Emilio Benenati

Daniel Arnström, Emilio Benenati, Giuseppe Belgioioso

We present \texttt{DR-DAQP}, an open-source solver for strongly monotone affine variational inequaliries that combines Douglas-Rachford operator splitting with an active-set acceleration strategy. The key idea is to estimate the active set along the iterations to attempt a Newton-type correction. This step yields the exact AVI solution when the active set is correctly estimated, thus overcoming the asymptotic convergence limitation inherent in first-order methods. Moreover, we exploit warm-starting and pre-factorization of relevant matrices to further accelerate evaluation of the algorithm iterations. We prove convergence and establish conditions under which the algorithm terminates in finite time with the exact solution. Numerical experiments on randomly generated AVIs show that \texttt{DR-DAQP} is up to two orders of magnitude faster than the state-of-the-art solver \texttt{PATH}. On a game-theoretic MPC benchmark, \texttt{DR-DAQP} achieves solve times several orders of magnitude below those of the mixed-integer solver \texttt{NashOpt}. A high-performing C implementation is available at \textt{https://github.com/darnstrom/daqp}, with easily-accessible interfaces to Julia, MATLAB, and Python.

Emilio Benenati, Giuseppe Belgioioso

We present an efficient algorithm to compute the explicit open-loop solution to both finite and infinite-horizon dynamic games subject to state and input constraints. Our approach relies on a multiparametric affine variational inequality characterization of the open-loop Nash equilibria and extends the classical explicit constrained LQR and MPC frameworks to multi-agent non-cooperative settings. A key practical implication is that linear-quadratic game-theoretic MPC becomes viable even at very high sampling rates for multi-agent systems of moderate size. Extensive numerical experiments demonstrate order-of-magnitude improvements in online computation time and solution accuracy compared with state-of-the-art game-theoretic solvers.

Reza Rahimi Baghbadorani, Emilio Benenati, Sergio Grammatico

This paper considers constrained linear dynamic games with quadratic objective functions, which can be cast as affine variational inequalities. By leveraging the problem structure, we apply the Douglas-Rachford splitting, which generates a solution algorithm with linear convergence rate. The fast convergence of the method enables receding-horizon control architectures. Furthermore, we demonstrate that {the associated VI admits a closed-form solution within a neighborhood of the attractor, thus allowing for a further reduction in computation time.} Finally, we benchmark the proposed method via numerical experiments in an automated driving application.

Giuseppe L'Erario, Luca Fiorio, Gabriele Nava et al.

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.