2as if ρ t ⋆ , t = 0, . . . , T and Π t ⋆ , t = 0, . . . , T − 1 are optimal for (3), then ρ t ⋆ , t = 0, . . . , T and Π t ⋆ diag(ρ t ⋆ ), t = 0, . . . , T − 1 are feasible for problem (7). Next we need to show that, given the optimal solution ρ t ⋆ , t = 0, . . . , T and M t ⋆ , t = 0, . . . , T − 1 of (7), we can always reconstruct a feasible solution for (3). To do so, consider the matrices Π t ⋆

A fundamental open problem in monotone game theory is the computation of a specific generalized Nash equilibrium (GNE) among all the available ones, e.g. the optimal equilibrium with respect to a system-level objective. The existing GNE seeking algorithms have in fact convergence guarantees toward an arbitrary, possibly inefficient, equilibrium. In this paper, we solve this open problem by leveraging results from fixed-point selection theory and in turn derive distributed algorithms for the computation of an optimal GNE in monotone games. We then extend the technical results to the time-varying setting and propose an algorithm that tracks the sequence of optimal equilibria up to an asymptotic error, whose bound depends on the local computational capabilities of the agents.

The paper contributes towards the modeling, identification, and control of model jet engines. We propose a nonlinear, second order model in order to capture the model jet engines governing dynamics. The model structure is identified by applying sparse identification of nonlinear dynamics, and then the parameters of the model are found via gray-box identification procedures. Once the model has been identified, we approached the control of the model jet engine by designing two control laws. The first one is based on the classical Feedback Linearization technique while the second one on the Sliding Mode control. The overall methodology has been verified by modeling, identifying and controlling two model jet engines, i.e. P100-RX and P220-RXi developed by JetCat, which provide a maximum thrust of 100 N and 220 N, respectively.

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To optimally select a generalized Nash equilibrium, in this paper, we propose a semi-decentralized algorithm based on a double-layer Tikhonov regularization method. Technically, we extend the Tikhonov method for equilibrium selection in non-generalized games to the generalized case by coupling it with the preconditioned forward-backward splitting, which guarantees linear convergence to the solutions of the inner layer problem and allows for a semi-decentralized implementation. We then establish a conceptual connection and draw a comparison between the proposed algorithm and the hybrid steepest descent method, the other known distributed framework for solving the selection problem.