Distributed optimal coordination across multiple decision-makers and its application to demand response in Smart
Date of Issue2016
School of Electrical and Electronic Engineering
With the prevalence of coupling engineering systems such as multi-agent systems, wireless networks and the smart grid, solving optimization problems across multiple decision-makers emerges to be of theoretical significance and practical relevance. Resource allocation for systems with limited resources, energy consumption control for electricity users, and economic dispatch among a network of generators in smart grids are typical examples of multi-decision-maker optimization problems. These optimization problems are explored from the perspectives of non-cooperative games and networked optimization in this dissertation. The background, introduction and motivation for this topic are included in the first two chapters. The specific problems considered in the dissertation are summarized as follows. Energy consumption control among a network of electricity users in smart grids is considered. An aggregate game approach is proposed to solve it by noticing that the aggregate energy consumption is unknown to the electricity users during the energy consumption scheduling process. Average consensus based updating strategies are developed to search for the Nash equilibrium of the energy consumption game. A general energy consumption game with possibly multiple Nash equilibria is firstly explored. In this case, the Nash equilibrium is exponentially stable under the given strategy. In particular, energy consumption game (for heating ventilation and air conditioning systems) that admits a unique Nash equilibrium is then investigated. Based on the uniqueness of the Nash equilibrium, a non-local convergence result is derived. Furthermore, energy consumption games with stubborn players are studied. With the existence of stubborn players, the rational players' actions converge to a neighborhood of the best response strategies. By utilizing the proposed methods, the electricity users only need to communicate with their neighbors about their estimates on the averaged aggregate energy consumption. No private information is exchanged among the electricity users. Hence, the proposed methods are free of privacy concern. Since the Nash equilibrium may not be efficient from the system-level perspective, distributed optimization problems are investigated. In Chapter 4, a distributed extremum seeking framework is proposed to solve networked optimization problems. Under some conditions, the proposed method enables the agents' strategies to converge to the optimal solution without using the explicit expressions of the constraints functions, the cost functions or their gradients. Noticing that many engineering systems exhibit time-varying characteristic while continuous-time time-varying distributed optimization remains as an open problem, we consider it for systems with quadratic objective functions in this dissertation. Time-varying distributed optimization with neighboring coupled objective functions is firstly considered. A robust gradient based method is proposed to solve it. More generally coupled distributed optimization problems are then investigated by penalty function based methods. The penalty function based methods can be utilized to approximate the solution of the distributed optimization problem. The last problem considered is seeking the solution to non-cooperative games without using explicit model information. Different from existing works that regard the Nash equilibrium as a ``fixed point", Nash equilibrium is treated as a time-varying trajectory in this dissertation. The time-varying Nash equilibrium seeking problem is addressed by using an extremum seeking approach. Sinusoidal excitation signals are utilized in the extremum seeking loop to modulate and demodulate the players' actions. A delay-based subsystem is employed to estimate the gradient and a robust tracking strategy is designed to search for the Nash equilibrium based on the estimated gradients. For symmetric quadratic games, it is shown that the players' actions converge asymptotically to the Nash equilibrium trajectory. For more general quadratic games, a bounded convergence result is presented. In summary, this dissertation studies optimization problems across multiple decision-makers. If the decision-makers are self-interested, the problem may be modeled as non-cooperative games. Nash equilibrium seeking for non-cooperative games are considered. To achieve the system-level objective, networked optimization is investigated. An extremum seeking approach is proposed to solve it which is followed by some explorations on time-varying distributed optimization problems. To demonstrate the practical relevance of the non-cooperative games and the networked optimization problems, energy consumption control for electricity users in smart grids is studied.