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W. P. M. H. Heemels

Publications and source records attributed to W. P. M. H. Heemels.

At least 37 records · Page 2Linked to original sources
arXiv2026

From a Frequency-Domain Willems' Lemma to Data-Driven Predictive Control

Willems' fundamental lemma has recently received an impressive amount of attention from the data-driven control community. In this paper, we formulate a version of this celebrated result based on frequency-domain data. In doing so, we bridge the gap between recent developments in data-driven control, and the readily-available techniques and expertise for non-parametric frequency-domain identification. We also generalize our results to combine multiple frequency-domain data sets to form a sufficiently rich data set. Building on these results, we propose a data-driven predictive control scheme based on measured frequency-domain data of the plant. This novel scheme provides a frequency-domain counterpart of the well-known data-enabled predictive control scheme DeePC based on time-domain data. Under appropriate conditions, the new frequency-domain data-driven predictive control (FreePC) scheme is equivalent to the corresponding DeePC scheme. We demonstrate the benefits of FreePC and the use of frequency-domain data in several examples and a numerical case study, including the ability to collect data in closed loop, computational benefits, and intuitive visualization of the data.

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arXiv2026

Solution Concepts and Existence Results for Hybrid Systems with Continuous-time Inputs

In many scenarios, it is natural to model a plant's dynamical behavior using a hybrid dynamical system influenced by exogenous continuous-time inputs. While solution concepts and analytical tools for existence and completeness are well established for autonomous hybrid systems, corresponding results for hybrid dynamical systems involving continuous-time inputs are generally lacking. This work aims to address this gap. We first formalize notions of a solution for such systems. We then provide conditions that guarantee the existence and forward completeness of solutions. Moreover, we leverage results and ideas from viability theory to present more explicit conditions in terms of various tangent cone formulations. Variants are provided that depend on the regularity of the exogenous input signals.

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arXiv2025

Observer Design for Networked Linear Systems with Fast and Slow Dynamics under Measurement Noise

This paper addresses the emulation-based observer design for networked control systems (NCS) with linear plants that operate at two time scales in the presence of measurement noise. The system is formulated as a hybrid singularly perturbed dynamical system, enabling the systematic use of singular perturbation techniques to derive explicit bounds on the maximum allowable transmission intervals (MATI) for both fast and slow communication channels. Under the resulting conditions, the proposed observer guarantees that the estimation error satisfies a global exponential derivative-input-to-state stability (DISS)-like property, where the ultimate bound scales proportionally with the magnitudes of the measurement noise and the time derivative of the control input. The effectiveness of the approach is illustrated through a numerical example.

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arXiv2025

Value Function Approximation for Nonlinear MPC: Learning a Terminal Cost Function with a Descent Property

We present a novel method to synthesize a terminal cost function for a nonlinear model predictive controller (MPC) through value function approximation using supervised learning. Existing methods enforce a descent property on the terminal cost function by construction, thereby restricting the class of terminal cost functions, which in turn can limit the performance and applicability of the MPC. We present a method to approximate the true cost-to-go with a general function approximator that is convex in its parameters, and impose the descent condition on a finite number of states. Through the scenario approach, we provide probabilistic guarantees on the descent condition of the terminal cost function over the continuous state space. We demonstrate and empirically verify our method in a numerical example. By learning a terminal cost function, the prediction horizon of the MPC can be significantly reduced, resulting in reduced online computational complexity while maintaining good closed-loop performance.

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arXiv2025

Evolutionary Analysis of Continuous-time Finite-state Mean Field Games with Discounted Payoffs

We consider a class of continuous-time dynamic games involving a large number of players. Each player selects actions from a finite set and evolves through a finite set of states. State transitions occur stochastically and depend on the player's chosen action. A player's single-stage reward depends on their state, action, and the population-wide distribution of states and actions, capturing aggregate effects such as congestion in traffic networks. Each player seeks to maximize a discounted infinite-horizon reward. Existing evolutionary game-theoretic approaches introduce a model for the way individual players update their decisions in static environments without individual state dynamics. In contrast, this work develops an evolutionary framework for dynamic games with explicit state evolution, which is necessary to model many applications. We introduce a mean field approximation of the finite-population game and establish approximation guarantees. Since state-of-the-art solution concepts for dynamic games lack an evolutionary interpretation, we propose a new concept - the Mixed Stationary Nash Equilibrium (MSNE) - which admits one. We characterize an equivalence between MSNE and the rest points of the proposed mean field evolutionary model and we give conditions for the evolutionary stability of MSNE.

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arXiv2025

Continuity Conditions for Piecewise Quadratic Functions on Simplicial Conic Partitions are Equivalent

Analysis of continuous-time piecewise linear systems based on piecewise quadratic (PWQ) Lyapunov functions typically requires continuity of these functions over a partition of the state space. Several conditions for guaranteeing continuity of PWQ functions over state space partitions can be found in the literature. In this technical note, we show that these continuity conditions are equivalent over so-called simplicial conic partitions. As a consequence, the choice of which condition to impose can be based solely on practical considerations such as specific application or numerical aspects, without introducing additional conservatism in the analysis.

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arXiv2025

Evolutionary Dynamics in Continuous-time Finite-state Mean Field Games -- Part II: Stability

We study a dynamic game with a large population of players who choose actions from a finite set in continuous time. Each player has a state in a finite state space that evolves stochastically with their actions. A player's reward depends not only on their own state and action but also on the distribution of states and actions across the population, capturing effects such as congestion in traffic networks. In Part I, we introduced an evolutionary model and a new solution concept - the mixed stationary Nash Equilibrium (MSNE) - which coincides with the rest points of the mean field evolutionary model under meaningful families of revision protocols. In this second part, we investigate the evolutionary stability of MSNE. We derive conditions on both the structure of the MSNE and the game's payoff map that ensure local and global stability under evolutionary dynamics. These results characterize when MSNE can robustly emerge and persist against strategic deviations, thereby providing insight into its long-term viability in large population dynamic games.

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arXiv2025

Evolutionary Dynamics in Continuous-time Finite-state Mean Field Games -- Part I: Equilibria

We study a dynamic game with a large population of players who choose actions from a finite set in continuous time. Each player has a state in a finite state space that evolves stochastically with their actions. A player's reward depends not only on their own state and action but also on the distribution of states and actions across the population, capturing effects such as congestion in traffic networks. While prior work in evolutionary game theory has primarily focused on static games without individual player state dynamics, we present the first comprehensive evolutionary analysis of such dynamic games. We propose an evolutionary model together with a mean field approximation of the finite-population game and establish strong approximation guarantees. We show that standard solution concepts for dynamic games lack an evolutionary interpretation, and we propose a new concept - the Mixed Stationary Nash Equilibrium (MSNE) - which admits one. We analyze the relationship between MSNE and the rest points of the mean field evolutionary model and study the evolutionary stability of MSNE.

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arXiv2025

MPC strategies for density profile control with pellet fueling in nuclear fusion tokamaks under uncertainty

Control of the density profile based on pellet fueling for the ITER nuclear fusion tokamak involves a multi-rate nonlinear system with safety-critical constraints, input delays, and discrete actuators with parametric uncertainty. To address this challenging problem, we propose a multi-stage MPC (msMPC) approach to handle uncertainty in the presence of mixed-integer inputs. While the scenario tree of msMPC accounts for uncertainty, it also adds complexity to an already computationally intensive mixed-integer MPC (MI-MPC) problem. To achieve real-time density profile controller with discrete pellets and uncertainty handling, we systematically reduce the problem complexity by (1) reducing the identified prediction model size through dynamic mode decomposition with control, (2) applying principal component analysis to reduce the number of scenarios needed to capture the parametric uncertainty in msMPC, and (3) utilizing the penalty term homotopy for MPC (PTH-MPC) algorithm to reduce the computational burden caused by the presence of mixed-integer inputs. We compare the performance and safety of the msMPC strategy against a nominal MI-MPC in plant simulations, demonstrating the first predictive density control strategy with uncertainty handling, viable for real-time pellet fueling in ITER.

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arXiv2025

Verification and Synthesis of Discrete-Time Control Barrier Functions

Discrete-time Control Barrier Functions (DTCBFs) have recently attracted interest for guaranteeing safety and synthesizing safe controllers for discrete-time dynamical systems. This paper addresses the open challenges of verifying candidate DTCBFs and synthesizing DTCBFs for general nonlinear discrete-time systems with input constraints and arbitrary safe sets. In particular, we propose a branch-and-bound method, inspired by the $α$BB algorithm, for the verification of candidate DTCBFs in both cases, whether a corresponding control policy is known or unknown. We prove that this method, in a finite number of iterations, either verifies a given candidate function as a valid DTCBF or falsifies it by providing a counterexample (within predefined tolerances). As a second main contribution, we propose a novel bilevel optimization approach to synthesize a DTCBF and a corresponding control policy in finite time. This involves determining the unknown coefficients of a parameterized DTCBF and a parameterized control policy. Furthermore, we introduce various strategies to reduce the computational burden of the bilevel approach. We also demonstrate our methods using numerical case studies.

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arXiv2025

Nuclear fusion plasma fuelling with ice pellets using a neuromorphic controller

In reactor-grade tokamaks, pellet injection is the best candidate for core plasma fuelling. However, density control schemes that can handle the hybrid nature of this type of fuelling, i.e., the discrete impact of the pellets on the continuously evolving plasma density, are lacking. This paper proposes a neuromorphic controller, inspired by the integrate-and-fire neuronal model, to address this problem. The overall system is modelled as a hybrid system, and we analyse the proposed controller in closed loop with a single-input single-output linear time-invariant plasma model. The controller generates spikes, representing pellet launches, when the neuron variable reaches a certain threshold. Between the control actions, or spikes, the system evolves in open loop. We establish conditions on the controller variables and minimum actuator speed, depending on the reference value for the desired density, the pellet size and the time-constant of the plasma density, that guarantee a practical stability property for the closed-loop system. The results are illustrated in a numerical example.

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arXiv2025

Design, Modelling and Analysis of a Bio-inspired Spiking Temperature Regulator

In biology, homeostasis is the process of maintaining a stable internal environment, which is crucial for optimal functioning of organisms. One of the key homeostatic mechanisms is thermoregulation that allows the organism to maintain its core temperature within tight bounds despite being exposed to a wide range of varying external temperatures. Instrumental in thermoregulation is the presence of thermosensitive neurons at multiple places throughout the body, including muscles, the spinal cord, and the brain, which provide spiking sensory signals for the core temperature. In response to these signals, thermoeffectors are activated, creating a negative spiking feedback loop. Additionally, a feedforward signal is provided by warmth and cold-sensitive neurons in the skin, offering a measure for the external temperature. This paper presents an electronic circuit-based architecture design to replicate the biological process of thermoregulation, combined with a formal mathematical analysis. The considered architecture consists of four temperature sensitive neurons and a single actuator, configured in a negative feedback loop with feedforward control. To model the overall system mathematically, hybrid dynamical system descriptions are proposed that are used to analyze and simulate the performance of the design. The analysis and numerical case study illustrate the crucial role of feedforward control in reducing the dependency on the external temperature.

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arXiv2025

Feedback Optimization with State Constraints through Control Barrier Functions

Recently, there has been a surge of research on a class of methods called feedback optimization. These are methods to steer the state of a control system to an equilibrium that arises as the solution of an optimization problem. Despite the growing literature on the topic, the important problem of enforcing state constraints at all times remains unaddressed. In this work, we present the first feedback-optimization method that enforces state constraints. The method combines a class of dynamics called safe gradient flows with high-order control barrier functions. We provide a number of results on our proposed controller, including well-posedness guarantees, anytime constraint-satisfaction guarantees, equivalence between the closed-loop's equilibria and the optimization problem's critical points, and local asymptotic stability of optima.

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arXiv2025

High-Performance Trajectory Tracking MPC for Quadcopters with Coupled Time-Varying Constraints and Stability Proofs

In this paper, we present a cascade control structure to address the trajectory tracking problem for quadcopters, ensuring uniform global asymptotic stability of the state tracking error dynamics. An MPC strategy based on a 12-dimensional prediction model is proposed for the outer loop, explicitly accounting for time-varying coupled constraints, where multiple variables are interdependent and need to be handled together. The outer-loop controller generates an acceleration reference, which is then converted into attitude and angular velocity references, later tracked by a nonlinear inner-loop controller. Numerical simulations validate the approach, demonstrating enhanced performance in precise and fast tracking by imposing less conservative constraints than existing approaches, while still guaranteeing stability.

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arXiv2025

Online Learning of Interaction Dynamics with Dual Model Predictive Control for Multi-Agent Systems Using Gaussian Processes

The control of a single agent in complex and uncertain multi-agent environments requires careful consideration of the interactions between the agents. In this context, this paper proposes a dual model predictive control (MPC) method using Gaussian process (GP) models for multi-agent systems. While Gaussian process MPC (GP-MPC) has been shown to be effective in predicting the dynamics of other agents, current methods do not consider the influence of the control input on the covariance of the predictions, and hence lack the dual control effect. Therefore, we propose a dual MPC that directly optimizes the actions of the ego agent, and the belief of the other agents by jointly optimizing their state trajectories as well as the associated covariance while considering their interactions through a GP. We demonstrate our GP-MPC method in a simulation study on autonomous driving, showing improved prediction quality compared to a baseline stochastic MPC. The results show that GP-MPC can learn the interactions between the agents online, demonstrating the potential of GPs for dual MPC in uncertain and unseen scenarios.

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arXiv2025

Counterexample-Guided Synthesis of Robust Discrete-Time Control Barrier Functions

Learning-based methods have gained popularity for training candidate Control Barrier Functions (CBFs) to satisfy the CBF conditions on a finite set of sampled states. However, since the CBF is unknown a priori, it is unclear which sampled states belong to its zero-superlevel set and must satisfy the CBF conditions, and which ones lie outside it. Existing approaches define a set in which all sampled states are required to satisfy the CBF conditions, thus introducing conservatism. In this paper, we address this issue for robust discrete-time CBFs (R-DTCBFs). Furthermore, we propose a class of R-DTCBFs that can be used in an online optimization problem to synthesize safe controllers for general discrete-time systems with input constraints and bounded disturbances. To train such an R-DTCBF that is valid not only on sampled states but also across the entire region, we employ a verification algorithm iteratively in a counterexample-guided approach. We apply the proposed method to numerical case studies.

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arXiv2025

Synthesis of Discrete-time Control Barrier Functions for Polynomial Systems Based on Sum-of-Squares Programming

Discrete-time Control Barrier Functions (DTCBFs) are commonly utilized in the literature as a powerful tool for synthesizing control policies that guarantee safety of discrete-time dynamical systems. However, the systematic synthesis of DTCBFs in a computationally efficient way is at present an important open problem. This article first proposes a novel alternating-descent approach based on Sum-of-Squares programming to synthesize quadratic DTCBFs and corresponding polynomial control policies for discrete-time control-affine polynomial systems with input constraints and semi-algebraic safe sets. Subsequently, two distinct approaches are introduced to extend the proposed method to the synthesis of higher-degree polynomial DTCBFs. To demonstrate its efficacy, we apply the proposed method to numerical case studies.

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