Patrik Valábek

Patrik Valábek, Marek Wadinger, Michal Kvasnica et al.

Nonlinear dynamical systems with input delays pose significant challenges for prediction, estimation, and control due to their inherent complexity and the impact of delays on system behavior. Traditional linear control techniques often fail in these contexts, necessitating innovative approaches. This paper introduces a novel approach to approximate the Koopman operator using an LSTM-enhanced Deep Koopman model, enabling linear representations of nonlinear systems with time delays. By incorporating Long Short-Term Memory (LSTM) layers, the proposed framework captures historical dependencies and efficiently encodes time-delayed system dynamics into a latent space. Unlike traditional extended Dynamic Mode Decomposition (eDMD) approaches that rely on predefined dictionaries, the LSTM-enhanced Deep Koopman model is dictionary-free, which mitigates the problems with the underlying dynamics being known and incorporated into the dictionary. Quantitative comparisons with extended eDMD on a simulated system demonstrate highly significant performance gains in prediction accuracy in cases where the true nonlinear dynamics are unknown and achieve comparable results to eDMD with known dynamics of a system.

Dominik Beňo, Patrik Valábek, Martin Hromčík et al.

This paper presents an online linear model predictive control (MPC) framework for slew maneuvers that maintains star-tracker availability during ground-target tracking. The nonlinear rigid-body dynamics and geometric exclusion constraints are analytically linearized about the current state estimate at each control step, yielding a time-varying linear MPC formulation cast as a standard quadratic program (QP). This structure is compatible with established aerospace flight-software practices and offers a computational profile with lower online complexity than comparable nonlinear MPC schemes. The controller incorporates angular-rate, actuator, and star-tracker exclusion constraints over a receding horizon. Performance is assessed in high-fidelity nonlinear model-in-the-loop simulations using NASA's "42" spacecraft dynamics simulator, including a Monte Carlo campaign over varying target geometries and inertia perturbations.

Branislav Daráš, Patrik Valábek, Martin Klaučo

Data-driven predictive control methods can provide the constraint handling and optimization of model predictive control (MPC) without first-principles models. Two such methods differ in how they replace the model: Data-enabled predictive control (DeePC) uses behavioral systems theory to predict directly from input--output trajectories via Hankel matrices, while Koopman-based MPC (KMPC) learns a lifted linear state-space representation from data. Both methods are well studied on their own, but head-to-head comparisons on multivariable process control problems are few. This paper compares them on a pasteurization unit with three manipulated inputs and three measured outputs, using a neural-network-based digital twin as the plant simulator. Both controllers share identical prediction horizons, cost weights, and constraints, so that differences in closed-loop behavior reflect the choice of predictive representation. Results show that both methods achieve feasible constrained control with comparable tracking error, but with a clear trade-off: KMPC tracks more tightly under the chosen cost, while DeePC produces substantially smoother input trajectories. These results help practitioners choose between the two approaches for thermal processing applications.

Patrik Valábek, Michaela Horváthová, Martin Klaučo

This paper presents a deep Koopman-based Economic Model Predictive Control (EMPC) for efficient operation of a laboratory-scale pasteurization unit (PU). The method uses Koopman operator theory to transform the complex, nonlinear system dynamics into a linear representation, enabling the application of convex optimization while representing the complex PU accurately. The deep Koopman model utilizes neural networks to learn the linear dynamics from experimental data, achieving a 45% improvement in open-loop prediction accuracy over conventional N4SID subspace identification. Both analyzed models were employed in the EMPC formulation that includes interpretable economic costs, such as energy consumption, material losses due to inadequate pasteurization, and actuator wear. The feasibility of EMPC is ensured using slack variables. The deep Koopman EMPC and N4SID EMPC are numerically validated on a nonlinear model of multivariable PU under external disturbance. The disturbances include feed pump fail-to-close scenario and the introduction of a cold batch to be pastuerized. These results demonstrate that the deep Koopmand EMPC achieves a 32% reduction in total economic cost compared to the N4SID baseline. This improvement is mainly due to the reductions in material losses and energy consumption. Furthermore, the steady-state operation via Koopman-based EMPC requires 10.2% less electrical energy. The results highlight the practical advantages of integrating deep Koopman representations with economic optimization to achieve resource-efficient control of thermal-intensive plants.