Pub Date : 2025-11-01DOI: 10.1016/j.ejcon.2025.101310
Thomas Chaffey , Fulvio Forni
An analog of the describing function method is developed using square waves rather than sinusoids. Static nonlinearities map square waves to square waves, and their behavior is characterized by their response to square waves of varying amplitude — their amplitude response. The output of an LTI system to a square wave input is approximated by a square wave, to give an analog of the describing function. The classical describing function method for predicting oscillations in feedback interconnections is generalized to this square wave setting, and gives accurate predictions when oscillations are approximately square.
{"title":"Amplitude response and square wave describing functions","authors":"Thomas Chaffey , Fulvio Forni","doi":"10.1016/j.ejcon.2025.101310","DOIUrl":"10.1016/j.ejcon.2025.101310","url":null,"abstract":"<div><div>An analog of the describing function method is developed using square waves rather than sinusoids. Static nonlinearities map square waves to square waves, and their behavior is characterized by their response to square waves of varying amplitude — their <em>amplitude response</em>. The output of an LTI system to a square wave input is approximated by a square wave, to give an analog of the describing function. The classical describing function method for predicting oscillations in feedback interconnections is generalized to this square wave setting, and gives accurate predictions when oscillations are approximately square.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"86 ","pages":"Article 101310"},"PeriodicalIF":2.6,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145645611","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.2025.101297
Marek Wadinger, Rastislav Fáber, Erika Pavlovičová, Radoslav Paulen
This paper presents a comprehensive framework aimed at enhancing education in modeling, optimal control, and nonlinear Model Predictive Control (MPC) through a practical greenhouse climate control model. The framework includes a detailed mathematical model of lettuce growth and greenhouse environment, which are influenced by real-time external weather conditions obtained via an application programming interface (API). Using this data, the MPC-based approach dynamically adjusts greenhouse conditions, optimizing plant growth and energy consumption and minimizing the social cost of CO2. The presented results demonstrate the effectiveness of this approach in balancing energy use with crop yield and reducing CO2 emissions, contributing to economic efficiency and environmental sustainability. The framework also provides a valuable resource for making control systems education more engaging and effective. The main aim is to provide students with a hands-on platform to understand the principles of modeling, the power of MPC and the trade-offs between profitability and sustainability in agricultural systems. The framework gives students a hands-on experience, helping them to understand the control theory better, connecting it to the practical implementation, and developing their problem-solving skills. It can be accessed at ecompc4greenhouse.streamlit.app.
{"title":"Carbon neutral greenhouse: Economic model predictive control framework for education","authors":"Marek Wadinger, Rastislav Fáber, Erika Pavlovičová, Radoslav Paulen","doi":"10.1016/j.ejcon.2025.101297","DOIUrl":"10.1016/j.ejcon.2025.101297","url":null,"abstract":"<div><div>This paper presents a comprehensive framework aimed at enhancing education in modeling, optimal control, and nonlinear Model Predictive Control (MPC) through a practical greenhouse climate control model. The framework includes a detailed mathematical model of lettuce growth and greenhouse environment, which are influenced by real-time external weather conditions obtained via an application programming interface (API). Using this data, the MPC-based approach dynamically adjusts greenhouse conditions, optimizing plant growth and energy consumption and minimizing the social cost of CO<sub>2</sub>. The presented results demonstrate the effectiveness of this approach in balancing energy use with crop yield and reducing CO<sub>2</sub> emissions, contributing to economic efficiency and environmental sustainability. The framework also provides a valuable resource for making control systems education more engaging and effective. The main aim is to provide students with a hands-on platform to understand the principles of modeling, the power of MPC and the trade-offs between profitability and sustainability in agricultural systems. The framework gives students a hands-on experience, helping them to understand the control theory better, connecting it to the practical implementation, and developing their problem-solving skills. It can be accessed at <span><span>ecompc4greenhouse.streamlit.app</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"86 ","pages":"Article 101297"},"PeriodicalIF":2.6,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145645542","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}
In this paper, a novel ramp metering control with constraints compliance is introduced for a road traffic system with uncertain demand. The uncertain part of the flow entering the on-ramps is estimated relying on Integral Sliding Mode (ISM) based Unknown Input Observers (UIOs). The estimation is then employed in a Quadratic Programming (QP) problem, where constraints on queue lengths at the on-ramps are included via suitable Control Barrier Functions (CBFs). This results in an original approach that ensures adherence to queue length constraints by design, even under uncertain on-ramp demand conditions. The proposal is theoretically analyzed and assessed in simulation relying on the Cell Transmission Model (CTM) suitably extended to encompass the capacity drop effect. Simulation-based evaluations confirm the effectiveness of the proposed approach.
{"title":"Constrained ramp metering control based on sliding mode unknown input observers","authors":"Nikolas Sacchi , Michele Cucuzzella , Antonella Ferrara","doi":"10.1016/j.ejcon.2025.101369","DOIUrl":"10.1016/j.ejcon.2025.101369","url":null,"abstract":"<div><div>In this paper, a novel ramp metering control with constraints compliance is introduced for a road traffic system with uncertain demand. The uncertain part of the flow entering the on-ramps is estimated relying on Integral Sliding Mode (ISM) based Unknown Input Observers (UIOs). The estimation is then employed in a Quadratic Programming (QP) problem, where constraints on queue lengths at the on-ramps are included via suitable Control Barrier Functions (CBFs). This results in an original approach that ensures adherence to queue length constraints by design, even under uncertain on-ramp demand conditions. The proposal is theoretically analyzed and assessed in simulation relying on the Cell Transmission Model (CTM) suitably extended to encompass the capacity drop effect. Simulation-based evaluations confirm the effectiveness of the proposed approach.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"86 ","pages":"Article 101369"},"PeriodicalIF":2.6,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145645441","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 : 2025-10-30DOI: 10.1016/j.ejcon.2025.101407
Taewan Kim, Behçet Açıkmeşe
Funnel synthesis refers to a procedure for synthesizing a time-varying controlled invariant set and an associated control law around a nominal trajectory. The computation of the funnel involves solving a continuous-time differential equation or inequality, ensuring the invariance of the funnel. Previous approaches often compromise the invariance property of the funnel; for example, they may enforce the equation or the inequality only at discrete temporal nodes and do not have a formal guarantee of invariance at all times. This paper proposes a computational funnel synthesis method that can satisfy the invariance of the funnel without such compromises. We derive a finite number of linear matrix inequalities (LMIs) that imply the satisfaction of a continuous-time differential linear matrix inequality guaranteeing the invariance of the funnel at all times from the initial to the final time. To this end, we utilize LMI conditions ensuring matrix copositivity, which then imply continuous-time invariance. The primary contribution of the paper is to prove that the resulting funnel is indeed invariant over a finite time horizon. We validate the proposed method via a three-dimensional trajectory planning and control problem with obstacle avoidance constraints, and a six-degree-of-freedom powered descent guidance.
{"title":"Funnel synthesis via LMI copositivity conditions for nonlinear systems","authors":"Taewan Kim, Behçet Açıkmeşe","doi":"10.1016/j.ejcon.2025.101407","DOIUrl":"10.1016/j.ejcon.2025.101407","url":null,"abstract":"<div><div>Funnel synthesis refers to a procedure for synthesizing a time-varying controlled invariant set and an associated control law around a nominal trajectory. The computation of the funnel involves solving a continuous-time differential equation or inequality, ensuring the invariance of the funnel. Previous approaches often compromise the invariance property of the funnel; for example, they may enforce the equation or the inequality only at discrete temporal nodes and do not have a formal guarantee of invariance at all times. This paper proposes a computational funnel synthesis method that can satisfy the invariance of the funnel without such compromises. We derive a finite number of linear matrix inequalities (LMIs) that imply the satisfaction of a continuous-time differential linear matrix inequality guaranteeing the invariance of the funnel at all times from the initial to the final time. To this end, we utilize LMI conditions ensuring matrix copositivity, which then imply continuous-time invariance. The primary contribution of the paper is to prove that the resulting funnel is indeed invariant over a finite time horizon. We validate the proposed method via a three-dimensional trajectory planning and control problem with obstacle avoidance constraints, and a six-degree-of-freedom powered descent guidance.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"86 ","pages":"Article 101407"},"PeriodicalIF":2.6,"publicationDate":"2025-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145466460","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 : 2025-10-28DOI: 10.1016/j.ejcon.2025.101408
Atefeh Behnia, Mohammad Hossein Shafiei
This paper proposes a novel framework for designing an adaptive event-triggered output feedback controller for discrete-time systems with parametric uncertainty. The framework is developed using two distinct methodologies. The first approach decouples the design process: the output feedback gain is predefined independently of the event-triggered control (ETC) mechanism, followed by the synthesis of an excitation event law to guarantee closed-loop stability. The second, more integrated approach (the co-design method) simultaneously designs both the output feedback controller and the adaptive event-triggered control (AETC) law. The AETC law features an innovative adaptive update mechanism designed to preserve closed-loop performance while maximizing the average inter-event interval, thereby reducing communication and computational overhead. Simulation results reveal that the proposed co-design approach achieves reduction in control updates and improvement in RMS regulation error compared to conventional methods, demonstrating superior performance and efficient resource utilization.
{"title":"Emulation and co-design approaches for adaptive event-triggered output feedback control of discrete-time nonlinear systems","authors":"Atefeh Behnia, Mohammad Hossein Shafiei","doi":"10.1016/j.ejcon.2025.101408","DOIUrl":"10.1016/j.ejcon.2025.101408","url":null,"abstract":"<div><div>This paper proposes a novel framework for designing an adaptive event-triggered output feedback controller for discrete-time systems with parametric uncertainty. The framework is developed using two distinct methodologies. The first approach decouples the design process: the output feedback gain is predefined independently of the event-triggered control (ETC) mechanism, followed by the synthesis of an excitation event law to guarantee closed-loop stability. The second, more integrated approach (the co-design method) simultaneously designs both the output feedback controller and the adaptive event-triggered control (AETC) law. The AETC law features an innovative adaptive update mechanism designed to preserve closed-loop performance while maximizing the average inter-event interval, thereby reducing communication and computational overhead. Simulation results reveal that the proposed co-design approach achieves reduction in control updates and improvement in RMS regulation error compared to conventional methods, demonstrating superior performance and efficient resource utilization.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"86 ","pages":"Article 101408"},"PeriodicalIF":2.6,"publicationDate":"2025-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145466459","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 : 2025-10-24DOI: 10.1016/j.ejcon.2025.101403
Wen Kang , Emilia Fridman , Er-Xin Pang
This paper addresses non-local control design of 1-D nonlinear Korteweg–de Vries–Burgers equation in the presence of variable input delay, actuator saturation as well as sampled-data switching control. By using the modal decomposition approach, we divide the original system into unstable modes and infinitely many stable modes. Based on the unstable modes, we design a finite-dimensional controller to stabilize the system. The well-posedness of the closed-loop system is established by semigroup theory and the step method. To prove regional -stability of the closed-loop system, we construct an appropriate Lyapunov–Krasovskii functional and derive sufficient conditions for stability. An estimate is provided for the set of initial conditions starting from which the state trajectories of the system are exponentially converging to origin. Switched controller is designed based on the sampled-data state-depend switching law. Numerical example illustrates the efficiency of the method.
{"title":"Delayed stabilization of Korteweg–de Vries–Burgers equation by constrained control","authors":"Wen Kang , Emilia Fridman , Er-Xin Pang","doi":"10.1016/j.ejcon.2025.101403","DOIUrl":"10.1016/j.ejcon.2025.101403","url":null,"abstract":"<div><div>This paper addresses non-local control design of 1-D nonlinear Korteweg–de Vries–Burgers equation in the presence of variable input delay, actuator saturation as well as sampled-data switching control. By using the modal decomposition approach, we divide the original system into <span><math><mrow><mi>N</mi><mo>+</mo><mn>1</mn></mrow></math></span> unstable modes and infinitely many stable modes. Based on the <span><math><mrow><mi>N</mi><mo>+</mo><mn>1</mn></mrow></math></span> unstable modes, we design a finite-dimensional controller to stabilize the system. The well-posedness of the closed-loop system is established by semigroup theory and the step method. To prove regional <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-stability of the closed-loop system, we construct an appropriate Lyapunov–Krasovskii functional and derive sufficient conditions for stability. An estimate is provided for the set of initial conditions starting from which the state trajectories of the system are exponentially converging to origin. Switched controller is designed based on the sampled-data state-depend switching law. Numerical example illustrates the efficiency of the method.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"86 ","pages":"Article 101403"},"PeriodicalIF":2.6,"publicationDate":"2025-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145416544","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 : 2025-10-22DOI: 10.1016/j.ejcon.2025.101404
Xiaoru Sun, Chris T. Freeman
An artificial neural network (ANN) is combined with gradient descent to form a model-free iterative learning control (ILC) approach than can be applied to a wide range of nonlinear discrete-time systems. The ANN is recursively trained on the entire set of past data collected from the system and uses a passivity condition to determine when the ANN can be used to compute the next ILC update, or if an identification test is needed. Convergence properties are established alongside design selections that ensure the passivity condition is fulfilled. By minimising the reliance on identification tests, this methodology is substantially faster than existing model-free ILC algorithms. It is tested on a key stroke rehabilitation problem using functional electrical stimulation (FES) for hand/wrist tracking. Experimental results using the new ILC approach with eight participants show that three hand/wrist references can be tracked using an average of 56% fewer experimental inputs compared with the most accurate previous approach. As the first approach to combine ILC and machine learning in upper limb rehabilitation, the results demonstrate how their combination addresses their individual deficiencies.
{"title":"Artificial neural network based iterative learning control for stroke rehabilitation","authors":"Xiaoru Sun, Chris T. Freeman","doi":"10.1016/j.ejcon.2025.101404","DOIUrl":"10.1016/j.ejcon.2025.101404","url":null,"abstract":"<div><div>An artificial neural network (ANN) is combined with gradient descent to form a model-free iterative learning control (ILC) approach than can be applied to a wide range of nonlinear discrete-time systems. The ANN is recursively trained on the entire set of past data collected from the system and uses a passivity condition to determine when the ANN can be used to compute the next ILC update, or if an identification test is needed. Convergence properties are established alongside design selections that ensure the passivity condition is fulfilled. By minimising the reliance on identification tests, this methodology is substantially faster than existing model-free ILC algorithms. It is tested on a key stroke rehabilitation problem using functional electrical stimulation (FES) for hand/wrist tracking. Experimental results using the new ILC approach with eight participants show that three hand/wrist references can be tracked using an average of 56% fewer experimental inputs compared with the most accurate previous approach. As the first approach to combine ILC and machine learning in upper limb rehabilitation, the results demonstrate how their combination addresses their individual deficiencies.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"86 ","pages":"Article 101404"},"PeriodicalIF":2.6,"publicationDate":"2025-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145362452","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 : 2025-10-22DOI: 10.1016/j.ejcon.2025.101405
Mohammadreza Doostmohammadian , Sergio Pequito
Distributed resource allocation (DRA) is fundamental to modern networked systems, spanning applications from economic dispatch in smart grids to CPU scheduling in data centers. Conventional DRA approaches require reliable communication, yet real-world networks frequently suffer from link failures, packet drops, and communication delays due to environmental conditions, network congestion, and security threats.
We introduce a novel resilient DRA algorithm that addresses these critical challenges, and our main contributions are as follows: (1) guaranteed constraint feasibility at all times, ensuring resource-demand balance even during algorithm termination or network disruption; (2) robust convergence despite sector-bound nonlinearities at nodes/links, accommodating practical constraints like quantization and saturation; and (3) optimal performance under merely uniformly-connected networks, eliminating the need for continuous connectivity.
Unlike existing approaches that require persistent network connectivity and provide only asymptotic feasibility, our graph-theoretic solution leverages network percolation theory to maintain performance during intermittent disconnections. This makes it particularly valuable for mobile multi-agent systems where nodes frequently move out of communication range. Theoretical analysis and simulations demonstrate that our algorithm converges to optimal solutions despite heterogeneous time delays and substantial link failures, significantly advancing the reliability of distributed resource allocation in practical network environments.
{"title":"Distributed allocation and resource scheduling algorithms resilient to link failure","authors":"Mohammadreza Doostmohammadian , Sergio Pequito","doi":"10.1016/j.ejcon.2025.101405","DOIUrl":"10.1016/j.ejcon.2025.101405","url":null,"abstract":"<div><div>Distributed resource allocation (DRA) is fundamental to modern networked systems, spanning applications from economic dispatch in smart grids to CPU scheduling in data centers. Conventional DRA approaches require reliable communication, yet real-world networks frequently suffer from link failures, packet drops, and communication delays due to environmental conditions, network congestion, and security threats.</div><div>We introduce a novel resilient DRA algorithm that addresses these critical challenges, and our main contributions are as follows: (1) guaranteed constraint feasibility at all times, ensuring resource-demand balance even during algorithm termination or network disruption; (2) robust convergence despite sector-bound nonlinearities at nodes/links, accommodating practical constraints like quantization and saturation; and (3) optimal performance under merely uniformly-connected networks, eliminating the need for continuous connectivity.</div><div>Unlike existing approaches that require persistent network connectivity and provide only asymptotic feasibility, our graph-theoretic solution leverages network percolation theory to maintain performance during intermittent disconnections. This makes it particularly valuable for mobile multi-agent systems where nodes frequently move out of communication range. Theoretical analysis and simulations demonstrate that our algorithm converges to optimal solutions despite heterogeneous time delays and substantial link failures, significantly advancing the reliability of distributed resource allocation in practical network environments.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"86 ","pages":"Article 101405"},"PeriodicalIF":2.6,"publicationDate":"2025-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145362451","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 : 2025-10-20DOI: 10.1016/j.ejcon.2025.101406
Moein Doakhan, Mansour Kabganian, Ali Azimi
This work addresses the problem of rigid-body payload transportation using flexible formation control of four quadrotors. While maintaining formation in aerial payload transportation provides advantages such as uniform load distribution, collision avoidance, and prevention of cable entanglement, a rigid formation may not always be feasible or optimal under every maneuver. In the proposed approach, the quadrotor formation is flexibly adapted to the desired maneuver, ensuring uniform and minimal energy consumption, which is a critical requirement given the finite flight endurance of quadrotors. To this end, the problem is formulated as a nonlinear constrained optimization, and a decomposition technique is proposed to enable real-time implementation. A three-loop control structure based on sliding mode control is developed, and simulation results demonstrate reduced energy consumption in the presence of disturbances and under nonlinear maneuvers.
{"title":"Aerial Payload Transportation with Energy-Efficient Flexible Formation Control of Quadrotors","authors":"Moein Doakhan, Mansour Kabganian, Ali Azimi","doi":"10.1016/j.ejcon.2025.101406","DOIUrl":"10.1016/j.ejcon.2025.101406","url":null,"abstract":"<div><div>This work addresses the problem of rigid-body payload transportation using flexible formation control of four quadrotors. While maintaining formation in aerial payload transportation provides advantages such as uniform load distribution, collision avoidance, and prevention of cable entanglement, a rigid formation may not always be feasible or optimal under every maneuver. In the proposed approach, the quadrotor formation is flexibly adapted to the desired maneuver, ensuring uniform and minimal energy consumption, which is a critical requirement given the finite flight endurance of quadrotors. To this end, the problem is formulated as a nonlinear constrained optimization, and a decomposition technique is proposed to enable real-time implementation. A three-loop control structure based on sliding mode control is developed, and simulation results demonstrate reduced energy consumption in the presence of disturbances and under nonlinear maneuvers.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"86 ","pages":"Article 101406"},"PeriodicalIF":2.6,"publicationDate":"2025-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145466458","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 : 2025-10-18DOI: 10.1016/j.ejcon.2025.101400
Sanaz Akbarisisi, Wim Michiels
Systems governed by delay differential equations are distinguished by having infinite-dimensional dynamics. This key feature in the context of linear delay systems reflects itself in the associated eigenvalue problem. Moreover, in numerous applications, including power systems and machining, an accurate description leads to time-periodic models. Time-periodic delay differential algebraic equations (TPDDAEs) can offer a useful framework for modeling such systems. We propose a spectrum-based approach for their stability analysis and design of a time-periodic feedback controller of a fixed order. In the design procedure, we adopt two approaches to ensure the smoothness of the optimal time-periodic output gain. As our first approach, we penalize the total variation of the feedback gain, which is translated to a quadratic penalty term in the optimization problem. Conversely, in the second approach, the feedback gain is constrained to be characterized by a finite number of harmonics of its Fourier series representation. To demonstrate the efficacy and applicability of our results, as well as the effectiveness of the incorporated algebraic equations, we conclude our work with some numerical case studies.
{"title":"Spectrum-based stability analysis and stabilization of systems with time-periodic delay differential algebraic equations","authors":"Sanaz Akbarisisi, Wim Michiels","doi":"10.1016/j.ejcon.2025.101400","DOIUrl":"10.1016/j.ejcon.2025.101400","url":null,"abstract":"<div><div>Systems governed by delay differential equations are distinguished by having infinite-dimensional dynamics. This key feature in the context of linear delay systems reflects itself in the associated eigenvalue problem. Moreover, in numerous applications, including power systems and machining, an accurate description leads to time-periodic models. Time-periodic delay differential algebraic equations (TPDDAEs) can offer a useful framework for modeling such systems. We propose a spectrum-based approach for their stability analysis and design of a time-periodic feedback controller of a fixed order. In the design procedure, we adopt two approaches to ensure the smoothness of the optimal time-periodic output gain. As our first approach, we penalize the total variation of the feedback gain, which is translated to a quadratic penalty term in the optimization problem. Conversely, in the second approach, the feedback gain is constrained to be characterized by a finite number of harmonics of its Fourier series representation. To demonstrate the efficacy and applicability of our results, as well as the effectiveness of the incorporated algebraic equations, we conclude our work with some numerical case studies.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"86 ","pages":"Article 101400"},"PeriodicalIF":2.6,"publicationDate":"2025-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145362450","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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