arXiv subjects

Siep Weiland

Publications and source records attributed to Siep Weiland.

At least 19 recordsLinked to original sources

arXiv2026

When Persistency is not Exciting in Data-Driven Predictive Control

Understanding how to collect data that is "meaningful" for control purposes is of paramount importance in data-driven control. While existing approaches have primarily relied on the satisfaction of a rank condition to assess the quality of an experiment, we show that satisfying it is not always sufficient to achieve satisfactory closed-loop performance. Focusing on scenarios where white-noise-like excitation cannot be used for data collection, we examine the frequency-domain implications of linear behavioral representation. This analysis demonstrates that leakage effects are the main driver for data to represent the dynamics of the system. These findings are reflected in our numerical results. Data-enabled predictive controllers built on datasets with insufficient bandwidth, despite fulfilling standard rank conditions, suffer from severe ill-conditioning and fail to achieve reference tracking.

eess.SY↗

arXiv2026

Opinion-Guided Layered Strategies for Decentralized Coordination

Autonomous agents increasingly interact with other independent agents, and such interactions typically admit multiple joint behaviors. When two agents prefer different ones, their independent strategies may be mutually incompatible and fail to reach a coordinated outcome; when they are identical, neither can differentiate its role when needed. Ideally, an agent should coordinate with any agent it encounters, regardless of which admissible joint behavior that agent aims to realize. We therefore propose a new form of strategy, the opinion-guided strategy, which keeps all the admissible joint behaviors available and postpones the selection to execution time, when the other agent's behavior reveals which one to realize. To realize this, nonlinear opinion dynamics are leveraged in a layered realization to guide the agent to a common admissible joint behavior in response to the other agent's evolving behavior, even without communication. We formally establish the conditions under which the strategy remains robust to every preference the other agent may hold. This robustness has an important implication: two agents running identical strategies can break symmetry when needed, a capability that conventional strategies lack. Three case studies across different applications show that the opinion-guided strategy coordinates with every randomly encountered agent, as long as it is willing to realize one of the admissible joint behaviors. One of them corresponds to a general-sum game: unlike conventional approaches devoted to finding a unique Nash equilibrium in advance, the opinion-guided strategy keeps every equilibrium open and guarantees the agents reach one, decided by their runtime interaction.

cs.MA↗

arXiv2026

Constrained Performance Boosting Control for Nonlinear Systems

We present the Alternating Direction Method of Multipliers (ADMM) for Performance Boosting (PB), an approach for designing neural controllers for stable nonlinear systems subject to state and input constraints. The method builds on an internal model control formulation of PB. In this setting, the controller is parametrized as a stable neural operator, so closed-loop stability is guaranteed by construction, and its weights are trained offline to improve performance. To provide a systematic procedure for promoting constraint satisfaction during training, we reformulate the finite-horizon problem of the PB formulation by introducing auxiliary state and input trajectories. This augmentation allows us to cast an ADMM-based algorithm that alternates between two steps: a gradient-descent-based update of the controller parameters, having the same structure as the PB training problem without explicit constraints, and a projection step that promotes the trajectory feasibility. As a result, this procedure handles constraints during training without altering the controller architecture or compromising its stability-by-design guarantees. Indeed, the stability guarantee follows from the chosen stable controller parametrization, which is not changed in our framework with respect to the foundational PB formulation, and is independent of ADMM convergence. At the same time, this closed-loop stability guarantee does not imply performance optimality or closed-loop constraint satisfaction, which depend on the convergence of ADMM-PB, which is not yet guaranteed in this work. Our numerical results show that, compared with a baseline based on barrier-inspired soft penalties in the loss, ADMM-PB achieves lower constraint violations, at the price of more conservative closed-loop behavior.

eess.SY↗

arXiv2026

Unifying Controller Design for Stabilizing Nonlinear Systems with Norm-Bounded Control Inputs

This paper revisits a classical challenge in the design of stabilizing controllers for nonlinear systems with a norm-bounded input constraint. By extending Lin-Sontag's universal formula and introducing a generic (state-dependent) scaling term, a unifying controller design method is proposed. The incorporation of this generic scaling term gives a unified controller and enables the derivation of alternative universal formulas with various favorable properties, which makes it suitable for tailored control designs to meet specific requirements and provides versatility across different control scenarios. Additionally, we present a constructive approach to determine the optimal scaling term, leading to an explicit solution to an optimization problem, named optimization-based universal formula. The resulting controller ensures asymptotic stability, satisfies a norm-bounded input constraint, and optimizes a predefined cost function. Finally, the essential properties of the unified controllers are analyzed, including smoothness, continuity at the origin, stability margin, and inverse optimality. Simulations validate the approach, showcasing its effectiveness in addressing a challenging stabilizing control problem of a nonlinear system.

eess.SY↗

arXiv2026

A Digital Twin of Evaporative Thermo-Fluidic Process in Fixation Unit of DoD Inkjet Printers

In inkjet printing, optimal paper moisture is crucial for print quality, achieved through hot-air impingement in the fixation unit. This paper presents a modular digital twin of the fixation unit, modeling the thermo-fluidic drying process and monitoring its spatio-temporal performance. The novel approach formulates the digital twin as an infinite-dimensional state estimator that infers fixation states from limited sensor data, while remaining robust to disturbances. Modularity is achieved through a graph-theoretic model, where each node represents thermo-fluidic dynamics in different sections of the fixation unit. Evaporation is modeled as a nonlinear boundary effect coupled with node dynamics via Linear Fractional Representation. Using the Partial Integral Equation (PIE) framework, we develop a unified approach for stability, input-output analysis, simulation, and rapid prototyping, validated with operational data from a commercial printer. An $\mathcal{H}_{\infty}$-optimal Luenberger state estimator is then synthesized to estimate thermal states from available sensor data, enabling real-time monitoring of spatio-temporal thermal effects on paper sheets.

eess.SY↗

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 $Π$-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 Π-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.

eess.SY↗

arXiv2025

Tensor-based reduction of linear parameter-varying state-space models

The Linear Parameter-Varying (LPV) framework is a powerful tool for controlling nonlinear and complex systems, but the conversion of nonlinear models into LPV forms often results in high-dimensional and overly conservative LPV models. To be able to apply control strategies, there is often a need for model reduction in order to reduce computational needs. This paper presents the first systematic approach for the joint reduction of state order and scheduling signal dimension of LPV state space models. The existing methods typically address these reductions separately. By formulating a tensorial form of LPV models with an affine dependency on the scheduling variables, we leverage tensor decomposition to find the dominant components of state and scheduling subspaces. We extend the common Petrov-Galerkin projection approach to LPV framework by adding a scheduling projection. This extension enables the joint reduction. To find suitable subspaces for the extended Petrov-Galerkin projection, we have developed two different methods: tensor-based LPV moment matching, and an approach through Proper Orthogonal Decomposition. Advantages of the proposed methods are demonstrated on two different series-interconnected mass-spring-damper systems with nonlinear springs: one primarily used for comparison with other methods and a more elaborate higher-order model designed to assess scalability.

eess.SY↗

arXiv2025

A Tunable Universal Formula for Safety-Critical Control

Sontag's universal formula is a widely used technique for stabilizing control through control Lyapunov functions. Recently, it has been extended to address safety-critical control by incorporating control barrier functions (CBFs). However, deriving a universal formula that satisfies requirements on essential properties, including safety, smoothness, and robustness against input disturbances, is still an open problem. To address this challenge, this paper introduces a novel solution - a tunable universal formula - by incorporating a (state-dependent) tunable term into Sontag's formula. This tunable term enables the regulation of safety-critical control performances, allowing the attainment of desired properties through a proper selection of tunable terms. Generally, the tunable universal formula can be seen as a controller that improves the quadratic program (QP)-synthesized controllers in terms of robustness and smoothness, while also reducing the conservatism (corresponding to robustness) in Sontag's formula. Furthermore, we extend the tunable universal formula to address safety-critical control problems with norm-bounded input constraints, showcasing its applicability across diverse control scenarios. Finally, we demonstrate the efficacy of our method through a two-link manipulator safe tracking example, investigating the essential properties including safety, smoothness, and robustness against input disturbances under various tunable terms.

eess.SY↗

arXiv2025

Moving Obstacle Collision Avoidance via Chance-Constrained MPC with CBF

Model predictive control (MPC) with control barrier functions (CBF) is a promising solution to address the moving obstacle collision avoidance (MOCA) problem. Unlike MPC with distance constraints (MPC-DC), this approach facilitates early obstacle avoidance without the need to increase prediction horizons. However, the existing MPC-CBF method is deterministic and fails to account for perception uncertainties. This paper proposes a generalized MPC-CBF approach for stochastic scenarios, which maintains the advantages of the deterministic method for addressing the MOCA problem. Specifically, the chance-constrained MPC-CBF (CC-MPC-CBF) technique is introduced to ensure that a user-defined collision avoidance probability is met by utilizing probabilistic CBFs. However, due to the potential empty intersection between the reachable set and the safe region confined by CBF constraints, the CC-MPC-CBF problem can pose challenges in achieving feasibility. To address this issue, we propose a sequential implementation approach that involves solving a standard MPC optimization problem followed by a predictive safety filter optimization, which leads to improved feasibility. Furthermore, we introduce an iterative convex optimization scheme to further expedite the resolution of the predictive safety filter, which results in an efficient approach to tackling the non-convex CC-MPC-CBF problem. We apply our proposed algorithm to a double integrator system for MOCA, and we showcase its resilience to obstacle measurement uncertainties and favorable feasibility properties.

eess.SY↗

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.

math.OC↗

arXiv2024

Active Compensation of Position Dependent Flexible Dynamics in High-Precision Mechatronics

Growing demands in the semiconductor industry necessitate increasingly stringent requirements on throughput and positioning accuracy of lithographic equipment. Meeting these demands involves employing highly aggressive motion profiles, which introduce position-dependent flexible dynamics, thus compromising achievable position tracking performance. This paper introduces a control approach enabling active compensation of position-dependent flexible dynamics by extending the conventional rigid-body control structure to include active control of flexible dynamics. To facilitate real-time implementation of the control algorithm, appropriate position-dependent weighting functions are introduced, ensuring computationally efficient execution of the proposed approach. The efficacy of the proposed control design approach is demonstrated through experiments conducted on a state-of-the-art extreme ultraviolet (EUV) wafer stage.

eess.SY↗

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.

math.OC↗

arXiv2024

Extension of the Partial Integral Equation Representation to GPDE Input-Output Systems

It has been shown that the existence of a Partial Integral Equation (PIE) representation of a Partial Differential Equation (PDE) simplifies many numerical aspects of analysis, simulation, and optimal control. However, the PIE representation has not previously been extended to many of the complex, higher-order PDEs such as may be encountered in speculative or data-based models. In this paper, we propose PIE representations for a large class of such PDE models, including higher-order derivatives, boundary-valued inputs, and coupling with Ordinary Differential Equations. The main technical contribution which enables this extension is a generalization of Cauchy's rule for repeated integration. The process of conversion of a complex PDE model to a PIE is simplified through a PDE modeling interface in the open-source software PIETOOLS. Several numerical tests and illustrations are used to demonstrate the results.

math.OC↗

arXiv2024

Convex Equilibrium-Free Stability and Performance Analysis of Discrete-Time Nonlinear Systems

This paper considers the equilibrium-free stability and performance analysis of discrete-time nonlinear systems. We consider two types of equilibrium-free notions. Namely, the universal shifted concept, which considers stability and performance w.r.t. all equilibrium points of the system, and the incremental concept, which considers stability and performance between trajectories of the system. In this paper, we show how universal shifted stability and performance of discrete-time systems can be analyzed by making use of the time-difference dynamics. Moreover, we extend the existing results for incremental dissipativity for discrete-time systems based on dissipativity analysis of the differential dynamics to more general state-dependent storage functions for less conservative results. Finally, we show how both these equilibrium-free notions can be cast as a convex analysis problem by making use of the linear parameter-varying framework, which is also demonstrated by means of an example.

eess.SY↗

arXiv2024

Quadrotor Stabilization with Safety Guarantees: A Universal Formula Approach

Safe stabilization is a significant challenge for quadrotors, which involves reaching a goal position while avoiding obstacles. Most of the existing solutions for this problem rely on optimization-based methods, demanding substantial onboard computational resources. This paper introduces a novel approach to address this issue and provides a solution that offers fast computational capabilities tailored for onboard execution. Drawing inspiration from Sontag's universal formula, we propose an analytical control strategy that incorporates the conditions of control Lyapunov functions (CLFs) and control barrier functions (CBFs), effectively avoiding the need for solving optimization problems onboard. Moreover, we extend our approach by incorporating the concepts of input-to-state stability (ISS) and input-to-state safety (ISSf), enhancing the universal formula's capacity to effectively manage disturbances. Furthermore, we present a projection-based approach to ensure that the universal formula remains effective even when faced with control input constraints. The basic idea of this approach is to project the control input derived from the universal formula onto the closest point within the control input domain. Through comprehensive simulations and experimental results, we validate the efficacy and highlight the advantages of our methodology.

cs.RO↗

arXiv2023

Equilibrium-Independent Control of Continuous-Time Nonlinear Systems via the LPV Framework -- Extended Version

In this paper, we consider the analysis and control of continuous-time nonlinear systems to ensure universal shifted stability and performance, i.e., stability and performance w.r.t. each forced equilibrium point of the system. This "equilibrium-free" concept is especially beneficial for control problems that require the tracking of setpoints and rejection of persistent disturbances, such as input loads. In this paper, we show how the velocity form, i.e., the time-differentiated dynamics of the system, plays a crucial role in characterizing these properties and how the analysis of it can be solved by the application of Linear Parameter-Varying (LPV) methods in a computationally efficient manner. Furthermore, by leveraging the properties of the velocity form and the LPV framework, a novel controller synthesis method is presented which ensures closed-loop universal shifted stability and performance. The proposed controller design is verified in a simulation study and also experimentally on a real system. Additionally, we compare the proposed method to a standard LPV control design, demonstrating the improved stability and performance guarantees of the new approach.

eess.SY↗

arXiv2023

Nonlinear Tracking and Rejection using Linear Parameter-Varying Control

The Linear Parameter-Varying (LPV) framework has been introduced with the intention to provide stability and performance guarantees for analysis and controller synthesis for Nonlinear (NL) systems via convex methods. By extending results of the Linear Time-Invariant framework, mainly based on quadratic stability and performance using dissipativity theory, it has been assumed that they generalize tracking and disturbance rejection guarantees for NL systems. However, as has been shown in literature, stability and performance through standard dissipativity is not sufficient in order to satisfy the desired guarantees in case of reference tracking and disturbance rejection for nonlinear systems. We propose to solve this problem by the application of incremental dissipativity, which does ensure these specifications. A novel approach is proposed to synthesize and realize an NL controller which is able to guarantee incremental stability and performance for NL systems via convex optimization using methods from the LPV framework. Through simulations and experiments, the presented method is compared to standard LPV controller designs, showing significant performance improvements.

eess.SY↗

arXiv2022

Decoupling multivariate functions using a nonparametric filtered tensor decomposition

Multivariate functions emerge naturally in a wide variety of data-driven models. Popular choices are expressions in the form of basis expansions or neural networks. While highly effective, the resulting functions tend to be hard to interpret, in part because of the large number of required parameters. Decoupling techniques aim at providing an alternative representation of the nonlinearity. The so-called decoupled form is often a more efficient parameterisation of the relationship while being highly structured, favouring interpretability. In this work two new algorithms, based on filtered tensor decompositions of first order derivative information are introduced. The method returns nonparametric estimates of smooth decoupled functions. Direct applications are found in, i.a. the fields of nonlinear system identification and machine learning.

stat.ML↗