subsystem attenuates constant external
disturbances, is monotone or "near-monotone", the unintended interaction map is
monotone, and the prescribed interaction map does not contain feedback loops.
We employ this result to guide the design of resource-limited genetic circuits.
More generally, our result provide conditions under which robustness of
constituent subsystems is sufficient to guarantee robustness of the network to
unintended interactions
Control of underactuated mechanical systems via passivity-based and geometric techniques
Il controllo di sistemi meccanici è attualmente uno tra i più attivi settori di
ricerca, a causa delle diverse applicazioni di sistemi meccanici nella vita reale.
Gli ultimi decenni hanno visto un accresciuto interesse nel controllo di sistemi
meccanici sottoattuati. Questi sistemi sono caratterizzati dal possedere più
gradi di libertà che attuatori, vale a dire, uno o più gradi di libertà non sono attuati. Questa classe di sistemi meccanici è molto rappresentata nella vita reale.
Esempi ne sono navi, veicoli spaziali, veicoli sottomarini, elicotteri, automobili,
robot mobili, robot spaziali e manipolatori sottoattuati.
Questa tesi si concentra su differenti generalizzazioni di alcuni risultati esistenti sul controllo di questa classe di sistemi, presenti nel lavoro di A. Tornambè, R. Ortega e J. W. Grizzle, con i quali ho collaborato nei tre anni del dottorato. Questi risultati sono stati ottenuti usando due diversi approcci: quello
basato sulla passività e quello geometrico.
Tre classi di problemi vengono trattate:
1. Disaccoppiamento ingresso-uscita per sistemi meccanici lineari sottoattuati;
2. Stabilizzazione asintotica di equilibri arbitrari in sistemi meccanici non
lineari sottoattuati;
3. Stabilizzazione esponenziale di orbite periodiche in sistemi meccanici non
lineari sottoattuati soggetti a impatti, con applicazioni alla robotica bipede.Control of mechanical systems is currently among one of the most active
fields of research, due to the diverse applications of mechanical systems in real
life. The last decades have shown an increasing interest in the control of underactuated mechanical systems. These systems are characterized by the fact of
possessing more degrees of freedom than actuators, i.e., one or more degrees of
freedom are unactuated. This class of mechanical systems are abundant in real
life; examples of such systems include surface vessels, spacecraft, underwater vehicles, helicopters, road vehicles, mobile robots, space robots and underactuated
manipulators.
The thesis focuses on different generalizations of some of the existing results
on the control of this class of systems, given in the existing work of A. Tornamb,
R. Ortega and J. W. Grizzle, who I collaborated with during the last three
years. They have been attained by using techniques borrowed from two different
approaches: the passivity-based and the geometric ones.
Three classes of problems are dealt with, namely:
1. Input-output decoupling for linear underactuated mechanical systems;
2. asymptotic stabilization of arbitrary equilibria in nonlinear mechanical
systems with underactuation degree one
3. exponential stabilization of periodic orbits in nonlinear underactuated mechanical systems with impulse effects, with applications to biped robot locomotio
Network Synchronization and Control Based on Inverse Optimality : A Study of Inverter-Based Power Generation
This thesis dwells upon the synthesis of system-theoretical tools to understand and control the behavior of nonlinear networked systems. This work is at the crossroads of three topics: synchronization in coupled high-order oscillators, inverse optimal control and the application of inverter-based power systems. The control and stability of power systems leverages the theoretical results obtained for synchronization in coupled high-order oscillators and inverse optimal control.First, we study the dynamics of coupled high-order nonlinear oscillators. These are characterized by their rotational invariance, meaning that their dynamics remain unchanged following a static shift of their angles. We provide sufficient conditions for local frequency synchronization based on both direct, indirect Lyapunov methods and center manifold theory. Second, we study inverse optimal control problems, embedded in networked settings. In this framework, we depart from a given stabilizing control law, with an associated control Lyapunov function and reverse engineer the cost functional to guarantee the optimality of the controller. In this way, inverse optimal control generates a whole family of optimal controllers corresponding to different cost functions. This provides analytically explicit and numerically feasible solutions in closed-form. This approach circumvents the complexity of solving partial differential equations descending from dynamic programming and Bellman's principle of optimality. We show this to be the case also in the presence of disturbances in the dynamics and the cost. In networks, the controller obtained from inverse optimal control has a topological structure (e.g., it is distributed) and thus feasible for implementation. The tuning is analogous to that of linear quadratic regulators.Third, motivated by the pressing changes witnessed by the electrical grid toward renewable energy generation, we consider power system stability and control as the main application of this thesis. In particular, we apply our theoretical findings to study a network of power electronic inverters. We first propose a controller we term the matching controller, a control strategy that, based on DC voltage measurements, endows the inverters with an oscillatory behavior at a common desired frequency. In closed-loop with the matching control, inverters can be considered as nonlinear oscillators. Our study of the dynamics of nonlinear oscillator network provides feasible physical conditions that ask for damping on DC- and AC-side of each converter, that are sufficient for system-wide frequency synchronization.Furthermore, we showcase the usefulness of inverse optimal control for inverter-based generation at two different settings to synthesize robust angle controllers with respect to common disturbances in the grid and provable stability guarantees. All the controllers proposed in this thesis, provide the electrical grid with important services, namely power support whenever needed, as well as power sharing among all inverters
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