Alberto Bemporad

Sophie Hall, Alberto Bemporad

We present a method for computing explicit solutions to parametric generalized Nash equilibrium (GNE) problems with convex quadratic cost functions and linear coupling and local constraints. Assuming that the parameters enter only the linear terms of the cost functions and the constraint right-hand sides, we provide the exact multiparametric solution of the GNE problem. Such a solution enables: (i) minimal real-time computation; (ii) inherent interpretability and explainability, as well as exact enumeration of all multiple equilibria; (iii) selection of desired GNE solution types in the case of infinitely many equilibria; and (iv) zero-shot updates of the GNE solution in response to changes in constraint right-hand sides and/or linear costs. In line with explicit model predictive control (MPC) approaches, we apply our method to solve game-theoretic MPC problems, also known as receding horizon games, explicitly. We compare its performance against centralized solvers in a battery charging game and a toy two-mass-spring-damper system control problem. A Python implementation of the algorithms presented in this paper is available at https://github.com/bemporad/nash_mpqp.

Marco Forgione, Ankush Chakrabarty, Dario Piga et al.

System identification has greatly benefited from deep learning techniques, particularly for modeling complex, nonlinear dynamical systems with partially unknown physics where traditional approaches may not be feasible. However, deep learning models often require large datasets and significant computational resources at training and inference due to their high-dimensional parameterizations. To address this challenge, we propose a meta-learning framework that discovers a low-dimensional manifold within the parameter space of an over-parameterized neural network architecture. This manifold is learned from a meta-dataset of input-output sequences generated by a class of related dynamical systems, enabling efficient model training while preserving the network's expressive power for the considered system class. Unlike bilevel meta-learning approaches, our method employs an auxiliary neural network to map datasets directly onto the learned manifold, eliminating the need for costly second-order gradient computations during meta-training and reducing the number of first-order updates required in inference, which could be expensive for large models. We validate our approach on a family of Bouc-Wen oscillators, which is a well-studied nonlinear system identification benchmark. We demonstrate that we are able to learn accurate models even in small-data scenarios.

Alberto Bemporad, Roland Tóth

We present a general system identification procedure capable of estimating of a broad spectrum of state-space dynamical models, including linear time-invariant (LTI), linear parameter-varying} (LPV), and nonlinear (NL) dynamics, along with rather general classes of noise models. Similar to the LTI case, we show that for this general class of model structures, including the NL case, the model dynamics can be separated into a deterministic process and a stochastic noise part, allowing to seamlessly tune the complexity of the combined model both in terms of nonlinearity and noise modeling. We parameterize the involved nonlinear functional relations by means of artificial neural-networks (ANNs), although alternative parametric nonlinear mappings can also be used. To estimate the resulting model structures, we optimize a prediction-error-based criterion using an efficient combination of a constrained quasi-Newton approach and automatic differentiation, achieving training times in the order of seconds compared to existing state-of-the-art ANN methods which may require hours for models of similar complexity. We formally establish the consistency guarantees for the proposed approach and demonstrate its superior estimation accuracy and computational efficiency on several benchmark LTI, LPV, and NL system identification problems.