Extremum Seeking for Stefan PDE with Moving Boundary

This paper presents the design and analysis of the extremum seeking for static maps with input passed through a partial differential equation (PDE) of the diffusion type defined on a time-varying spatial domain whose boundary position is governed by an ordinary differential equation (ODE). This is the first effort to pursue an extension of extremum seeking from the heat PDE to the Stefan PDE. We compensate the average-based actuation dynamics by a controller via backstepping transformation for the moving boundary, which is utilized to transform the original coupled PDE-ODE into a target system whose exponential stability of the average equilibrium of the average system is proved. The discussion for the delay-compensated extremum seeking control of the Stefan problem is also presented and illustrated with numerical simulations.Comment: 10 pages and 10 figure

Free-electron laser spectrum evaluation and automatic optimization

The radiation generated by a seeded free-electron laser (FEL) is characterized by a high temporal coherence, which is close to the Fourier limit in the ideal case. The setup and optimization of a FEL is a non-trivial and challenging operation. This is due to the plethora of highly sensitive machine parameters and to the complex correlations between them. The fine tuning of the FEL process is normally supervised by physicists and is carried out by scanning various parameters with the aim of optimizing the spectrum of the emitted pulses in terms of intensity and line-width. In this article we introduce a novel quantitative method for the evaluation of the FEL spectrum via a quality index. Moreover, we investigate the possibility of optimization of the FEL parameters using this index as the objective function of an automatic procedure. We also present the results of the preliminary tests performed in the FERMI FEL focused on the effectiveness and ability of the automatic procedure to assist in the task of machine tuning and optimization

CONTROL AND ESTIMATION ALGORITHMS FOR MULTIPLE-AGENT SYSTEMS

Tese arquivada ao abrigo da Portaria nº 227/2017 de 25 de julhoIn this thesis we study crucial problems within complex, large scale, networked control systems and mobile sensor networks. The ¯rst one is the problem of decomposition of a large-scale system into several interconnected subsystems, based on the imposed information structure constraints. After associating an intelligent agent with each subsystem, we face with a problem of formulating their local estimation and control laws and designing inter-agent communication strategies which ensure stability, desired performance, scalability and robustness of the overall system. Another problem addressed in this thesis, which is critical in mobile sensor networks paradigm, is the problem of searching positions for mobile nodes in order to achieve optimal overall sensing capabilities. Novel, overlapping decentralized state and parameter estimation schemes based on the consensus strategy have been proposed, in both continuous-time and discrete-time. The algorithms are proposed in the form of a multi-agent network based on a combination of local estimators and a dynamic consensus strategy, assuming possible intermittent observations and communication faults. Under general conditions concerning the agent resources and the network topology, conditions are derived for the stability and convergence of the algorithms. For the state estimation schemes, a strategy based on minimization of the steady-state mean-square estimation error is proposed for selection of the consensus gains; these gains can also be adjusted by local adaptation schemes. It is also demonstrated that there exists a connection between the network complexity and e±ciency of denoising, i.e., of suppression of the measurement noise in°uence. Several numerical examples serve to illustrate characteristic properties of the proposed algorithm and to demonstrate its applicability to real problems. Furthermore, several structures and algorithms for multi-agent control based on a dynamic consensus strategy have been proposed. Two novel classes of structured, overlapping decentralized control algorithms are presented. For the ¯rst class, an agreement between the agents is implemented at the level of control inputs, while the second class is based on the agreement at the state estimation level. The proposed control algorithms have been illustrated by several examples. Also, the second class of the proposed consensus based control scheme has been applied to decentralized overlapping tracking control of planar formations of UAVs. A comparison is given with the proposed novel design methodology based on the expansion/contraction paradigm and the inclusion principle. Motivated by the applications to the optimal mobile sensor positioning within mobile sensor networks, the perturbation-based extremum seeking algorithm has been modifed and extended. It has been assumed that the integrator gain and the perturbation amplitude are time varying (decreasing in time with a proper rate) and that the output is corrupted with measurement noise. The proposed basic, one dimensional, algorithm has been extended to two dimensional, hybrid schemes and directly applied to the planar optimal mobile sensor positioning, where the vehicles can be modeled as velocity actuated point masses, force actuated point masses, or nonholonomic unicycles. The convergence of all the proposed algorithms, with probability one and in the mean square sense, has been proved. Also, the problem of target assignment in multi-agent systems using multi-variable extremum seeking algorithm has been addressed. An algorithm which e®ectively solves the problem has been proposed, based on the local extremum seeking of the specially designed global utility functions which capture the dependance among di®erent, possibly con°icting objectives of the agents. It has been demonstrated how the utility function parameters and agents' initial conditions impact the trajectories and destinations of the agents. All the proposed extremum seeking based algorithms have been illustrated with several simulations

Multi-Unit Optimization for a System with Mutiple Non-Identical Units and Multipe Inputs-Application to Photovoltaic Arrays

L’optimisation est devenue un domaine clé dans l’industrie de transformation pour rester compétitif sur le marché mondial, s’adapter aux nouvelles contraintes environnementales et supporter l’augmentation des coûts énergétiques. Pour répondre à ces nouvelles exigences, les industries se doivent d’optimiser leurs installations afin de réduire les coûts d'exploitation, améliorer l'efficacité de la production, répondre aux spécifications de qualité des produits et sécurité des procédés. Avec le développement de nouvelles technologies de contrôle, il est aujourd’hui possible de maintenir un procédé à son point d’opération optimal. L’optimisation en temps réel (RTO) est un outil permettant d’amener et maintenir un système à son point de fonctionnement optimal. Ce domaine de recherche a reçu une attention considérable dans l'industrie des procédés. Les méthodes d’optimisation en temps réels permettent de contrôler le comportement d’un procédé en ajustant les points de consigne des régulateurs de procédé pour suivre les changements de conditions opératoires et les perturbations externes qui prennent place au sein d’une usine. Parmi les différentes approches d’optimisation en temps réel, les méthodes de commande extrémale sont celles qui permettent de satisfaire les conditions nécessaires d'optimalité. Dans la commande extrémale, l'optimisation est traitée comme un problème de contrôle du gradient de la fonction objectif à zéro. La principale différence entre les diverses méthodes de commande extrémale repose sur la façon dont le gradient est estimé. La plupart de ces méthodes impliquent l’application d’une perturbation temporelle périodique. De plus, afin d’isoler les effets de la dynamique du système sur le gradient estimé, une séparation de plusieurs échelles de temps est requise. La méthode d’optimisation multi-unités est une méthode de commande extrémale dans laquelle la perturbation est appliquée entre les unités plutôt que sur un domaine temporel. Une séparation d'échelle de temps n'est plus nécessaire. La convergence est de ce fait plus rapide. La méthode d’optimisation multi-unités nécessite la présence de plusieurs unités identiques, chacune d'entre elles fonctionnant à des valeurs d'entrée qui diffèrent par une constante prédéterminée de décalage. Bien que cette méthode soit utile lorsque le système se compose de plusieurs unités, la convergence au point optimal a seulement été prouvée pour des unités au sein d’un procédé parfaitement identiques ou lorsqu’il y a seulement deux unités non identiques. En pratique, cette hypothèse est rarement vérifiée puisqu’un procédé industriel réel peut avoir plus de deux unités non identiques. Par conséquent, dans cette étude, une méthode d'optimisation basée sur l’optimisation multi-unités est proposée pour répondre à cette problématique. L'algorithme proposé est pour le cas d'une fonction objectif statique convexe avec deux entrées. L’algorithme comporte entre autre des corrections successives pour compenser les différences entre les surfaces statiques des fonctions objectif associées à chaque unité. La dernière partie de cette thèse contient l'étude de cas où la méthode d'optimisation multi-unités est utilisée pour déterminer la puissance électrique maximale de panneaux photovoltaïques. L'électricité est principalement produite à partir de combustibles fossiles, de combustible nucléaire et de ressources renouvelables telles que le soleil, le vent, l'eau et la biomasse. L'énergie solaire est de plus en plus considérée pour la production de bioénergie et ce, en raison des récents progrès dans la fabrication de panneaux solaires et de la volatilité des prix des combustibles fossiles. Un inconvénient qui freine toutefois l'utilisation de l'énergie solaire est son coût d'investissement élevé. Une façon de réduire les coûts et d’augmenter la rentabilité des panneaux solaires est d'améliorer l'efficacité des panneaux photovoltaïques (PV) en termes de puissance électrique de sortie. La tension et le courant des panneaux photovoltaïques dépendent de la température, de l'ensoleillement, de l'angle du rayonnement solaire, et d'autres conditions atmosphériques. Comme ces paramètres sont modifiés régulièrement, il est important de suivre le point de puissance maximale d'exploitation (MPOP) pour garder un maximum d'efficacité à chaque instant. Ainsi, des ajustements en temps réel de la charge externe appliquée aux panneaux photovoltaïque sont nécessaires afin de prendre en compte la puissance maximale des panneaux photovoltaïques. Dans cette recherche, la méthode d’optimisation multi-unités est appliquée pour résoudre le problème de suivi du point de puissance maximale des panneaux photovoltaïques. Les résultats confirment la force de la méthode d'optimisation multi-unités et permettent de vérifier également le fait que les différences entre les unités peuvent être corrigées pour que chacune d’entre elles atteignent son optimum. ---------- Optimization has become a key area in process industries due to the increasing global market competition, environmental constraints and energy costs. These factors induce operating companies to optimize plant operation in order to reduce operating cost, improve production efficiency, meet product quality specifications, and process safety. Besides, as better controllers are developed to adequately control a plant; the focus can be shifted to the solution of controller designs that guarantee optimal plant performance. Real-time optimization (RTO) is a valuable tool, to bring and maintain a system at its optimal operating point that has received considerable attention in the process industry. Real-time optimization methods could monitor the behavior of processes, adjusting the set points of process controllers to track significant changes in the plant optimum. Among different approaches of RTO, extremum-seeking control methods are those which are able to satisfy the necessary conditions of optimality. In other words, in extremum-seeking control methods, optimization is recast as a problem of controlling the gradient of objective function to zero. The main difference between the various extremum-seeking methods lies in the way the gradient is estimated. Most of these schemes involve injecting a periodic temporal perturbation signal and several time-scale separations are necessary to isolate the effects of the system dynamics on the estimated gradient. Multi-unit optimization is an extremum seeking control method in which the perturbation is along the unit dimension rather than in time domain so time-scale separation is not needed and the convergence is faster for slow dynamic processes. This method requires the presence of multiple identical units, with each of them operated at input values that differ by a pre-determined constant offset. Although this method is useful when the system consist of multiple units, convergence to optimal point has been proven for systems with many identical units or two non-identical units, whereas a real industrial system model could have more than two non-identical units. Therefore, in this research, an optimization procedure based on multi-unit method is developed with respect to the number of units and number of inputs. The proposed algorithm is for the case of a static convex objective function with two inputs. It consists of sequential corrections to compensate the differences between static surfaces of the objective functions related to each unit. The last part of this thesis contains the case study of the multi-unit optimization method to track maximum power point of photovoltaic arrays. Electricity is mainly produced from fossil fuels, nuclear fuel and renewable resources such as sun, wind, water and biomass. Solar energy is at the forefront of clean and renewable resources and, due to advances in solar panel manufacturing and because of the volatile fuel costs, its advantage is increasing. But the actual drawback which still exists in using solar energy is its high investment cost. One way to reduce costs and increase the profitability of solar panels turns out to enhance the efficiency of photovoltaic (PV) arrays in terms of output power. The voltage and current of PV arrays depend on temperature, insolation, angle of solar irradiance, and other atmospheric conditions. As these parameters are regularly modified, it’s important to track the maximum power operating point (MPOP) to keep a maximum efficiency at every instant. Thus, real-time adjustments of the external load are required to take maximum power from PV panels. In this research, multi-unit is applied as a recent technique to solve maximum power point tracking problem for PV arrays. The results confirm the strength of the multi-unit optimization method. It also verifies the fact that differences between the units can be corrected leading each of them to their respective optima

Boundary tracking and source seeking of oceanic features using autonomous vehicles

The thesis concerns the study and the development of boundary tracking and source seeking approaches for autonomous vehicles, specifically for marine autonomous systems. The underlying idea is that the characterization of most environmental features can be posed from either a boundary tracking or a source seeking perspective. The suboptimal sliding mode boundary tracking approach is considered and, as a first contribution, it is extended to the study of three dimensional features. The approach is aimed at controlling the movement of an underwater glider tracking a three-dimensional underwater feature and it is validated in a simulated environment. Subsequently, a source seeking approach based on sliding mode extremum seeking ideas is proposed. This approach is developed for the application to a single surface autonomous vehicle, seeking the source of a static or dynamic two dimensional spatial field. A sufficient condition which guarantees the finite time convergence to a neighbourhood of the source is introduced. Furthermore, a probabilistic learning boundary tracking approach is proposed, aimed at exploiting the available preliminary information relating to the spatial phenomenon of interest in the control strategy. As an additional contribution, the sliding mode boundary tracking approach is experimentally validated in a set of sea-trials with the deployment of a surface autonomous vehicle. Finally, an embedded system implementing the proposed boundary tracking strategy is developed for future installation on board of the autonomous vehicle. This work demonstrates the possibility to perform boundary tracking with a fully autonomous vehicle and to operate marine autonomous systems without remote control or pre-planning. Conclusions are drawn from the results of the research presented in this thesis and directions for future work are identified