arXiv subjects

Irene Schimperna

Publications and source records attributed to Irene Schimperna.

7 recordsLinked to original sources

arXiv2026

Exponential stability of data-driven nonlinear MPC based on input/output models

We consider nonlinear model predictive control (MPC) schemes without stabilizing terminal conditions, where the model used in the optimization step is generated based on input-output data only. We establish exponential stability for sufficiently long prediction horizons assuming exponential stabilizability and a proportional error bound. Moreover, we verify the imposed condition on the approximation using kernel interpolation and demonstrate the practical applicability to nonlinear systems by numerical simulations.

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arXiv2026

Stability of data-driven Koopman MPC with terminal conditions

This paper derives conditions under which Model Predictive Control (MPC) with terminal conditions, using a data-driven surrogate model as a prediction model, asymptotically stabilizes the plant despite approximation errors. In particular, we prove recursive feasibility and asymptotic stability if a proportional error bound holds, where proportional means that the bound is linear in the norm of the state and the input. For a broad class of nonlinear systems, this condition can be satisfied using data-driven surrogate models generated by kernel Extended Dynamic Mode Decomposition (kEDMD) using the Koopman operator. Last, the applicability of the proposed framework is demonstrated in a numerical case study.

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arXiv2026

Data-driven Model Predictive Control: Asymptotic Stability despite Approximation Errors exemplified in the Koopman framework

In this paper, we analyze stability of nonlinear model predictive control (MPC) using data-driven surrogate models in the optimization step. First, we establish asymptotic stability of the origin, a controlled steady state, w.r.t. the MPC closed loop without stabilizing terminal conditions for sufficiently long prediction horizons. To this end, we prove that cost controllability of the original system is preserved if sufficiently accurate proportional bounds on the approximation error hold. Here, proportional refers to state and control. The proportionality of the error bounds is a key element to derive asymptotic stability in presence of modeling errors and not only practical asymptotic stability. Second, we exemplarily verify the imposed assumptions for data-driven surrogates generated with kernel extended dynamic mode decomposition based on Koopman operator theory. Hereby, we do not impose invariance assumptions on finite dictionaries, but rather derive all conditions under non-restrictive conditions. Finally, we demonstrate our findings with numerical simulations.

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arXiv2025

Offset-free Nonlinear MPC with Koopman-based Surrogate Models

In this paper, we design offset-free nonlinear Model Predictive Control (MPC) for surrogate models based on Extended Dynamic Mode Decomposition (EDMD). The model used for prediction in MPC is augmented with a disturbance term, that is estimated by an observer. If the full information about the equilibrium of the real system is not available, a reference calculator is introduced in the algorithm to compute the MPC state and input references. The control algorithm guarantees offset-free tracking of the controlled output under the assumption that the modeling errors are asymptotically constant. The effectiveness of the proposed approach is showcased with numerical simulations for two popular benchmark systems: the van-der-Pol oscillator and the four-tanks process.

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arXiv2025

Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees

Extended dynamic mode decomposition (EDMD) is a popular data-driven method to predict the action of the Koopman operator, i.e., the evolution of an observable function along the flow of a dynamical system. In this paper, we leverage a recently-introduced kernel EDMD method for control systems for data-driven model predictive control. Building upon pointwise error bounds proportional in the state, we rigorously show practical asymptotic stability of the origin w.r.t. the MPC closed loop without stabilizing terminal conditions. The key novelty is that we avoid restrictive invariance conditions. Last, we verify our findings by numerical simulations.

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arXiv2024

Robust offset-free constrained Model Predictive Control with Long Short-Term Memory Networks -- Extended version

This paper develops a control scheme, based on the use of Long Short-Term Memory neural network models and Nonlinear Model Predictive Control, which guarantees recursive feasibility with slow time variant set-points and disturbances, input and output constraints and unmeasurable state. Moreover, if the set-point and the disturbance are asymptotically constant, offset-free tracking is guaranteed. Offset-free tracking is obtained by augmenting the model with a disturbance, to be estimated together with the states of the Long Short-Term Memory network model by a properly designed observer. Satisfaction of the output constraints in presence of observer estimation error, time variant set-points and disturbances is obtained using a constraint tightening approach.

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arXiv2023

Robust constrained nonlinear Model Predictive Control with Gated Recurrent Unit model -- Extended version

In this paper we propose a robust Model Predictive Control where a Gated Recurrent Unit network model is used to learn the input-output dynamic of the system under control. Robust satisfaction of input and output constraints and recursive feasibility in presence of model uncertainties are achieved using a constraint tightening approach. Moreover, new terminal cost and terminal set are introduced in the Model Predictive Control formulation to guarantee Input-to-State Stability of the closed loop system with respect to the uncertainty term.

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