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A supervised learning approach for the solution of large-scale nonlinear stabilization problems is presented. A stabilizing feedback law is trained from a dataset generated from State-dependent Riccati Equation solves. The training phase is enriched by the use gradient information in the loss function, which is weighted through the use of hyperparameters. High-dimensional nonlinear stabilization tests demonstrate that real-time sequential large-scale Algebraic Riccati Equation solves can be substituted by a suitably trained feedforward neural network.
The synthesis of suboptimal feedback laws for controlling nonlinear dynamics arising from semi-discretized PDEs is studied. An approach based on the State-dependent Riccati Equation (SDRE) is presented for H2 and Hinf control problems. Depending on t
A sparse regression approach for the computation of high-dimensional optimal feedback laws arising in deterministic nonlinear control is proposed. The approach exploits the control-theoretical link between Hamilton-Jacobi-Bellman PDEs characterizing
In this paper we propose a new computational method for designing optimal regulators for high-dimensional nonlinear systems. The proposed approach leverages physics-informed machine learning to solve high-dimensional Hamilton-Jacobi-Bellman equations
Recent research has shown that supervised learning can be an effective tool for designing optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the behavior of these neural network (NN) controllers is still not well underst
Stabilizing feedback operators are presented which depend only on the orthogonal projection of the state onto the finite-dimensional control space. A class of monotone feedback operators mapping the finite-dimensional control space into itself is con