arXiv subjects

Lalo Magni

Publications and source records attributed to Lalo Magni.

5 recordsLinked to original sources

arXiv2025

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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arXiv2025

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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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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arXiv2023

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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arXiv2014

An MPC approach to output-feedback control of stochastic linear discrete-time systems

In this paper we propose an output-feedback Model Predictive Control (MPC) algorithm for linear discrete-time systems affected by a possibly unbounded additive noise and subject to probabilistic constraints. In case the noise distribution is unknown, the chance constraints on the input and state variables are reformulated by means of the Chebyshev - Cantelli inequality. The recursive feasibility of the proposed algorithm is guaranteed and the convergence of the state to a suitable neighbor of the origin is proved under mild assumptions. The implementation issues are thoroughly addressed showing that, with a proper choice of the design parameters, its computational load can be made similar to the one of a standard stabilizing MPC algorithm. Two examples are discussed in details, with the aim of providing an insight on the performance achievable by the proposed control scheme.

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