A Neural-Network based Approach for Nash Equilibrium Seeking in Mixed-order Multi-player Games

Noticing that agents with different dynamics may work together, this paper considers Nash equilibrium computation for a class of games in which first-order integrator-type players and second-order integrator-type players interact in a distributed network. To deal with this situation, we firstly exploit a centralized method for full information games. In the considered scenario, the players can employ its own gradient information, though it may rely on all players' actions. Based on the proposed centralized algorithm, we further develop a distributed counterpart. Different from the centralized one, the players are assumed to have limited access into the other players' actions. In addition, noticing that unmodeled dynamics and disturbances are inevitable for practical engineering systems, the paper further considers games in which the players' dynamics are suffering from unmodeled dynamics and time-varying disturbances. In this situation, an adaptive neural network is utilized to approximate the unmodeled dynamics and disturbances, based on which a centralized Nash equilibrium seeking algorithm and a distributed Nash equilibrium seeking algorithm are established successively. Appropriate Lyapunov functions are constructed to investigate the effectiveness of the proposed methods analytically. It is shown that if the considered mixed-order game is free of unmodeled dynamics and disturbances, the proposed method would drive the players' actions to the Nash equilibrium exponentially. Moreover, if unmodeled dynamics and disturbances are considered, the players' actions would converge to arbitrarily small neighborhood of the Nash equilibrium. Lastly, the theoretical results are numerically verified by simulation examples

Distributed Linear Quadratic Control and Filtering:a suboptimality approach

Design of distributed protocols for multi-agent systems has received extensive attention in the past two decades. A challenging problem in this context is to develop distributed synchronizing protocols that minimize given cost criteria. Recent years have also witnessed an increasing interest in problems of distributed state estimation for large-scale systems. Two challenging problems in this context are the problems of distributed H-2 and H-infinity optimal filtering.In this dissertation, we study both distributed linear quadratic optimal control problems and distributed filtering problems. In the framework of distributed linear quadratic control, both for leaderless and leader-follower multi-agent systems we provide design methods for computing state-feedback-based distributed suboptimal synchronizing protocols. In the framework of distributed H-2 suboptimal control, both for homogeneous and heterogeneous multi-agent systems we establish design methods for computing state-feedback-based and output-feedback-based distributed suboptimal synchronizing protocols.The distributed H-2 and H-infinity optimal filtering problem are the problems of designing local filter gains such that the H-2 or H-infinity norm of the transfer matrix from the disturbance input to the output estimation error is minimized, while all local filters reconstruct the full system state asymptotically. Due to their non-convex nature, it is not clear whether optimal solutions exist. Instead of studying these optimal filtering problems, in this dissertation we therefore address suboptimality versions of these problems and provide conceptual algorithms for obtaining H-2 and H-infinity suboptimal distributed filters, respectively

The Role of Inverter-based Generation in Future Energy Systems: An Oriented Decentralized Strategy for Reactive Power Sharing in Islanded AC Microgrids and a Techno-Economic Approach to Inertia Requirements Assessment of the Italian Transmission Network

One of the most impacting changes in the electricity energy scenario of the latest decades is the extensive increase of Distributed Energy Resources (DER) including Electrical Storage Systems (EES), fuel cells and Renewable Energy Sources (RES), such as Photovoltaic (PV) and Wind Turbines (WT). The integration of a rapidly increasing share of inverter-based generation poses relevant challenges in terms of frequency and voltage control both in Islanded Microgrids (MG) and traditional transmission networks. For the sake of complementarity, the thesis focuses on reactive power and voltage regulation in MG and frequency instability problems in a future Italian transmission network. In MG with converter-based energy production, one of the main problems is the proper reactive power sharing among DER and related voltage regulation. In this concern the most used approach is based on the conventional droop control; however, it presents some relevant drawbacks. In SECTION A an Advanced Droop Control strategy (ADC) and an Advanced Boost Control strategy (ABC) are proposed, to approach primary voltage control and reactive power sharing among Grid-Supporting inverters in islanded MG. The strategies are presented defining their control laws and the control schemes together with the relevant stability analysis. Then, an analytical procedure is developed for each control methods to set proper control parameters. Next, a comparison between the new strategies and droop conventional control is performed with simulations on a common benchmark MG, in order to show that new strategies, according to their specific control logics, are able to guarantee improved performance in terms of the combined regulation of voltage and reactive power. Considering the traditional electric system, one of the main consequences of the increasing penetration of RES is, besides of the decrease of the system short-circuit power, the reduction of the electric system inertia: this could lead to frequency instability problems in case of severe perturbations, especially for what concerns the Rate of Change of Frequency (RoCoF)and the frequency nadir. In SECTION B, the thesis provides a technical-economic methodology for the estimation of the amount of additional inertia that will be needed in the Italian Transmission Network in a prospective 2030 scenario, in order to limit the RoCoF within sustainable values. Moreover, the algorithm optimally commits synthetic inertia contribution from RES and Battery Energy Storage Systems (BESS) and installation of Synchronous Compensators (SC) among the Italian market areas. The method is designed to be sufficiently simple to process a relevant number of working scenarios in order to exploit the relevant quantity of information owned by the TSO. Results have shown to be highly accurate as outline by comparison with detailed time domain simulations

Neither easy nor impossible: Local development economics and policy

This assai leads the reader on an analytical path to development, with institutions as its central focus. While its main emphasis is on the problematic nature of development in lagging or backward regions, contributions from the literature on developing countries have also been taken into account, and European countries, Italy and the South of Italy (the Mezzogiorno) also feature in the debate. There is no doubt that lagging regions in advanced countries are very different from backward regions in poor countries. I think that there are two basic assumptions that hold for both. First, the most important constraints on development are internal; second, in order to combat underdevelopment strong actions that break with tradition are needed. These two assumptions are often ignored by development literature. These studies may be well written, fun to read and able to communicate faithfully their authors views on social and economic life, but their perspective is necessarily different from that of people who are actively involved in social and economic development efforts or tackling underdevelopment. The assai offers some interpretative starting points. The path distances itself from five concepts that are widely held but superficial. The first is that economic development in a backward or lagging area depends on growth in advanced areas, given that capital will flow where there is an abundant supply of labour and because technical progress is easier for latecomers than for innovators. The common view is that there is spontaneous economic convergence simply because capital has low returns in advanced areas and high returns in backward areas. In advanced areas, moreover, already on the threshold of improved technology, technical progress is more of a struggle, whereas in backward areas all that is needed is to imitate others. Since this idea has no real empirical basis, those who hold this view claim that the differences between regions persist because markets work badly, segmented as they are by rules and behaviour that allow unjustified returns. Without these artificial distortions, they argue, resources would be spontaneously used where they were most productive. In this view, the most relevant development policy (and for many, the only possible policy) is to reduce curbs to maximum competition in all sectors and in all walks of life. There are many reasons for thinking that this is irrelevant. Many crucial resources are in fact attracted to advanced areas, not because there is over-regulation. If anything, the opposite. Opening up markets that work well would therefore seem to be a result of development rather than a way to achieve it. In order to achieve development what is needed is more intentional public intervention: more State, not less. The path undertaken to reach this conclusion is arduous, however. Not many people today share the view that the State can play a relevant role. The path requires a critical reappraisal of four other common views. The second widespread view that we need to demolish, then, is the idea that -. even if we accept that economic development in a backward area is impeded by the fact that resources are attracted to advanced areas - there will always be immobile resources that can spontaneously trigger development and sustain it. This view is supported by the limits on mobility of resources. Taking into account that important resources such as the environmental, historical, cultural heritage of a region are substantially immobile, those who hold this view believe that these resources cannot be lost as a result of the capacity for attraction of an advanced area. They believe that these immobile resources sooner or later will stimulate those who know how to exploit them effectively and profitably. The reason why this view is unhelpful is that existing immobile resources can and often do remain inaccessible. Potentially profitable resources never actually become useful for development because the conditions for exploiting them have not been achieved, or nobody has ever thought of using them. A case study illustrating how this can happen is presented in the Appendix of Chapter Three. Proceeding along our path, a third commonly held view must be set aside. Even if they accept that the process of valorising immobile resources is not always so easy, economists often say that this is not a problem if in the backward area the cost of labour is very low. The objection is that the difficulty of valorising immobile resources is made up for by a particularly advantageous condition of low labour costs. If there were no institutions keeping wages artificially high, unemployment or under-employment would be solved by salaries so low that the labour cost per production unit would be advantageous even in situations of low productivity. This, people claim, would help overcome other curbs on development. This approach is on the surface quite correct, but it neglects to take into account one feature. Low labour costs could well get an area out of underdevelopment, but there are no guarantees that if will keep that area out. It is thus necessary to deal with the fourth widely help view. Admitting, at this point, that underdevelopment in a backward area cannot be overcome spontaneously, even where there are low labour costs, and accepting that development needs an action that breaks with tradition, then, it is claimed, bottom-up collective action on the part of civil society can provide precisely this break. Those who hold this view believe that in order to trigger and sustain a development process collective goods such as, for example, material and immaterial infrastructures, insurance, training, and promotional services, are essential. They do not feel, however, that corresponding public action is needed. They are convinced that, collectively, civil society can achieve the goods and services needed. This idea ignores the serious difficulties that bottom-up collective action meets with if it is not supported by public action, as Chapter Three illustrates. This brings us to the fifth and final point of view that we need to deal with. Admitting that bottom-up collective action is unsuccessful, a break with tradition can be guaranteed simply by decentralising institutions, providing local authorities with the sufficient skills and resources to take care of their own needs. We argue that decentralizing on its own is not a solution. Development policies require State intervention to be organized in a complex institutional framework, as Chapter Five shows.local development, institutions