arXiv subjects

Mircea Lazar

Publications and source records attributed to Mircea Lazar.

At least 19 recordsLinked to original sources

arXiv2026

Tube MPC for Bilinear Koopman Models using Robust Control Contraction Metrics

This paper presents a robust tube model predictive control (MPC) framework for nonlinear systems represented by bilinear Koopman models identified from data. We derive discrete-time robust control contraction metrics (RCCMs) for bilinear Koopman models, which certify a contraction property that explicitly accounts for the mismatch between the Koopman model and the true dynamics. To synthesize such certificates for the typically high-dimensional lifted state, we propose a scalable learning approach that trains neural network parameterizations of the metric and of an associated feedback controller over a sparsely sampled subset of the lifted state space. The resulting certificates are used to construct a robust tube MPC scheme with tightened constraints, for which we establish recursive feasibility, robust constraint satisfaction and input-to-state stability (ISS) of the closed-loop system with respect to the mismatch between the Koopman model and the true dynamics. By exploiting the linear parameter-varying structure of bilinear Koopman models, the MPC problem becomes convex for a fixed scheduling sequence, while the geodesic computation underlying the contractive feedback is reformulated, via a Chebyshev pseudospectral discretization, as a sequence of quadratic programs. The complete framework is validated on a nonlinear pendulum benchmark with a state-dependent input gain.

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arXiv2026

Koopman operator theory: fundamentals, control, and applications

The Koopman operator has gained considerable attention due to its ability to provide a global linear representation of highly complex dynamical systems. The operator describes nonlinear dynamics in a linear way through the lens of real- or complex-valued observable functions. Recently proposed data-driven techniques, like extended dynamic mode decomposition (EDMD), its kernelized variant, and machine-learning methods, can be used to generate finite-dimensional approximations accompanied by finite-data error bounds. In this tutorial paper, we provide a concise introduction into Koopman operator theory and its use in systems and control. A particular focus is put on data-driven surrogate models, their extension to systems with inputs, and controller design using Koopman operator theory. Moreover, we demonstrate the key techniques, i.e., EDMD and Koopman MPC. To this end, we provide simulation studies including source code on GitHub to enable the interested reader to experience the Koopman operator in systems and control step by step.

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arXiv2026

Autonomous Driving with Priority-Ordered STL Specifications Under Multimodal Uncertainty

Autonomous vehicles must plan trajectories that satisfy multiple requirements, such as safety, traffic-rule compliance, and passenger comfort. However, in safety-critical scenarios, it is not always possible to satisfy all requirements simultaneously, necessitating their prioritization based on importance. At the same time, the uncertainty in the predicted trajectories of surrounding road users, such as other vehicles and pedestrians, must be explicitly accounted for. In this work, we propose an uncertainty-aware trajectory planning framework that incorporates a predefined priority ordering over Signal Temporal Logic (STL) specifications and preserves the induced lexicographic ordering under multimodal uncertainty. We implement this formulation with Model Predictive Path Integral (MPPI) control and demonstrate the effectiveness of our method on simulation scenarios, showing that our framework efficiently handles conflicting objectives under realistic multimodal uncertainty.

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arXiv2026

PE-MHL: Physics-Encoded Modular Hybrid Layers for Scalable Learning of Complex Systems

Hybrid models that combine physics-based and data-driven components have shown strong potential for achieving accuracy and interpretability in control applications. While recent methods have made progress in incorporating physical consistency, challenges remain in scalability, robustness to noise, and control of model complexity. This paper proposes a Physics-Encoded Modular Hybrid Layer (PE-MHL) framework, in which a baseline physics-based model is incrementally refined through the addition of new sub-models, where each new component adds complexity while preserving what previous components have already learned. We establish a theoretical guarantee for this construction: with a least-squares initialization of each new sub-model, the training error is monotonically non-increasing in the number of sub-models and provably converges. Empirical evaluations on a nonlinear NARX benchmark and the Quanser Aero 2 platform demonstrate that PE-MHL outperforms equivalently sized monolithic networks in both accuracy and generalization, while also providing more stable training dynamics and better preservation of underlying data structures.

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arXiv2026

Koopman operator learning for predictive control via Khatri-Rao kernel regression

This paper develops a data-driven realization of the generalized Koopman operator (GeKo), in which states and inputs are lifted independently and the dynamics are expressed as a tensor bilinear system. The first contribution is a time-sequenced multi-step Khatri-Rao kernel regression formulation that exposes the operator to evolved snapshots along trajectories rather than only single one-step pairs, which reduces compounded prediction error. Secondly, we develop a kernel- and input-agnostic structured SVD reduction that compresses the lifted state and input spaces while preserving the Khatri-Rao realization. We instantiate the framework with random Fourier features and describe a complete predictive-control pipeline, including a multi-step roll-out diagnostic that guides the choice of MPC horizon. The framework is validated on the chaotic Lorenz system, where the learned reduced-order GeKo model stabilizes an unstable equilibrium from a range of initial conditions.

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arXiv2026

Dynamic Output-Feedback Controller Synthesis for Dissipativity and $H_2$ Performance from Noisy Input-Output Data

In this paper we propose dynamic output-feedback controller synthesis methods for discrete-time linear time-invariant systems. The synthesis goal is either to achieve dissipativity with respect to a given quadratic supply rate, or to achieve given $H_2$ performance level. It is assumed that the autoregressive model of system dynamics is unknown, expect for the noisy disturbance term which is not part of the performance channel. Instead, we have a recorded trajectory of inputs and outputs which can be corrupted by an unknown but bounded disturbance. Methods are formulated in terms of linear matrix inequalities parametrized by a scalar variable, while in noiseless case they reduce to linear matrix inequalities. Within the considered setting, synthesis procedures are non-conservative.

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arXiv2026

Efficient sparse GP-MPC with accurate mean and variance propagation applied for quadcopter flight control

This paper presents a computationally efficient approach for Gaussian process model predictive control (GP-MPC), where Gaussian process (GP) regression is used to complement a baseline model of the system dynamics. The proposed method achieves propagation of both the predicted mean and variance, thereby significantly reducing conservativeness compared with existing GP-MPC formulations. The nonlinear GP-MPC problem is reformulated into an exact linear parameter-varying (LPV) structure that preserves the nonlinear prediction dynamics in affine form without introducing further approximation. Moreover, closed-form derivations of moment matching (MM) predictions for sparse GPs are developed, including both mean and variance propagation under uncertain inputs, which improves scalability to larger datasets. This further enables recasting the resulting GP-MPC problem as a sequence of quadratic programs (QPs), which can be solved efficiently. The proposed framework significantly improves runtime efficiency while maintaining prediction accuracy, as demonstrated through simulation and real-world experiments on a Crazyflie 2.1 micro quadcopter.

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arXiv2026

Mamba Sequence Modeling meets Model Predictive Control

In this paper, we consider the design of Model Predictive Control (MPC) algorithms based on Mamba neural networks. Mamba is a neural network architecture capable of sub-quadratic computational scaling in sequence length with state-of-the-art modeling capabilities. We provide a consistent and complete mathematical description of the Mamba neural network is provided. Then, adjustments and optimizations are made to construct a decoder-only Mamba multi-step predictor for MPC and an input-output formulation is given for sequence-to-sequence modeling of dynamical systems. The performance of Mamba-MPC is evaluated on several numerical examples and compared to a Long-Short-Term-Memory based MPC (LSTM-MPC) equivalent. First, a Single-Input-Single-Output (SISO) Van der Pol oscillator is considered, where stability, reference tracking, and noise robustness are evaluated. Then, a MIMO Four Tank setup is introduced where Multiple-Input-Multiple-Output (MIMO) reference tracking is evaluated. Lastly, Mamba-MPC is implemented on a physical Quanser Aero2 setup for closed-loop reference tracking. The results demonstrate that Mamba-MPC is able to stabilize and track a reference for SISO and MIMO systems, both in simulation and on a physical setup. Moreover, Mamba-MPC consistently outperforms LSTM-MPC in predictive control and is significantly computationally faster.

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arXiv2026

Output-Feedback Controller Synthesis for Dissipativity and $H_2$ Performance of Autoregressive Systems from Noisy Input-Output Data

In this paper we propose a data-driven output-feedback controller synthesis method for discrete-time linear time-invariant systems in the form of autoregressive model with exogenous input. The synthesis goal is either to achieve dissipativity with respect to a given quadratic supply rate, or to achieve given $H_2$ performance level. It is assumed that the model of the plant is unknown, except for the disturbance term. To compensate for the lack of model knowledge, we have a recorded trajectory of the controlled input and the output available for control, which can be corrupted by an unknown but bounded disturbance. Derived controller synthesis method is in the form of linear matrix inequalities and is nonconservative within the considered problem setting.

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arXiv2025

A Unified Representation of Neural Networks Architectures

In this paper we consider the limiting case of neural networks (NNs) architectures when the number of neurons in each hidden layer and the number of hidden layers tend to infinity thus forming a continuum, and we derive approximation errors as a function of the number of neurons and/or hidden layers. Firstly, we consider the case of neural networks with a single hidden layer and we derive an integral infinite width neural representation that generalizes existing continuous neural networks (CNNs) representations. Then we extend this to deep residual CNNs that have a finite number of integral hidden layers and residual connections. Secondly, we revisit the relation between neural ODEs and deep residual NNs and we formalize approximation errors via discretization techniques. Then, we merge these two approaches into a unified homogeneous representation of NNs as a Distributed Parameter neural Network (DiPaNet) and we show that most of the existing finite and infinite-dimensional NNs architectures are related via homogenization/discretization with the DiPaNet representation. Our approach is purely deterministic and applies to general, uniformly continuous matrix weight functions. Relations with neural fields and other neural integro-differential equations are discussed along with further possible generalizations and applications of the DiPaNet framework.

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arXiv2025

Scalable Nonlinear DeePC: Bridging Direct and Indirect Methods and Basis Reduction

This paper studies regularized data-enabled predictive control (DeePC) within a nonlinear framework and its relationship to subspace predictive control (SPC). The $\Pi$-regularization is extended to general basis functions and it is shown that, under suitable conditions, the resulting basis functions DeePC formulation constitutes a relaxation of basis functions SPC. To improve scalability, we introduce an SVD-based dimensionality reduction that preserves the equivalence with SPC, and we derive a reduced {\Pi}-regularization. A LASSO based sparse basis selection method is proposed to obtain a reduced basis from lifted data. Simulations on a nonlinear van der Pol oscillator model indicate that, in the absence of noise, DeePC and SPC yield equivalent absolute mean tracking errors (AMEs) when large penalties are applied. In contrast, under noisy measurements, careful tuning of the DeePC regularization results in a reduced AME, outperforming SPC.

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arXiv2025

Situation-Aware Interactive MPC Switching for Autonomous Driving

Autonomous driving in interactive traffic scenarios remains challenging because of the mutual influence among vehicles and the inherent uncertainty of surrounding agents. Several model predictive control (MPC) formulations have been proposed to address this challenge, each adopting a different model of inter-agent interaction. While higher-fidelity interaction models enable more intelligent behavior, they incur substantially greater computational cost. Since strong interactions arise only occasionally in real traffic, a practical strategy for balancing performance and computational overhead is to invoke an appropriate controller based on situational demands. To this end, we first conduct a comparative study to assess and hierarchize the interactive capabilities of different MPC formulations. Building on this hierarchy, we then develop a neural network-based classifier for situation-aware switching among these controllers. We demonstrate that, by invoking the most advanced interactive MPC only in rare but critical situations and relying on a basic MPC in the majority of situations, situation-aware switching substantially improves overall performance while significantly reducing computational load.

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arXiv2025

Offset-free Data-Driven Predictive Control for Grid-Connected Power Converters in Weak Grid Faults

Grid-connected power converters encounter significant stability challenges during weak grid faults, when conventional PI-based controllers exhibit an oscillatory response and poor fault-ride-through performance. This paper addresses this problem by replacing the conventional outer PI controllers that regulate DC-link and PCC voltages with an offset-free data-driven predictive controller. The developed algorithm leverages either pre-fault or fault-time data to construct input-output predictors, yielding offset-free control without the need for physics-based modelling. Simulation results show that pre-fault offset-free DPC doubles the critical equivalent grid impedance that can be handled and reduces the root mean squared error during faults by a factor of 40, while maintaining computation times comparable to conventional PI control. These findings demonstrate that the developed offset-free data predictive controller offers a simple, robust, and computationally efficient alternative to conventional control, significantly enhancing fault-ride-through capabilities of converters in weak grids.

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arXiv2025

From Product Hilbert Spaces to the Generalized Koopman Operator and the Nonlinear Fundamental Lemma

The generalization of the Koopman operator to systems with control input and the derivation of a nonlinear fundamental lemma are two open problems that play a key role in the development of data-driven control methods for nonlinear systems. In this paper we derive a novel solution to these problems based on basis functions expansion in a product Hilbert space constructed as the tensor product between the Hilbert spaces of the state and input observable functions, respectively. We identify relaxed invariance conditions that guarantee existence of a bounded linear operator, i.e., the generalized Koopman operator, from the constructed product Hilbert space to the Hilbert space corresponding to the lifted state propagated forward in time. Compared to classical Koopman invariance conditions, measure preservation is not required. Moreover, we derive a nonlinear fundamental lemma by exploiting the constructed exact infinite-dimensional bilinear Koopman representation and Hankel operators. The effectiveness of the developed generalized Koopman embedding is illustrated on the Van der Pol oscillator and in predictive control of a soft-robotic manipulator model.

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arXiv2025

Physics-guided gated recurrent units for inversion-based feedforward control

Inversion-based feedforward control relies on an accurate model that describes the inverse system dynamics. The gated recurrent unit (GRU), which is a recent architecture in recurrent neural networks, is a strong candidate for obtaining such a model from data. However, due to their black-box nature, GRUs face challenges such as limited interpretability and vulnerability to overfitting. Recently, physics-guided neural networks (PGNNs) have been introduced, which integrate the prior physical model structure into the prediction process. This approach not only improves training convergence, but also facilitates the learning of a physics-based model. In this work, we integrate a GRU in the PGNN framework to obtain a PG-GRU, based on which we adopt a two-step approach to feedforward control design. First, we adopt stable inversion techniques to design a stable linear model of the inverse dynamics. Then, a GRU trained on the residual is tailored to inverse system identification. The resulting PG-GRU feedforward controller is validated by means of real-life experiments on a two-mass spring-damper system, where it demonstrates roughly a two-fold improvement compared to the linear feedforward and a preview-based GRU feedforward in terms of the integral absolute error.

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arXiv2025

Neural Parameter-varying Data-enabled Predictive Control of Cold Atmospheric Pressure Plasma Jets

Cold Atmospheric Pressure Plasma Jets (APPJs) show significant potential for biomedical applications, but their inherent complexity, characterized by nonlinear dynamics and strong sensitivity to operating conditions like tip-to-surface distance, presents challenges for real-time control. This paper introduces the Neural Parameter-varying Data-enabled Predictive Control (NPV-DeePC) framework to address these issues. By integrating hypernetworks into the neural DeePC paradigm, NPV-DeePC adaptively captures system nonlinearities and parameter variations, dynamically adjusts the neural network's learned representation of the system, enabling accurate multi-step trajectory prediction and control. Simulation studies on surface temperature tracking and thermal dose delivery demonstrate that NPV-DeePC achieves higher accuracy and adaptability than existing controllers. Moreover, its computational efficiency supports real-time implementation, making it a practical approach for precise APPJ control and a generalizable solution for other nonlinear, parameter-varying systems.

eess.SY↗

arXiv2025

Dynamic Output-Feedback Controller Synthesis for Dissipativity and $H_2$ Performance from Noisy Input-State Data

In this paper we propose dynamic output-feedback controller synthesis methods for discrete-time linear time-invariant systems. The synthesis goal is to achieve dissipativity with respect to a given quadratic supply rate or a given $H_2$ performance level. It is assumed that the model of system dynamics is unknown, expect for the disturbance term. Instead, we have a recorded trajectory of the control input and the state, which can be corrupted by an unknown but bounded disturbance. The state data is used only for the purpose of controller synthesis, while the designed controller is output feedback controller, i.e., the full state is not used for control in real time. The presented synthesis method is formulated in terms of linear matrix inequalities parametrized by a scalar variable, while in noiseless case it reduces to linear matrix inequalities. Within the considered setting, the synthesis procedure is non-conservative.

math.OC↗

arXiv2025

Deep Operator Neural Network Model Predictive Control

In this paper, we consider the design of model predictive control (MPC) algorithms based on deep operator neural networks (DeepONets). These neural networks are capable of accurately approximating real and complex valued solutions of continuous time nonlinear systems without relying on recurrent architectures. The DeepONet architecture is made up of two feedforward neural networks: the branch network, which encodes the input function space, and the trunk network, which represents dependencies on temporal variables or initial conditions. Utilizing the original DeepONet architecture as a predictor within MPC for Multi Input Multi Output (MIMO) systems requires multiple branch networks, to generate multi output predictions, one for each input. Moreover, to predict multiple time steps into the future, the network has to be evaluated multiple times. Motivated by this, we introduce a multi step DeepONet (MS-DeepONet) architecture that computes in one shot multi step predictions of system outputs from multi step input sequences, which is better suited for MPC. We prove that the MS DeepONet is a universal approximator in terms of multi step sequence prediction. Additionally, we develop automated hyper parameter selection strategies and implement MPC frameworks using both the standard DeepONet and the proposed MS DeepONet architectures in PyTorch. The implementation is publicly available on GitHub. Simulation results demonstrate that MS-DeepONet consistently outperforms the standard DeepONet in learning and predictive control tasks across several nonlinear benchmark systems: the van der Pol oscillator, the quadruple tank process, and a cart pendulum unstable system, where it successfully learns and executes multiple swing up and stabilization policies.

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