Jonas Nicodemus

PINNs-based-MPC. We discuss nonlinear model predictive control (NMPC) for multi-body dynamics via physics-informed machine learning methods. Physics-informed neural networks (PINNs) are a promising tool to approximate (partial) differential equations. PINNs are not suited for control tasks in their original form since they are not designed to handle variable control actions or variable initial values. We thus present the idea of enhancing PINNs by adding control actions and initial conditions as additional network inputs. The high-dimensional input space is subsequently reduced via a sampling strategy and a zero-hold assumption. This strategy enables the controller design based on a PINN as an approximation of the underlying system dynamics. The additional benefit is that the sensitivities are easily computed via automatic differentiation, thus leading to efficient gradient-based algorithms. Finally, we present our results using our PINN-based MPC to solve a tracking problem for a complex mechanical system, a multi-link manipulator.

energy-matching. This repository contains the code for the paper Energy matching in reduced passive and port-Hamiltonian systems. The goal is to obtain low-dimensional port-Hamiltonian (pH) models that effectively approximate both the input-output dynamics and the energy (Hamiltonian) of a full-order model (FOM).

phdmd. We present a novel physics-informed system identification method to construct a passive linear time-invariant system. In more detail, for a given quadratic energy functional, measurements of the input, state, and output of a system in the time domain, we find a realization that approximates the data well while guaranteeing that the energy functional satisfies a dissipation inequality. To this end, we use the framework of port-Hamiltonian (pH) systems and modify the dynamic mode decomposition to be feasible for continuous-time pH systems. We propose an iterative numerical method to solve the corresponding least-squares minimization problem. We construct an effective initialization of the algorithm by studying the least-squares problem in a weighted norm, for which we present the analytical minimum-norm solution. The efficiency of the proposed method is demonstrated with several numerical examples.

QuadraticOutputSystems.jl. Linear control systems with quadratic output in Julia

klap. This repository contains the code for the paper KLAP: KYP Lemma based low-rank approximation for H2-optimal passivation.

PortHamiltonianSystems.jl. Port-Hamiltonian systems in Julia