Search

The paper proposes a general framework to manage a team of Autonomous Underwater Vehicles (AUVs), while keeping the communication constraints, during missions execution. Virtual spring-damper couplings (passive by definition) define the distributed interaction forces between neighbouring vehicles. In this way, through passivity theory, a suitable Lyapunov function for the closed loop system is built to ensure stable convergence of the network vehicles to an equilibrium point, also providing robustness in presence of communication fading and delays, very common in the marine environment. Simulations of typical missions show the effectiveness of the proposed approach. An equivalence between this typical port-Hamiltonian framework and a specific class of potential games, the Bilateral Symmetric Interaction (BSI) one, is also established. Hence, modelling the network with passive elements, it is possible to shape the transient behaviour of the players and the reached equilibria at the end of the game. [ABSTRACT FROM AUTHOR]

We develop a data-driven approach to the computation of a-posteriori feasibility certificates for sets of solutions of variational inequalities affected by uncertainty. Specifically, we focus on variational inequalities with a deterministic mapping and an uncertain feasible set, and represent uncertainty by means of scenarios. Building upon recent advances in the scenario approach literature, we quantify the robustness properties of the entire set of solutions of a variational inequality, with feasibility set constructed using the scenario approach, against a new unseen realization of the uncertainty. Our results extend existing ones that typically impose that the solution set is a singleton and require certain non-degeneracy properties: hence, we thereby offer probabilistic feasibility guarantees for any feasible solution of the underlying variational inequality. We show that assessing the violation probability of an entire set of solutions requires enumeration of the support constraints that "shape" this set, and also propose a procedure to enumerate the support constraints that does not require a description of the solution set. We illustrate our results through numerical simulations on a robust game involving an electric vehicle charging coordination problem. [ABSTRACT FROM AUTHOR]

Abstract This paper proposes a decentralised explicit (closed-form) iterative formula that solves convex programming problems with linear equality constraints and interval bounds on the decision variables. In particular, we consider a team of decision agents, each setting the value of a subset of the variables, and a team of information agents, in charge of ensuring that the equality constraints are fulfilled. The structure of the constraint matrix imposes a communication pattern between decision and information agents, which can be represented as a bipartite graph. We associate each information agent with an integral variable and each decision agent with a saturated function, which takes the interval bounds into account, and we design a decentralised dynamic mechanism that globally converges to the optimal solution. Under mild conditions, the convergence is shown to be exponential. We also provide a discrete-time algorithm, based on the Euler system, and we give an upper bound for the step parameter to ensure convergence. Although the considered optimisation problem is static, we show that the proposed scheme can be successfully applied to find the optimal solution of network-decentralised dynamic control problems. [ABSTRACT FROM AUTHOR]