arXiv subjects

Mircea Lazar

Publications and source records attributed to Mircea Lazar.

At least 37 records · Page 2Linked to original sources

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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arXiv2025

imuQP: An Inverse-Matrix-Updates-Based Fast QP Solver Suitable for Real-Time MPC

This paper presents a new fast active-set quadratic programming (QP) solver based on inverse matrix updates, which is suitable for real-time model predictive control (MPC). This QP solver, called imuQP (inverse matrix update QP), is based on Karush-Kuhn-Tucker (KKT) conditions and is inspired by Hildreth's QP solver. An extensive convergence and optimality analysis of imuQP, including infeasibility detection, is presented. The memory footprint and computational complexity of imuQP are analyzed and compared with qpOASES, a well-known active-set QP solver in literature. Speed and accuracy of imuQP are compared with state-of-the-art active-set QP solvers by simulating a chain of spring-connected masses in MATLAB. For illustration, MPC with integral action is used, to remove offset when tracking a constant reference, with a small sampling period of Ts = 4 ms. Simulation results show that imuQP is suitable for fast systems - with small Ts - and is competitive with state-of-the-art active-set QP solvers.

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arXiv2025

A Kernelized Operator Approach to Nonlinear Data-Enabled Predictive Control

This paper considers the design of nonlinear data-enabled predictive control (DeePC) using kernel functions. Compared with existing methods that use kernels to parameterize multi-step predictors for nonlinear DeePC, we adopt a novel, operator-based approach. More specifically, we employ a universal product kernel parameterization of nonlinear systems operators as a prediction mechanism for nonlinear DeePC. We show that by using a product reproducing kernel Hilbert space (RKHS) to learn the system trajectories, big data sets can be handled effectively to construct the corresponding product Gram matrix. Moreover, we show that the structure of the adopted product RKHS representation allows for a computationally efficient DeePC formulation. Compared to existing methods, our approach achieves substantially faster computation times for the same data size. This allows for the use of much larger data sets and enhanced control performance.

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arXiv2024

A universal reproducing kernel Hilbert space for learning nonlinear systems operators

In this work, we consider the problem of learning nonlinear operators that correspond to discrete-time nonlinear dynamical systems with inputs. Given an initial state and a finite input trajectory, such operators yield a finite output trajectory compatible with the system dynamics. Inspired by the universal approximation theorem of operators tailored to radial basis functions neural networks, we construct a class of kernel functions as the product of kernel functions in the space of input trajectories and initial states, respectively. We prove that for positive definite kernel functions, the resulting product reproducing kernel Hilbert space is dense and even complete in the space of nonlinear systems operators, under suitable assumptions. This provides a universal kernel-functions-based framework for learning nonlinear systems operators, which is intuitive and easy to apply to general nonlinear systems.

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arXiv2024

Kernelized offset-free data-driven predictive control for nonlinear systems

This paper presents a kernelized offset-free data-driven predictive control scheme for nonlinear systems. Traditional model-based and data-driven predictive controllers often struggle with inaccurate predictors or persistent disturbances, especially in the case of nonlinear dynamics, leading to tracking offsets and stability issues. To overcome these limitations, we employ kernel methods to parameterize the nonlinear terms of a velocity model, preserving its structure and efficiently learning unknown parameters through a least squares approach. This results in a offset-free data-driven predictive control scheme formulated as a nonlinear program, but solvable via sequential quadratic programming. We provide a framework for analyzing recursive feasibility and stability of the developed method and we demonstrate its effectiveness through simulations on a nonlinear benchmark example.

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arXiv2024

Constraints-Informed Neural-Laguerre Approximation of Nonlinear MPC with Application in Power Electronics

This paper considers learning online (implicit) nonlinear model predictive control (MPC) laws using neural networks and Laguerre functions. Firstly, we parameterize the control sequence of nonlinear MPC using Laguerre functions, which typically yields a smoother control law compared to the original nonlinear MPC law. Secondly, we employ neural networks to learn the coefficients of the Laguerre nonlinear MPC solution, which comes with several benefits, namely the dimension of the learning space is dictated by the number of Laguerre functions and the complete predicted input sequence can be used to learn the coefficients. To mitigate constraints violation for neural approximations of nonlinear MPC, we develop a constraints-informed loss function that penalizes the violation of polytopic state constraints during learning. Box input constraints are handled by using a clamp function in the output layer of the neural network. We demonstrate the effectiveness of the developed framework on a nonlinear buck-boost converter model with sampling rates in the sub-millisecond range, where online nonlinear MPC would not be able to run in real time. The developed constraints-informed neural-Laguerre approximation yields similar performance with long-horizon online nonlinear MPC, but with execution times of a few microseconds, as validated on a field-programmable gate array (FPGA) platform.

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arXiv2024

Risk-Aware Real-Time Task Allocation for Stochastic Multi-Agent Systems under STL Specifications

This paper addresses the control synthesis of heterogeneous stochastic linear multi-agent systems with real-time allocation of signal temporal logic (STL) specifications. Based on previous work, we decompose specifications into sub-specifications on the individual agent level. To leverage the efficiency of task allocation, a heuristic filter evaluates potential task allocation based on STL robustness, and subsequently, an auctioning algorithm determines the definitive allocation of specifications. Finally, a control strategy is synthesized for each agent-specification pair using tube-based model predictive control (MPC), ensuring provable probabilistic satisfaction. We demonstrate the efficacy of the proposed methods using a multi-shuttle scenario that highlights a promising extension to automated driving applications like vehicle routing.

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arXiv2024

Finite Control Set Model Predictive Control with Limit Cycle Stability Guarantees

This paper considers the design of finite control set model predictive control (FCS-MPC) for discrete-time switched affine systems. Existing FCS-MPC methods typically pursue practical stability guarantees, which ensure convergence to a bounded invariant set that contains a desired steady state. As such, current FCS-MPC methods result in unpredictable steady-state behavior due to arbitrary switching among the available finite control inputs. Motivated by this, we present a FCS-MPC design that aims to stabilize a steady-state limit cycle compatible with a desired output reference via a suitable cost function. We provide conditions in terms of periodic terminal costs and finite control set control laws that guarantee asymptotic stability of the developed limit cycle FCS-MPC algorithm. Moreover, we develop conditions for recursive feasibility of limit cycle FCS-MPC in terms of periodic terminal sets and we provide systematic methods for computing ellipsoidal and polytopic periodically invariant sets that contain a desired steady-state limit cycle. Compared to existing periodic terminal ingredients for tracking MPC with a continuous control set, we design and compute terminal ingredients using a finite control set. The developed methodology is validated on switched systems and power electronics benchmark examples.

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arXiv2024

Neural Data-Enabled Predictive Control

Data-enabled predictive control (DeePC) for linear systems utilizes data matrices of recorded trajectories to directly predict new system trajectories, which is very appealing for real-life applications. In this paper we leverage the universal approximation properties of neural networks (NNs) to develop neural DeePC algorithms for nonlinear systems. Firstly, we point out that the outputs of the last hidden layer of a deep NN implicitly construct a basis in a so-called neural (feature) space, while the output linear layer performs affine interpolation in the neural space. As such, we can train off-line a deep NN using large data sets of trajectories to learn the neural basis and compute on-line a suitable affine interpolation using DeePC. Secondly, methods for guaranteeing consistency of neural DeePC and for reducing computational complexity are developed. Several neural DeePC formulations are illustrated on a nonlinear pendulum example.

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arXiv2024

Structured physics-guided neural networks for electromagnetic commutation applied to industrial linear motors

Mechatronic systems are described by an interconnection of the electromagnetic part, i.e., a static position-dependent nonlinear relation between currents and forces, and the mechanical part, i.e., a dynamic relation from forces to position. Commutation inverts a model of the electromagnetic part of the system, and thereby removes the electromagnetic part from the position control problem. Typical commutation algorithms rely on simplified models derived from physics-based knowledge, which do not take into account position dependent parasitic effects. In turn, these commutation related model errors translate into position tracking errors, which limit the system performance. Therefore, in this work, we develop a data-driven approach to commutation using physics-guided neural networks (PGNNs). A novel PGNN model is proposed which structures neural networks (NNs) to learn specific motor dependent parasitic effects. The PGNN is used to identify a model of the electromagnetic part using force measurements, after which it is analytically inverted to obtain a PGNN-based commutation algorithm. Motivated by industrial applications, we develop an input transformation to deal with systems with fixed commutation, i.e., when the currents cannot be controlled. Real-life experiments on an industrial coreless linear motor (CLM) demonstrate a factor 10 improvement in the commutation error in driving direction and a factor 4 improvement in the position error with respect to classical commutation in terms of the mean--squared error (MSE).

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arXiv2024

Koopman Data-Driven Predictive Control with Robust Stability and Recursive Feasibility Guarantees

In this paper, we consider the design of data-driven predictive controllers for nonlinear systems from input-output data via linear-in-control input Koopman lifted models. Instead of identifying and simulating a Koopman model to predict future outputs, we design a subspace predictive controller in the Koopman space. This allows us to learn the observables minimizing the multi-step output prediction error of the Koopman subspace predictor, preventing the propagation of prediction errors. To avoid losing feasibility of our predictive control scheme due to prediction errors, we compute a terminal cost and terminal set in the Koopman space and we obtain recursive feasibility guarantees through an interpolated initial state. As a third contribution, we introduce a novel regularization cost yielding input-to-state stability guarantees with respect to the prediction error for the resulting closed-loop system. The performance of the developed Koopman data-driven predictive control methodology is illustrated on a nonlinear benchmark example from the literature.

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arXiv2024

Risk-Aware MPC for Stochastic Systems with Runtime Temporal Logics

This paper concerns the risk-aware control of stochastic systems with temporal logic specifications dynamically assigned during runtime. Conventional risk-aware control typically assumes that all specifications are predefined and remain unchanged during runtime. In this paper, we propose a novel, provably correct model predictive control scheme for linear systems with additive unbounded stochastic disturbances that dynamically evaluates the feasibility of runtime signal temporal logic specifications and automatically reschedules the control inputs accordingly. The control method guarantees the probabilistic satisfaction of newly accepted specifications without sacrificing the satisfaction of the previously accepted ones. The proposed control method is validated by a robotic motion planning case study.

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arXiv2024

Multivariable control of modular multilevel converters with convergence and safety guarantees

Well-designed current control is a key factor in ensuring the efficient and safe operation of modular multilevel converters (MMCs). Even though this control problem involves multiple control objectives, conventional current control schemes are comprised of independently designed decoupled controllers, e.g., proportional-integral (PI) or proportional-resonant (PR). Due to the bilinearity of the MMC dynamics, tuning PI and PR controllers so that good performance and constraint satisfaction are guaranteed is quite challenging. This challenge becomes more relevant in an AC/AC MMC configuration due to the complexity of tracking the single-phase sinusoidal components of the MMC output. In this paper, we propose a method to design a multivariable controller, i.e., a static feedback gain, to regulate the MMC currents. We use a physics-informed transformation to model the MMC dynamics linearly and synthesise the proposed controller. We use this linear model to formulate a linear matrix inequality that computes a feedback gain that guarantees safe and effective operation, including (i) limited tracking error, (ii) stability, and (iii) meeting all constraints. To test the efficacy of our method, we examine its performance in a direct AC/AC MMC simulated in Simulink/PLECS and in a scaled-down AC/AC MMC prototype to investigate the ultra-fast charging of electric vehicles.

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arXiv2024

On unifying control barrier and Lyapunov functions using QP and Sontag's formula with an application to tumor dynamics

A common tool in system theory for formulating control laws that achieve local asymptotic stability are Control Lyapunov functions (CLFs), while Control Barrier functions (CBFs) are typically employed to enforce safety constraints. Combining these two types of functions is of interest, because it leads to stabilizing controllers with safety guarantees. A common approach to merge CLFs and CBFs is to solve an optimization problem where both CLF and CBF inequalities are imposed as constraints. In this paper, we show via an example from the literature that this approach can lead to undesirable behavior (i.e., slow convergence and oscillating inputs). Then, we propose a novel cost function that penalizes the deviation from Sontag's formula by using a state-dependent weighting matrix. We show that by minimizing the developed cost function subject to a CBF constraint, local asymptotic stability is obtained with an explicit domain of attraction, without using a CLF constraint. To deal with vanishing properties of the weight matrix as the state approaches the equilibrium, we introduce a hybrid continuous control law that recovers Sontag's formula locally. The effectiveness of the developed hybrid stabilizing control law based on CLFs and CBFs is illustrated in stabilization of a 3D tumor model, subject to physiological constraints (i.e., all states must be positive), which yields useful insights into optimal cancer treatment design.

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arXiv2023

Basis functions nonlinear data-enabled predictive control: Consistent and computationally efficient formulations

This paper considers the extension of data-enabled predictive control (DeePC) to nonlinear systems via general basis functions. Firstly, we formulate a basis functions DeePC behavioral predictor and we identify necessary and sufficient conditions for equivalence with a corresponding basis functions multi-step identified predictor. The derived conditions yield a dynamic regularization cost function that enables a well-posed (i.e., consistent) basis functions formulation of nonlinear DeePC. To optimize computational efficiency of basis functions DeePC we further develop two alternative formulations that use a simpler, sparse regularization cost function and ridge regression, respectively. Consistency implications for Koopman DeePC as well as several methods for constructing the basis functions representation are also indicated. The effectiveness of the developed consistent basis functions DeePC formulations is illustrated on a benchmark nonlinear pendulum state-space model, for both noise free and noisy data.

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arXiv2023

Abstracting Linear Stochastic Systems via Knowledge Filtering

In this paper, we propose a new model reduction technique for linear stochastic systems that builds upon knowledge filtering and utilizes optimal Kalman filtering techniques. This new technique will reduce the dimension of the noise disturbance and will allow any controller designed for the reduced model to be refined into a controller for the original stochastic system, while preserving any specification on the output. Although initially the reduced model will be time-varying, a method will be provided with which the reduced model can become time-invariant if it satisfies some minor technical conditions. We present our theoretical findings with an example that supports the proposed framework and illustrates how model reduction and controller refinement of stochastic systems can be achieved. We finish the paper by considering specific examples to analyze both completeness with respect to controller synthesis and model order reduction with respect to the state.

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arXiv2023

Physics-guided neural networks for feedforward control with input-to-state stability guarantees

The increasing demand on precision and throughput within high-precision mechatronics industries requires a new generation of feedforward controllers with higher accuracy than existing, physics-based feedforward controllers. As neural networks are universal approximators, they can in principle yield feedforward controllers with a higher accuracy, but suffer from bad extrapolation outside the training data set, which makes them unsafe for implementation in industry. Motivated by this, we develop a novel physics-guided neural network (PGNN) architecture that structurally merges a physics-based layer and a black-box neural layer in a single model. The parameters of the two layers are simultaneously identified, while a novel regularization cost function is used to prevent competition among layers and to preserve consistency of the physics-based parameters. Moreover, in order to ensure stability of PGNN feedforward controllers, we develop sufficient conditions for analyzing or imposing (during training) input-to-state stability of PGNNs, based on novel, less conservative Lipschitz bounds for neural networks. The developed PGNN feedforward control framework is validated on a real-life, high-precision industrial linear motor used in lithography machines, where it reaches a factor 2 improvement with respect to physics-based mass-friction feedforward and it significantly outperforms alternative neural network based feedforward controllers.

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arXiv2023

Stochastic Model Predictive Control with Dynamic Chance Constraints

This work introduces a stochastic model predictive control scheme for dynamic chance constraints. We consider linear discrete-time systems affected by unbounded additive stochastic disturbance. To synthesize an optimal controller, we solve two subsequent stochastic optimization problems. The first problem concerns finding the maximal feasible probabilities of the dynamic chance constraints. After obtaining the probabilities, the second problem concerns finding an optimal controller using stochastic model predictive control. We solve both stochastic optimization problems by reformulating them into deterministic ones using probabilistic reachable tubes and constraint tightening. We prove that the developed algorithm is recursively feasible and yields closed-loop satisfaction of the dynamic chance constraints. In addition, we will introduce a novel implementation using zonotopes to describe the tightening analytically. Finally, we will end with an example illustrating the method's benefits.

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