Pub Date : 2025-11-01DOI: 10.1016/j.ejcon.2025.101296
Youssef Ait Si , Antoine Girard , Adnane Saoud
This paper addresses the challenge of ensuring robustness in the presence of system perturbations for symbolic control techniques. Given a discrete-time control system that is related to its symbolic model by an alternating simulation relation. In this paper, we focus on computing the maximum robustness margin under which the symbolic model remains valid for a perturbed-version of the discrete-time control system. We first show that symbolic models are inherently equipped with a certain free robustness margins. We then provide constructive procedures to compute uniform and non-uniform (state and input dependent) robustness margins. We also show that the tightness of the robustness margin depends on the tightness of the reachability technique used to compute the symbolic model. We then explain how the computed robustness margin can be used for the sake of controller synthesis. Finally, we present two illustrative examples to demonstrate the effectiveness of our approach.
{"title":"Symbolic control: Unveiling free robustness margins","authors":"Youssef Ait Si , Antoine Girard , Adnane Saoud","doi":"10.1016/j.ejcon.2025.101296","DOIUrl":"10.1016/j.ejcon.2025.101296","url":null,"abstract":"<div><div>This paper addresses the challenge of ensuring robustness in the presence of system perturbations for symbolic control techniques. Given a discrete-time control system that is related to its symbolic model by an alternating simulation relation. In this paper, we focus on computing the maximum robustness margin under which the symbolic model remains valid for a perturbed-version of the discrete-time control system. We first show that symbolic models are inherently equipped with a certain free robustness margins. We then provide constructive procedures to compute uniform and non-uniform (state and input dependent) robustness margins. We also show that the tightness of the robustness margin depends on the tightness of the reachability technique used to compute the symbolic model. We then explain how the computed robustness margin can be used for the sake of controller synthesis. Finally, we present two illustrative examples to demonstrate the effectiveness of our approach.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"86 ","pages":"Article 101296"},"PeriodicalIF":2.6,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145645600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The assessment of robust stability and performance of systems affected by Linear Time-Invariant (LTI) and Linear Time-Varying (LTV) uncertainties with bounded rates of variation is still an open problem and yet of importance. To this purpose, Integral Quadratic Constraints (IQCs) can be used to derive sufficient conditions in terms of Frequency Domain Inequalities (FDIs) involving both dynamic and static multipliers. In this paper, a new fully frequency-based approach is proposed which offers two main advantages. Firstly, LTI uncertainties are characterized by the independent frequency-by-frequency multipliers of -analysis, which are much less conservative than those used in IQC approaches, for which a basis must be chosen arbitrarily. Secondly, sub-optimal (but relevant) solutions can be obtained by iteratively optimizing the static and frequency-dependent multipliers. This lightens the computational load and makes the method more applicable to real systems.
{"title":"Robust stability and performance analysis in the presence of LTI and LTV uncertainties with bounded rates of variation","authors":"Tommaso Casati , Clément Roos , Jean-Marc Biannic , Hélène Evain","doi":"10.1016/j.ejcon.2025.101298","DOIUrl":"10.1016/j.ejcon.2025.101298","url":null,"abstract":"<div><div>The assessment of robust stability and performance of systems affected by Linear Time-Invariant (LTI) and Linear Time-Varying (LTV) uncertainties with bounded rates of variation is still an open problem and yet of importance. To this purpose, Integral Quadratic Constraints (IQCs) can be used to derive sufficient conditions in terms of Frequency Domain Inequalities (FDIs) involving both dynamic and static multipliers. In this paper, a new fully frequency-based approach is proposed which offers two main advantages. Firstly, LTI uncertainties are characterized by the independent frequency-by-frequency multipliers of <span><math><mi>μ</mi></math></span>-analysis, which are much less conservative than those used in IQC approaches, for which a basis must be chosen arbitrarily. Secondly, sub-optimal (but relevant) solutions can be obtained by iteratively optimizing the static and frequency-dependent multipliers. This lightens the computational load and makes the method more applicable to real systems.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"86 ","pages":"Article 101298"},"PeriodicalIF":2.6,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145645601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01DOI: 10.1016/j.ejcon.2025.101332
Riccardo Brumali, Guido Carnevale, Giuseppe Notarstefano
In this paper, we propose MAcroscopic Consensus and micRoscopic gradient-based OPTimization (MACROPT), a novel distributed method for a network of agents able to learn a probabilistic macroscopic model and concurrently optimize it by acting on the microscopic agents’ states. The macroscopic model is defined through the aggregation of local kernels each representing a probabilistic feature of a single agent (e.g., its local sensing model), while the optimization is done with respect to a given cost index, e.g., the Kullback–Leibler divergence with respect to a target distribution. MACROPT improves the macroscopic model by microscopically coordinating the agents according to a distributed gradient-based policy. Concurrently, it allows each agent to locally learn the macroscopic model through a consensus-based mechanism. We analyze the resulting interconnected method through the lens of system theory. We demonstrate that MACROPT asymptotically converges to the set of stationary points of the nonconvex cost function. The theoretical findings are supported by numerical simulations in sensor network event-detection scenarios.
{"title":"Distributed learning and optimization of a multi-agent macroscopic probabilistic model","authors":"Riccardo Brumali, Guido Carnevale, Giuseppe Notarstefano","doi":"10.1016/j.ejcon.2025.101332","DOIUrl":"10.1016/j.ejcon.2025.101332","url":null,"abstract":"<div><div>In this paper, we propose MAcroscopic Consensus and micRoscopic gradient-based OPTimization (MACROPT), a novel distributed method for a network of agents able to learn a probabilistic macroscopic model and concurrently optimize it by acting on the microscopic agents’ states. The macroscopic model is defined through the aggregation of local kernels each representing a probabilistic feature of a single agent (e.g., its local sensing model), while the optimization is done with respect to a given cost index, e.g., the Kullback–Leibler divergence with respect to a target distribution. MACROPT improves the macroscopic model by microscopically coordinating the agents according to a distributed gradient-based policy. Concurrently, it allows each agent to locally learn the macroscopic model through a consensus-based mechanism. We analyze the resulting interconnected method through the lens of system theory. We demonstrate that MACROPT asymptotically converges to the set of stationary points of the nonconvex cost function. The theoretical findings are supported by numerical simulations in sensor network event-detection scenarios.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"86 ","pages":"Article 101332"},"PeriodicalIF":2.6,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145645449","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Modern vehicles have evolved from mechanical systems to complex and connected ones controlled by numerous digital computers interconnected through internal networks. While this development has improved their efficiency and safety, it also brings new potential risks, particularly cyber-attacks. Several studies have explored the security of vehicle dynamics against such threats. Among these dynamics, the vehicle’s lateral dynamics are crucial for maintaining stability and control during turns and maneuvers, making them a key focus of research. However, only a few recent studies have specifically investigated the security of lateral dynamics. This paper explores the potential for zero dynamics attacks on the vehicle’s lateral dynamics, where the attacker can remain undetected by leaving no trace on the system’s outputs. Three scenarios are studied: when the output includes yaw rate, lateral acceleration, and their combination. These two critical measurements of a vehicle’s lateral motion are accessible through the inertial measurement units (IMU) in every vehicle. For each scenario, the impact of zero dynamics attacks on system performance is analyzed and illustrated through simulations. Finally, the paper provides recommendations for securing vehicles’ lateral dynamics against such attacks.
{"title":"Cyber–physical security of vehicles: Zero dynamics attacks against vehicle’s lateral dynamics","authors":"Ghadeer Shaaban , Hassen Fourati , Alain Kibangou , Christophe Prieur , Mohammad Pirani","doi":"10.1016/j.ejcon.2025.101316","DOIUrl":"10.1016/j.ejcon.2025.101316","url":null,"abstract":"<div><div>Modern vehicles have evolved from mechanical systems to complex and connected ones controlled by numerous digital computers interconnected through internal networks. While this development has improved their efficiency and safety, it also brings new potential risks, particularly cyber-attacks. Several studies have explored the security of vehicle dynamics against such threats. Among these dynamics, the vehicle’s lateral dynamics are crucial for maintaining stability and control during turns and maneuvers, making them a key focus of research. However, only a few recent studies have specifically investigated the security of lateral dynamics. This paper explores the potential for zero dynamics attacks on the vehicle’s lateral dynamics, where the attacker can remain undetected by leaving no trace on the system’s outputs. Three scenarios are studied: when the output includes yaw rate, lateral acceleration, and their combination. These two critical measurements of a vehicle’s lateral motion are accessible through the inertial measurement units (IMU) in every vehicle. For each scenario, the impact of zero dynamics attacks on system performance is analyzed and illustrated through simulations. Finally, the paper provides recommendations for securing vehicles’ lateral dynamics against such attacks.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"86 ","pages":"Article 101316"},"PeriodicalIF":2.6,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145645446","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01DOI: 10.1016/j.ejcon.2025.101312
Victor Nan Fernandez-Ayala , Jorge Silva , Meng Guo , Dimos V. Dimarogonas
We propose a framework enabling mobile manipulators to reliably complete pick-and-place tasks for assembling structures from construction blocks. The picking uses an eye-in-hand visual servoing controller for object tracking with Control Barrier Functions (CBFs) to ensure fiducial markers in the blocks remain visible. An additional robot with an eye-to-hand setup ensures precise placement, critical for structural stability. We integrate human-in-the-loop capabilities for flexibility and fault correction and analyze robustness to camera pose errors, proposing adapted barrier functions to handle them. Lastly, experiments validate the framework on 6-DoF mobile arms.
{"title":"Robust visual servoing under human supervision for assembly tasks","authors":"Victor Nan Fernandez-Ayala , Jorge Silva , Meng Guo , Dimos V. Dimarogonas","doi":"10.1016/j.ejcon.2025.101312","DOIUrl":"10.1016/j.ejcon.2025.101312","url":null,"abstract":"<div><div>We propose a framework enabling mobile manipulators to reliably complete pick-and-place tasks for assembling structures from construction blocks. The picking uses an eye-in-hand visual servoing controller for object tracking with Control Barrier Functions (CBFs) to ensure fiducial markers in the blocks remain visible. An additional robot with an eye-to-hand setup ensures precise placement, critical for structural stability. We integrate human-in-the-loop capabilities for flexibility and fault correction and analyze robustness to camera pose errors, proposing adapted barrier functions to handle them. Lastly, experiments validate the framework on 6-DoF mobile arms.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"86 ","pages":"Article 101312"},"PeriodicalIF":2.6,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145645447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01DOI: 10.1016/j.ejcon.2025.101333
Emilio Corcione , Michael Kübler , Magnus Benke , Stephanie Mrzyglod , Jixing Zhang , Oliver Sawodny , Jörg Wrachtrup , Cristina Tarín
We present a novel approach to processing periodic signals with non-stationary fundamental frequency. These quasi-periodic signals feature a perpetually recurring underlying signal pattern and arise in various fields of science and engineering. The proposed method integrates a recursive extraction of the signal pattern with dynamic tracking of the instantaneous phase to effectively suppress measurement noise without prior knowledge of the signal characteristics or the frequency variation. The performance is showcased both in simulation and using experimental measurements of the cardiac cycle obtained by a nitrogen-vacancy diamond quantum sensor. Overall, high-fidelity signal reconstruction and convincing pattern learning is achieved, even in the presence of complex non-linear disturbances and non-Gaussian noise. Conclusively, the proposed technique constitutes a flexible and efficient solution, addressing limitations of existing methods and offering real-world applicability.
{"title":"Adaptive modelling and filtering of periodic signals with non-stationary fundamental frequency","authors":"Emilio Corcione , Michael Kübler , Magnus Benke , Stephanie Mrzyglod , Jixing Zhang , Oliver Sawodny , Jörg Wrachtrup , Cristina Tarín","doi":"10.1016/j.ejcon.2025.101333","DOIUrl":"10.1016/j.ejcon.2025.101333","url":null,"abstract":"<div><div>We present a novel approach to processing periodic signals with non-stationary fundamental frequency. These quasi-periodic signals feature a perpetually recurring underlying signal pattern and arise in various fields of science and engineering. The proposed method integrates a recursive extraction of the signal pattern with dynamic tracking of the instantaneous phase to effectively suppress measurement noise without prior knowledge of the signal characteristics or the frequency variation. The performance is showcased both in simulation and using experimental measurements of the cardiac cycle obtained by a nitrogen-vacancy diamond quantum sensor. Overall, high-fidelity signal reconstruction and convincing pattern learning is achieved, even in the presence of complex non-linear disturbances and non-Gaussian noise. Conclusively, the proposed technique constitutes a flexible and efficient solution, addressing limitations of existing methods and offering real-world applicability.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"86 ","pages":"Article 101333"},"PeriodicalIF":2.6,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145645527","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01DOI: 10.1016/j.ejcon.2025.101337
Joyce Lai, Peter Seiler
Disturbance rejection in high-precision control applications can be significantly improved upon via online convex optimization (OCO). This includes classical techniques such as recursive least squares (RLS) and more recent, regret-based formulations. However, these methods can cause instabilities in the presence of model uncertainty. This paper introduces a safety filter for systems with OCO in the form of adaptive finite impulse response (FIR) filtering to ensure robust disturbance rejection. The safety filter enforces a robust stability constraint on the FIR coefficients while minimally altering the OCO command in the -norm cost. Additionally, we show that the induced -norm allows for easy online implementation of the safety filter by directly limiting the OCO command. The constraint can be tuned to trade off robustness and performance. We provide a simple example to demonstrate the safety filter.
{"title":"Safety filter for robust disturbance rejection via online optimization","authors":"Joyce Lai, Peter Seiler","doi":"10.1016/j.ejcon.2025.101337","DOIUrl":"10.1016/j.ejcon.2025.101337","url":null,"abstract":"<div><div>Disturbance rejection in high-precision control applications can be significantly improved upon via online convex optimization (OCO). This includes classical techniques such as recursive least squares (RLS) and more recent, regret-based formulations. However, these methods can cause instabilities in the presence of model uncertainty. This paper introduces a safety filter for systems with OCO in the form of adaptive finite impulse response (FIR) filtering to ensure robust disturbance rejection. The safety filter enforces a robust stability constraint on the FIR coefficients while minimally altering the OCO command in the <span><math><mi>∞</mi></math></span>-norm cost. Additionally, we show that the induced <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span>-norm allows for easy online implementation of the safety filter by directly limiting the OCO command. The constraint can be tuned to trade off robustness and performance. We provide a simple example to demonstrate the safety filter.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"86 ","pages":"Article 101337"},"PeriodicalIF":2.6,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145645528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01DOI: 10.1016/j.ejcon.2025.101338
Tarun Pati , Maral Mordad , Sze Zheng Yong
This article introduces polytopic observer designs for discrete- and continuous-time linear systems with bounded uncertainties. In particular, by noting that polytopes are equivalent to constrained zonotopes with intervals in their generator spaces, we propose two choices of generators to fix the order of the polytopic observer. Moreover, this observation enables us to leverage existing interval observers to find interval estimates in the augmented generator space before projecting them onto the original state space as polytopes/constrained zonotopes. Further, we prove that the polytopic observers are at least as good as interval observers for the same uncertain linear system in terms of the volumes of their set estimates and the error system gains. As a side contribution, we also introduce a more computationally efficient approach to obtain interval observer gains. Finally, we demonstrate and discuss the effectiveness of the proposed approach on a broad range of examples.
{"title":"Polytopic observer designs for uncertain linear systems","authors":"Tarun Pati , Maral Mordad , Sze Zheng Yong","doi":"10.1016/j.ejcon.2025.101338","DOIUrl":"10.1016/j.ejcon.2025.101338","url":null,"abstract":"<div><div>This article introduces polytopic observer designs for discrete- and continuous-time linear systems with bounded uncertainties. In particular, by noting that polytopes are equivalent to constrained zonotopes with intervals in their generator spaces, we propose two choices of generators to fix the order of the polytopic observer. Moreover, this observation enables us to leverage existing interval observers to find interval estimates in the augmented generator space before projecting them onto the original state space as polytopes/constrained zonotopes. Further, we prove that the polytopic observers are at least as good as interval observers for the same uncertain linear system in terms of the volumes of their set estimates and the error system gains. As a side contribution, we also introduce a more computationally efficient approach to obtain interval observer gains. Finally, we demonstrate and discuss the effectiveness of the proposed approach on a broad range of examples.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"86 ","pages":"Article 101338"},"PeriodicalIF":2.6,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145645529","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01DOI: 10.1016/j.ejcon.2025.101361
Debojyoti Biswas , Eduardo D. Sontag , Noah J. Cowan
We consider a general class of translation-invariant systems with a specific category of output nonlinearities motivated by biological sensing. We show that no dynamic output feedback can stabilize this class of systems to an isolated equilibrium point. To overcome this fundamental limitation, we propose a simple control scheme that includes a low-amplitude periodic forcing function akin to so-called “active sensing” in biology, together with nonlinear output feedback. Our analysis shows that this approach leads to the emergence of an exponentially stable limit cycle. These findings offer a provably stable active sensing strategy and may thus help to rationalize the active sensing movements animals make when performing certain motor behaviors.
{"title":"An exact active sensing strategy for a class of bio-inspired systems","authors":"Debojyoti Biswas , Eduardo D. Sontag , Noah J. Cowan","doi":"10.1016/j.ejcon.2025.101361","DOIUrl":"10.1016/j.ejcon.2025.101361","url":null,"abstract":"<div><div>We consider a general class of translation-invariant systems with a specific category of output nonlinearities motivated by biological sensing. We show that no dynamic output feedback can stabilize this class of systems to an isolated equilibrium point. To overcome this fundamental limitation, we propose a simple control scheme that includes a low-amplitude periodic forcing function akin to so-called “active sensing” in biology, together with nonlinear output feedback. Our analysis shows that this approach leads to the emergence of an exponentially stable limit cycle. These findings offer a provably stable active sensing strategy and may thus help to rationalize the active sensing movements animals make when performing certain motor behaviors.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"86 ","pages":"Article 101361"},"PeriodicalIF":2.6,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145645539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01DOI: 10.1016/j.ejcon.2025.101293
Erik van den Eshof, Jorn van Kampen, Mauro Salazar
This paper presents an energy and thermal management system for electric race cars, where we tune a lift-off-throttle signal for the driver in real-time to respect energy budgets and thermal constraints. First, we compute globally optimal state trajectories in a real-time capable solving time, optimizing a 47 km horizon in 2.5 s. Next, for safe operation with a human driver, we simplify it to a maximum-power-or-coast operation in full-throttle regions (straights). Thereby, both the positions from which the vehicle should start coasting and the optimal throttle map are subject to tuning. To this end, we define the coasting sections with a threshold on the costate trajectory of the kinetic energy from the optimal solution. We devise an online implementable bisection algorithm to tune this threshold and adapt it using PI feedback. Finally, we validate the proposed approach for an electric endurance race car and compare three variants with varying implementation challenges: one re-optimizing and updating the kinetic costate trajectory online, one applying only the bisection algorithm online, and one relying exclusively on feedback control. Our results show that, under typical racing disturbances, our energy management achieves stint times ranging from less than 0.056% to 0.22% slower compared to offline optimization with a priori disturbance knowledge, paving the way for on-board implementations and testing.
{"title":"Human-in-the-loop energy and thermal management for electric racing cars through optimization-based control","authors":"Erik van den Eshof, Jorn van Kampen, Mauro Salazar","doi":"10.1016/j.ejcon.2025.101293","DOIUrl":"10.1016/j.ejcon.2025.101293","url":null,"abstract":"<div><div>This paper presents an energy and thermal management system for electric race cars, where we tune a lift-off-throttle signal for the driver in real-time to respect energy budgets and thermal constraints. First, we compute globally optimal state trajectories in a real-time capable solving time, optimizing a 47 km horizon in 2.5 s. Next, for safe operation with a human driver, we simplify it to a maximum-power-or-coast operation in full-throttle regions (straights). Thereby, both the positions from which the vehicle should start coasting and the optimal throttle map are subject to tuning. To this end, we define the coasting sections with a threshold on the costate trajectory of the kinetic energy from the optimal solution. We devise an online implementable bisection algorithm to tune this threshold and adapt it using PI feedback. Finally, we validate the proposed approach for an electric endurance race car and compare three variants with varying implementation challenges: one re-optimizing and updating the kinetic costate trajectory online, one applying only the bisection algorithm online, and one relying exclusively on feedback control. Our results show that, under typical racing disturbances, our energy management achieves stint times ranging from less than 0.056% to 0.22% slower compared to offline optimization with a priori disturbance knowledge, paving the way for on-board implementations and testing.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"86 ","pages":"Article 101293"},"PeriodicalIF":2.6,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145645540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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