One of the critical challenges in automated driving is ensuring safety of automated vehicles despite the unknown behavior of the other vehicles. Although motion prediction modules are able to generate a probability distribution associated with various behavior modes, their probabilistic estimates are often inaccurate, thus leading to a possibly unsafe motion plan. To overcome this challenge, we propose an Efficient RiskAware Branch MPC (EraBMPC) that appropriately accounts for the ambiguity in the estimated probability distribution. We formulate the risk-aware motion planning problem as a min-max optimization problem and develop an efficient iterative method by incorporating a regularization term in the probability update step. Via extensive numerical studies, we validate the convergence of our method and demonstrate its advantages compared to the state-of-the-art approaches.

We propose a data-driven, user-centric vehicle-to-grid (V2G) methodology based on multi-objective optimization to balance battery degradation and V2G revenue according to EV user preference. Given the lack of accurate and generalizable battery degradation models, we leverage input convex neural networks (ICNNs) to develop a data-driven degradation model trained on extensive experimental datasets. This approach enables our model to capture nonconvex dependencies on battery temperature and time while maintaining convexity with respect to the charging rate. Such a partial convexity property ensures that the second stage of our methodology remains computationally efficient. In the second stage, we integrate our data-driven degradation model into a multi-objective optimization framework to generate an optimal smart charging profile for each EV. This profile effectively balances the trade-off between financial benefits from V2G participation and battery degradation, controlled by a hyperparameter reflecting the user prioritization of battery health. Numerical simulations show the high accuracy of the ICNN model in predicting battery degradation for unseen data. Finally, we present a trade-off curve illustrating financial benefits from V2G versus losses from battery health degradation based on user preferences and showcase smart charging strategies under realistic scenarios.

In this paper we focus on noncooperative games with uncertain constraints coupling the agents’ decisions. We consider a setting where bounded deviations of agents’ decisions from the equilibrium are possible, and uncertain constraints are inferred from data. Building upon recent advances in the so called scenario approach, we propose a randomised algorithm that returns a nominal equilibrium such that a pre-specified bound on the probability of violation for yet unseen constraints is satisfied for an entire region of admissible deviations surrounding it—thus supporting neighbourhoods of equilibria with probabilistic feasibility certificates. For the case in which the game admits a potential function, whose minimum coincides with the social welfare optimum of the population, the proposed algorithmic scheme opens the road to achieve a trade-off between the guaranteed feasibility levels of the region surrounding the nominal equilibrium, and its system-level efficiency. Detailed numerical simulations corroborate our theoretical results.

We study coalitional games with exogenous uncertainty in the coalition value, in which each agent is allowed to have private samples of the uncertainty. As a consequence, the agents may have a different perception of stability of the grand coalition. In this context, we propose a novel methodology to study the out-of-sample coalitional rationality of allocations in the set of stable allocations (i.e., the core). Our analysis builds on the framework of probably approximately correct learning. Initially, we state a priori and a posteriori guarantees for the entire core. Furthermore, we provide a distributed algorithm to compute a compression set that determines the generalization properties of the a posteriori statements. We then refine our probabilistic robustness bounds by specialising the analysis to a single payoff allocation, taking, also in this case, both a priori and a posteriori approaches. Finally, we consider a relaxed ζ-core to include nearby allocations and also address the case of empty core. For this case, probabilistic statements are given on the eventual stability of allocations in the ζ-core.