Approximation, analysis and control of large-scale systems - Theory and Applications

This work presents some contributions to the fields of approximation, analysis and control of large-scale systems. Consequently the Thesis consists of three parts. The first part covers approximation topics and includes several contributions to the area of model reduction. Firstly, model reduction by moment matching for linear and nonlinear time-delay systems, including neutral differential time-delay systems with discrete-delays and distributed delays, is considered. Secondly, a theoretical framework and a collection of techniques to obtain reduced order models by moment matching from input/output data for linear (time-delay) systems and nonlinear (time-delay) systems is presented. The theory developed is then validated with the introduction and use of a low complexity algorithm for the fast estimation of the moments of the NETS-NYPS benchmark interconnected power system. Then, the model reduction problem is solved when the class of input signals generated by a linear exogenous system which does not have an implicit (differential) form is considered. The work regarding the topic of approximation is concluded with a chapter covering the problem of model reduction for linear singular systems. The second part of the Thesis, which concerns the area of analysis, consists of two very different contributions. The first proposes a new "discontinuous phasor transform" which allows to analyze in closed-form the steady-state behavior of discontinuous power electronic devices. The second presents in a unified framework a class of theorems inspired by the Krasovskii-LaSalle invariance principle for the study of "liminf" convergence properties of solutions of dynamical systems. Finally, in the last part of the Thesis the problem of finite-horizon optimal control with input constraints is studied and a methodology to compute approximate solutions of the resulting partial differential equation is proposed.Open Acces

A small-gain-like theorem for large-scale systems

International audienceThe behavior of the solutions of large-scale nonlinear dynamical systems close to their omega-limit sets is studied. Exploiting small-gain like conditions we extend the results in [1], considering the interconnection of p of subsystems, and the results in [2], presenting a block version of the weak nested Matrosov theorem

Energy-maximising control of wave energy converters using a moment-domain representation

Wave Energy Converters (WECs) have to be controlled to ensure maximum energy extraction from waves while considering, at the same time, physical constraints on the motion of the real device and actuator characteristics. Since the control objective for WECs deviates significantly from the traditional reference “tracking” problem in classical control, the specification of an optimal control law, that optimises energy absorption under different sea-states, is non-trivial. Different approaches based on optimal control methodologies have been proposed for this energy-maximising objective, with considerable diversity on the optimisation formulation. Recently, a novel mathematical tool to compute the steady-state response of a system has been proposed: the moment-based phasor transform. This mathematical framework is inspired by the theory of model reduction by moment-matching and considers both continuous and discontinuous inputs, depicting an efficient and closed-form method to compute such a steady-state behaviour. This study approaches the design of an energy-maximising optimal controller for a single WEC device by employing the moment-based phasor transform, describing a pioneering application of this novel moment-matching mathematical scheme to an optimal control problem. Under this framework, the energy-maximising optimal control formulation is shown to be a strictly concave quadratic program, allowing the application of well-known efficient real-time algorithms

Moment-based constrained optimal control of an array of wave energy converters

The roadmap to a successful commercialisation of wave energy inherently incorporates the concept of an array or farm of Wave Energy Converters (WECs). These interacting hydrodynamic structures require an optimised process that can ensure the maximum extraction of time-averaged energy from ocean waves, while respecting the physical limitations of each device and actuator characteristics. Recently, a novel optimal control framework based on the concept of moment, for a single WEC device, has been introduced in [1]. Such a strategy offers an energy-maximising computationally efficient solution that can systematically incorporate state and input constraints. This paper presents the mathematical extension of the optimal control framework of [1] to the case where an array of WECs is considered, providing an efficient solution that exploits the hydrodynamic interaction between devices to maximise the total absorbed energy