Pub Date : 2025-09-04DOI: 10.1016/j.nahs.2025.101631
Shengda Zeng , Jinsheng Du , Sergey A. Timoshin , Emilio Vilches
We study the well-posedness (existence and uniqueness of a solution) to state-dependent and state-independent Caputo–Katugampola fractional implicit sweeping processes with history-dependent operators in a real Hilbert space. First, using convex analysis tools we reduce these two types of sweeping processes to equivalent differential equations. Second, we employ the Banach fixed-point theorem and fixed-point argument for condensing mappings to examine the well-posedness of the latter equations. Third, we apply our results to circuit models that incorporate memristors and fractional capacitors, and conduct some numerical simulations for these models. We note that the results in this article extend the research of Adly and Haddad (2018), Migórski et al. (2019) and Jourani and Vilches (2019).
{"title":"A new kind of fractional implicit sweeping processes with history-dependent operators: Well-posedness and applications","authors":"Shengda Zeng , Jinsheng Du , Sergey A. Timoshin , Emilio Vilches","doi":"10.1016/j.nahs.2025.101631","DOIUrl":"10.1016/j.nahs.2025.101631","url":null,"abstract":"<div><div>We study the well-posedness (existence and uniqueness of a solution) to state-dependent and state-independent Caputo–Katugampola fractional implicit sweeping processes with history-dependent operators in a real Hilbert space. First, using convex analysis tools we reduce these two types of sweeping processes to equivalent differential equations. Second, we employ the Banach fixed-point theorem and fixed-point argument for condensing mappings to examine the well-posedness of the latter equations. Third, we apply our results to circuit models that incorporate memristors and fractional capacitors, and conduct some numerical simulations for these models. We note that the results in this article extend the research of Adly and Haddad (2018), Migórski et al. (2019) and Jourani and Vilches (2019).</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"59 ","pages":"Article 101631"},"PeriodicalIF":3.7,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144989545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2025-09-01DOI: 10.1016/j.nahs.2025.101628
Tiago Carvalho , Luiz Fernando Gonçalves , Bruno Rodrigues Freitas
In this paper, we employ the geometric theory of singular perturbations to obtain detailed insights concerning a class of piecewise smooth vector fields exhibiting a positive measure minimal set. The canonical form used in our analysis represents a larger class of piecewise smooth systems, encompassing models of discontinuous harmonic oscillators. Through a desingularization process, which entails the application of a -regularization function along with successive weighted blow-ups (directional, spherical and polar), we obtain an attractor for the trajectories of the desingularized vector field .
{"title":"Geometric singular perturbation on a positive measure minimal set of a planar piecewise smooth vector field","authors":"Tiago Carvalho , Luiz Fernando Gonçalves , Bruno Rodrigues Freitas","doi":"10.1016/j.nahs.2025.101628","DOIUrl":"10.1016/j.nahs.2025.101628","url":null,"abstract":"<div><div>In this paper, we employ the geometric theory of singular perturbations to obtain detailed insights concerning a class of piecewise smooth vector fields exhibiting a positive measure minimal set. The canonical form used in our analysis represents a larger class of piecewise smooth systems, encompassing models of discontinuous harmonic oscillators. Through a desingularization process, which entails the application of a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>-regularization function along with successive weighted blow-ups (directional, spherical and polar), we obtain an attractor for the trajectories of the desingularized vector field <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mi>ω</mi></mrow></msub></math></span>.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"58 ","pages":"Article 101628"},"PeriodicalIF":3.7,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144921839","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2025-08-11DOI: 10.1016/j.nahs.2025.101627
Alessandro Borri , Ilaria Di Loreto , Maria Domenica Di Benedetto
In this work, we present a novel contract-theoretic framework for controlling large-scale, interconnected, nonlinear systems by decomposing a global specification into local, time-varying assume–guarantee contracts. First, we decompose the system into local components and the global contract into local contracts; then, our main result gives sufficient conditions under which local causal sampled-data controllers — without foreknowledge of future contract changes — ensures satisfaction of the overall piecewise-constant specification, with possible interim violations. When the underlying dynamics are monotone, we further provide an efficient, constructive synthesis procedure. We demonstrate the approach on a glucose–insulin regulatory model with explicit pancreatic beta-cell dynamics, showcasing the potential of the proposed approach.
{"title":"Decompositional reach-and-stay contract-based control of nonlinear systems with an application to glucose control","authors":"Alessandro Borri , Ilaria Di Loreto , Maria Domenica Di Benedetto","doi":"10.1016/j.nahs.2025.101627","DOIUrl":"10.1016/j.nahs.2025.101627","url":null,"abstract":"<div><div>In this work, we present a novel contract-theoretic framework for controlling large-scale, interconnected, nonlinear systems by decomposing a global specification into local, time-varying assume–guarantee contracts. First, we decompose the system into local components and the global contract into local contracts; then, our main result gives sufficient conditions under which local <em>causal</em> sampled-data controllers — without foreknowledge of future contract changes — ensures satisfaction of the overall piecewise-constant specification, with possible interim violations. When the underlying dynamics are monotone, we further provide an efficient, constructive synthesis procedure. We demonstrate the approach on a glucose–insulin regulatory model with explicit pancreatic beta-cell dynamics, showcasing the potential of the proposed approach.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"58 ","pages":"Article 101627"},"PeriodicalIF":3.7,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144809676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2025-08-11DOI: 10.1016/j.nahs.2025.101624
Dong Hou, Zijun Cheng, Xin Zhao, Wenxue Li
This paper investigates the problem of exponential synchronization in stochastic multi-links networks with time-varying delays (SMNTDs). By employing graph theory and Lyapunov method, sufficient conditions for achieving th moment exponential synchronization (PMES) and almost surely exponential synchronization (ASES) are simultaneously derived, which are associated with network’s topology, time-varying delays and coupled weights. Moreover, the role of negative feedback control mechanisms is emphasized in maintaining network synchronization. Specifically, any control gain satisfying the sufficient conditions in our theorems guarantees synchronization, and increasing gain generally improves convergence speed and robustness. Numerical simulations based on a Chua’s circuit network illustrate the theoretical results, and further demonstrate how increasing control strength improves convergence speed and synchronization precision.
{"title":"Exponential synchronization for stochastic multi-links networks with time-varying delays","authors":"Dong Hou, Zijun Cheng, Xin Zhao, Wenxue Li","doi":"10.1016/j.nahs.2025.101624","DOIUrl":"10.1016/j.nahs.2025.101624","url":null,"abstract":"<div><div>This paper investigates the problem of exponential synchronization in stochastic multi-links networks with time-varying delays (SMNTDs). By employing graph theory and Lyapunov method, sufficient conditions for achieving <span><math><mi>p</mi></math></span>th moment exponential synchronization (PMES) and almost surely exponential synchronization (ASES) are simultaneously derived, which are associated with network’s topology, time-varying delays and coupled weights. Moreover, the role of negative feedback control mechanisms is emphasized in maintaining network synchronization. Specifically, any control gain satisfying the sufficient conditions in our theorems guarantees synchronization, and increasing gain generally improves convergence speed and robustness. Numerical simulations based on a Chua’s circuit network illustrate the theoretical results, and further demonstrate how increasing control strength improves convergence speed and synchronization precision.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"58 ","pages":"Article 101624"},"PeriodicalIF":3.7,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144809639","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2025-08-05DOI: 10.1016/j.nahs.2025.101626
Hyungbo Shim , Daniel Liberzon
This paper studies exponential stability of linear systems with slow and fast time variation and switching. We use averaging to eliminate the fast dynamics and only retain the slow dynamics. We then use a recent stability criterion for slowly time-varying and switched systems, combined with perturbation analysis, to prove stability of the original system. The analysis involves working with an impulsive system in new coordinates, which enables us to treat a more general class of systems compared to previous work.
{"title":"Stability of linear systems with slow and fast time variation and switching: General case","authors":"Hyungbo Shim , Daniel Liberzon","doi":"10.1016/j.nahs.2025.101626","DOIUrl":"10.1016/j.nahs.2025.101626","url":null,"abstract":"<div><div>This paper studies exponential stability of linear systems with slow and fast time variation and switching. We use averaging to eliminate the fast dynamics and only retain the slow dynamics. We then use a recent stability criterion for slowly time-varying and switched systems, combined with perturbation analysis, to prove stability of the original system. The analysis involves working with an impulsive system in new coordinates, which enables us to treat a more general class of systems compared to previous work.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"58 ","pages":"Article 101626"},"PeriodicalIF":3.7,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144773096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2025-08-05DOI: 10.1016/j.nahs.2025.101625
Pietro Gori, Michele Pierallini, Franco Angelini, Manolo Garabini
Switched systems, characterized by a family of subsystems governed by a switching rule, widely apply to complex real-world scenarios. However, their inherent switching dynamics pose significant challenges in phase analysis and control design. To address these challenges, we propose a framework for solving the Continuous-Time Constrained Linear Quadratic Regulator (CT-CLQR) problem for switched linear systems. Our approach partitions the time horizon into a finite number of intervals, each associated with a specific system mode. The duration of these intervals is parameterized by the switching instants, enabling a reformulation of the problem. We indirectly optimize the switching sequence by fixing the switching sequence and optimizing the interval durations. We derive analytical expressions for the cost function and its gradient, which are critical for efficient optimization. Unlike state-of-the-art methods that impose equality constraints on state evolution, our approach inherently considers the state evolution in the cost function. This not only simplifies the problem formulation but also reduces computational overhead by precomputing shared terms offline, enhancing efficiency during online operations. The proposed method significantly advances existing techniques, offering improved computational efficiency and flexibility. We demonstrate the effectiveness of our approach through comprehensive numerical examples, showcasing its potential for practical applications.
{"title":"Continuous-time constrained linear quadratic regulator for switched linear systems","authors":"Pietro Gori, Michele Pierallini, Franco Angelini, Manolo Garabini","doi":"10.1016/j.nahs.2025.101625","DOIUrl":"10.1016/j.nahs.2025.101625","url":null,"abstract":"<div><div>Switched systems, characterized by a family of subsystems governed by a switching rule, widely apply to complex real-world scenarios. However, their inherent switching dynamics pose significant challenges in phase analysis and control design. To address these challenges, we propose a framework for solving the Continuous-Time Constrained Linear Quadratic Regulator (CT-CLQR) problem for switched linear systems. Our approach partitions the time horizon into a finite number of intervals, each associated with a specific system mode. The duration of these intervals is parameterized by the switching instants, enabling a reformulation of the problem. We indirectly optimize the switching sequence by fixing the switching sequence and optimizing the interval durations. We derive analytical expressions for the cost function and its gradient, which are critical for efficient optimization. Unlike state-of-the-art methods that impose equality constraints on state evolution, our approach inherently considers the state evolution in the cost function. This not only simplifies the problem formulation but also reduces computational overhead by precomputing shared terms offline, enhancing efficiency during online operations. The proposed method significantly advances existing techniques, offering improved computational efficiency and flexibility. We demonstrate the effectiveness of our approach through comprehensive numerical examples, showcasing its potential for practical applications.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"58 ","pages":"Article 101625"},"PeriodicalIF":3.7,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144779860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2025-07-29DOI: 10.1016/j.nahs.2025.101622
O.L.V. Costa , F. Dufour , A. Genadot
The main goal of this paper is to present a non-stationary value iteration scheme for the adaptive average control of Piecewise Deterministic Markov Processes (PDMPs), introduced by M.H.A. Davis in Davis (1984, 1993) as a family of continuous-time Markov processes punctuated by random jumps and with inter-jump movement driven by a deterministic flow. It is assumed in this paper that there are no boundary jumps. We study the adaptive average optimal control problem of PDMPs, considering that the jump intensity , the post-jump transition kernel , as well as the cost depend on an unknown parameter . For a sequence of strongly consistent estimators of (that is, converge to almost surely) a non-stationary value iteration (depending on the current estimate ) is shown to be optimal for the long-run average control problem. We assume a total variation norm condition on the parameters and of the process (which generalizes the minorization condition considered in Costa, Dufour and Genadot (2024), resulting in a span-contraction operator. The paper concludes with a numerical example.
{"title":"Non-stationary value iteration for adaptive average control of piecewise deterministic Markov processes","authors":"O.L.V. Costa , F. Dufour , A. Genadot","doi":"10.1016/j.nahs.2025.101622","DOIUrl":"10.1016/j.nahs.2025.101622","url":null,"abstract":"<div><div>The main goal of this paper is to present a non-stationary value iteration scheme for the adaptive average control of Piecewise Deterministic Markov Processes (PDMPs), introduced by M.H.A. Davis in Davis (1984, 1993) as a family of continuous-time Markov processes punctuated by random jumps and with inter-jump movement driven by a deterministic flow. It is assumed in this paper that there are no boundary jumps. We study the adaptive average optimal control problem of PDMPs, considering that the jump intensity <span><math><mi>λ</mi></math></span>, the post-jump transition kernel <span><math><mi>Q</mi></math></span>, as well as the cost <span><math><mi>C</mi></math></span> depend on an unknown parameter <span><math><msup><mrow><mi>β</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span>. For a sequence of strongly consistent estimators <span><math><mrow><mo>{</mo><msubsup><mrow><mi>β</mi></mrow><mrow><mi>n</mi></mrow><mrow><mo>∗</mo></mrow></msubsup><mo>}</mo></mrow></math></span> of <span><math><msup><mrow><mi>β</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span> (that is, <span><math><msubsup><mrow><mi>β</mi></mrow><mrow><mi>n</mi></mrow><mrow><mo>∗</mo></mrow></msubsup></math></span> converge to <span><math><msup><mrow><mi>β</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span> almost surely) a non-stationary value iteration (depending on the current estimate <span><math><msubsup><mrow><mi>β</mi></mrow><mrow><mi>n</mi></mrow><mrow><mo>∗</mo></mrow></msubsup></math></span>) is shown to be optimal for the long-run average control problem. We assume a total variation norm condition on the parameters <span><math><mi>λ</mi></math></span> and <span><math><mi>Q</mi></math></span> of the process (which generalizes the minorization condition considered in Costa, Dufour and Genadot (2024), resulting in a span-contraction operator. The paper concludes with a numerical example.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"58 ","pages":"Article 101622"},"PeriodicalIF":3.7,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144721952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2025-07-11DOI: 10.1016/j.nahs.2025.101619
Pritesh Patel , Sayan Basu Roy , Shubhendu Bhasin
This paper introduces a switched model reference adaptive control (S-MRAC) architecture for uncertain switched multi-input multi-output (MIMO) linear time-invariant (LTI) systems with a switched reference model. One distinctive aspect of the suggested method is the use of memory to augment the parameter estimator, leading to parameter learning even during inactive periods of the subsystems. Together with an intermittently initial excitation (IIE) condition, the memory augmentation-based approach guarantees exponential stability of the tracking and parameter estimation error systems. An online parameter estimator with a dual-layer low-pass filter and a bank of memory filters is at the heart of the proposed architecture. The addition of the modification term in adaptive law facilitates the computation of a unified expression of dwell time that is valid for both excitation and non-excitation scenarios. Further, the dwell time expression is tunable and thus, allows for fast switching. Simulation results are showcased to confirm the efficacy of the suggested outcome.
{"title":"Globally exponentially stable adaptive control of switched linear systems: A memory augmented approach","authors":"Pritesh Patel , Sayan Basu Roy , Shubhendu Bhasin","doi":"10.1016/j.nahs.2025.101619","DOIUrl":"10.1016/j.nahs.2025.101619","url":null,"abstract":"<div><div>This paper introduces a switched model reference adaptive control (S-MRAC) architecture for uncertain switched multi-input multi-output (MIMO) linear time-invariant (LTI) systems with a switched reference model. One distinctive aspect of the suggested method is the use of memory to augment the parameter estimator, leading to parameter learning even during inactive periods of the subsystems. Together with an intermittently initial excitation (IIE) condition, the memory augmentation-based approach guarantees exponential stability of the tracking and parameter estimation error systems. An online parameter estimator with a dual-layer low-pass filter and a bank of memory filters is at the heart of the proposed architecture. The addition of the <span><math><mrow><mi>σ</mi><mo>−</mo></mrow></math></span> modification term in adaptive law facilitates the computation of a unified expression of dwell time that is valid for both excitation and non-excitation scenarios. Further, the dwell time expression is tunable and thus, allows for fast switching. Simulation results are showcased to confirm the efficacy of the suggested outcome.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"58 ","pages":"Article 101619"},"PeriodicalIF":3.7,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144596371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2025-07-07DOI: 10.1016/j.nahs.2025.101620
Fethi Bencherki , Semiha Türkay , Hüseyin Akçay
In this paper, we present a framework to identify discrete-time, single-input/single-output, switched linear systems (SISO-SLSs) from input–output data measurements. Continuous state is not assumed to be measured. The key step is a deadbeat observer-based transformation of the SLS model to a switched auto-regressive with exogenous input (SARX) model. Discrete states are estimated by a three-stage algorithm from input–output data. First, a sparse optimization problem is solved to detect segments with large dwell times. Then, a clustering algorithm is applied to midpoint estimates in these segments, revealing the system order, the number of discrete states, and the observer discrete states. In the third stage, back-transformation from the observer to a finite set of SLS Markov parameters is carried out and a subspace algorithm extracts discrete states from SLS Markov parameters. A MOESP subspace algorithm is also proposed to estimate discrete states directly from input–output data in segments with large dwell times. Switch and discrete-state identifiability issues are carefully examined and persistence of excitation (PE) conditions on input–output data, switching signal, and system structure are derived to retrieve discrete states. Monte Carlo simulations and case studies are presented to illustrate the derived results.
{"title":"Observer-based switched-linear system identification","authors":"Fethi Bencherki , Semiha Türkay , Hüseyin Akçay","doi":"10.1016/j.nahs.2025.101620","DOIUrl":"10.1016/j.nahs.2025.101620","url":null,"abstract":"<div><div>In this paper, we present a framework to identify discrete-time, single-input/single-output, switched linear systems (SISO-SLSs) from input–output data measurements. Continuous state is not assumed to be measured. The key step is a deadbeat observer-based transformation of the SLS model to a switched auto-regressive with exogenous input (SARX) model. Discrete states are estimated by a three-stage algorithm from input–output data. First, a sparse optimization problem is solved to detect segments with large dwell times. Then, a clustering algorithm is applied to midpoint estimates in these segments, revealing the system order, the number of discrete states, and the observer discrete states. In the third stage, back-transformation from the observer to a finite set of SLS Markov parameters is carried out and a subspace algorithm extracts discrete states from SLS Markov parameters. A MOESP subspace algorithm is also proposed to estimate discrete states directly from input–output data in segments with large dwell times. Switch and discrete-state identifiability issues are carefully examined and persistence of excitation (PE) conditions on input–output data, switching signal, and system structure are derived to retrieve discrete states. Monte Carlo simulations and case studies are presented to illustrate the derived results.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"58 ","pages":"Article 101620"},"PeriodicalIF":3.7,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144571197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2025-07-05DOI: 10.1016/j.nahs.2025.101618
Anita Krawczyk, Andrzej Nowakowski
We study a mathematical model of a tumor described and investigated in Mathur et al. (2024). Hypoxia is often a factor that contributes to tumor resistance against anticancer treatments. However, the use of Hypoxia-Activated Prodrugs (HAPs) turns this challenge into an advantage, offering potential benefits in treatment. By specifically targeting hypoxic tumor regions, HAPs can enhance the efficacy of drug delivery, making hypoxia a beneficial aspect in the therapeutic approach. In Mathur et al. (2024) optimal schedules for different finite number of simulation of treatment combinations is study. Optimization is done by observation of tissue under treatment. We develop approximate sufficient optimality conditions for that mathematical model of cancer with controls on the boundary. It is a starting point to present numerical algorithm with verification theorem of approximate solution. Numerical calculations are performed to optimize the density of the active drug within the tissue. The results show that the maximum density of active drugs can be achieved by increasing the injection of the drug and reducing oxygen levels, with optimal control parameters set. We refer our result to the simulations done by other authors with direct treatments.
我们研究了Mathur等人（2024）描述和研究的肿瘤的数学模型。缺氧通常是肿瘤抵抗抗癌治疗的一个因素。然而，缺氧激活前药（HAPs）的使用将这一挑战转化为优势，在治疗中提供了潜在的益处。通过特异性靶向低氧肿瘤区域，HAPs可以提高药物递送效率，使低氧成为治疗方法中的一个有益方面。Mathur et al.（2024）对不同有限次处理组合模拟的最优调度进行了研究。优化是通过观察治疗组织来完成的。我们为边界上有控制的癌症数学模型建立了近似的充分最优性条件。以近似解的验证定理为出发点，提出数值算法。进行数值计算以优化组织内活性药物的密度。结果表明，在设定最佳控制参数的情况下，通过增加药物的注射量和降低氧浓度可以达到活性药物的最大浓度。我们参考了其他作者直接处理的模拟结果。
{"title":"Optimization of HAP administration in cancer therapy","authors":"Anita Krawczyk, Andrzej Nowakowski","doi":"10.1016/j.nahs.2025.101618","DOIUrl":"10.1016/j.nahs.2025.101618","url":null,"abstract":"<div><div>We study a mathematical model of a tumor described and investigated in Mathur et al. (2024). Hypoxia is often a factor that contributes to tumor resistance against anticancer treatments. However, the use of Hypoxia-Activated Prodrugs (HAPs) turns this challenge into an advantage, offering potential benefits in treatment. By specifically targeting hypoxic tumor regions, HAPs can enhance the efficacy of drug delivery, making hypoxia a beneficial aspect in the therapeutic approach. In Mathur et al. (2024) optimal schedules for different finite number of simulation of treatment combinations is study. Optimization is done by observation of tissue under treatment. We develop approximate sufficient optimality conditions for that mathematical model of cancer with controls on the boundary. It is a starting point to present numerical algorithm with verification theorem of approximate solution. Numerical calculations are performed to optimize the density of the active drug within the tissue. The results show that the maximum density of active drugs can be achieved by increasing the injection of the drug and reducing oxygen levels, with optimal control parameters set. We refer our result to the simulations done by other authors with direct treatments.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"58 ","pages":"Article 101618"},"PeriodicalIF":3.7,"publicationDate":"2025-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144563747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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