We describe Urban Driving Games (UDGs) as a particular class of differential games that model the interactions and incentives of the urban driving task. The drivers possess a "communal" interest, such as not colliding with each other, but are also self-interested in fulfilling traffic rules and personal objectives. Subject to their physical dynamics, the preference of the agents is expressed via a lexicographic relation that puts as first priority the shared objective of not colliding. Under mild assumptions, we show that communal UDGs have the structure of a lexicographic ordinal potential game which allows us to prove several interesting properties. Namely, socially efficient equilibria can be found by solving a single (lexicographic) optimal control problem and iterated best response schemes have desirable convergence guarantees.
Efficient management of energy resources is crucial in smart buildings. In this work, model predictive control (MPC) is used to minimize the economic costs of prosumers equipped with production units, energy storage systems, and electric vehicles. To this purpose, the predictive control manages the available energy resources by exploiting future information about energy prices, absorption and production power profiles, and electric vehicle (EV) usage, such as times of departure and arrival and predicted energy consumption. The predictive control is compared with a rule-based technique, herein referred to as a heuristic approach, that acts in an instant-by-instant fashion without considering any future information. The reported results show that the studied predictive approach allows one to achieve charging profiles that adapt to variable operating conditions, aiming at optimal performances in terms of economic cost minimization in time-varying price scenarios, reduction of rms current stresses, and recharging capability of EV batteries. Specifically, unlike the heuristic method, the MPC approach is proven to be capable of efficiently managing the available energy resources to ensure a full recharge of the EV battery during nighttime while always respecting all system constraints. In addition, the proposed control is shown to be capable of keeping the peak power absorption from the grid constrained within set limits, which is a valuable feature in scenarios with widespread adoption of EVs in order to limit the stress on the electrical system.
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