Pub Date : 2025-09-11DOI: 10.1016/j.nahs.2025.101634
Mingyu Wang , Xiaofeng Zong , Xin Chen
This paper investigates the finite-time stability of a jump diffusion system with Brownian motion and random jump components. First, we establish a novel Lyapunov-type finite-time stability theorem, which provides a direct way for selecting an appropriate Lyapunov function. It is important to note that our finite-time stability result is significantly distinct from the case involving only Brownian motion. The presence of the jump term disrupts the continuity of the system’s solution paths, thereby introducing additional complexities in the analysis of finite-time stability. Subsequently, we employ this theorem to design a finite-time controller to ensure the finite-time stochastic stability of the tracking error in a drill-bit system. The proposed control strategy guarantees that the tracking error converges to the origin within finite time and remains there thereafter with probability one. Finally, simulation results are presented to validate the effectiveness of the proposed control law in achieving precise drill-bit tracking control.
{"title":"Finite-time stability of jump diffusion system and its application in drill-bit tracking control","authors":"Mingyu Wang , Xiaofeng Zong , Xin Chen","doi":"10.1016/j.nahs.2025.101634","DOIUrl":"10.1016/j.nahs.2025.101634","url":null,"abstract":"<div><div>This paper investigates the finite-time stability of a jump diffusion system with Brownian motion and random jump components. First, we establish a novel Lyapunov-type finite-time stability theorem, which provides a direct way for selecting an appropriate Lyapunov function. It is important to note that our finite-time stability result is significantly distinct from the case involving only Brownian motion. The presence of the jump term disrupts the continuity of the system’s solution paths, thereby introducing additional complexities in the analysis of finite-time stability. Subsequently, we employ this theorem to design a finite-time controller to ensure the finite-time stochastic stability of the tracking error in a drill-bit system. The proposed control strategy guarantees that the tracking error converges to the origin within finite time and remains there thereafter with probability one. Finally, simulation results are presented to validate the effectiveness of the proposed control law in achieving precise drill-bit tracking control.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"59 ","pages":"Article 101634"},"PeriodicalIF":3.7,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046680","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 : 2025-09-10DOI: 10.1016/j.nahs.2025.101633
Shaowen Miao , Aiwen Lai , Jan Komenda , Sébastien Lahaye
In this paper, we address the problem of initial-state detectability (I-detectability) for timed discrete-event systems modeled by time-interval automata (TIAs). An I-observer, defined over a timed event set, is developed to check both strong and weak I-detectability. Additionally, an I-detector structure is designed as an alternative method for verifying strong I-detectability, which is more efficient than the I-observer in certain cases. In addition, we are the first to formally define the concepts of strong and weak timed initial-state detectability (-I-detectability) within the framework of timed discrete-event systems. Specifically, I-detectability necessitates that the initial state of a system can be detected after a finite number of observations. From another perspective, -I-detectability entails that the initial state can be ascertained after a delay of time units. Under the assumption that every cycle in the TIA has strictly positive weight, we establish that a TIA is -I-detectable if and only if it satisfies the condition of being I-detectable. Finally, we introduce an algebraic method to compute the upper bound of time that needs to elapse before the initial state can be determined in an I-detectable TIA.
本文研究了由时间间隔自动机（TIAs）建模的时间离散事件系统的初始状态可检测性问题。在一个定时事件集上定义了一个i -观测器，用于检查强和弱i -可探测性。此外，设计了一个i检测器结构作为验证强i可探测性的替代方法，在某些情况下，它比i观察者更有效。此外，我们首次在时间离散事件系统的框架内正式定义了强和弱时间初始状态可探测性（t - i -可探测性）的概念。具体来说，i -可探测性要求系统的初始状态可以在有限次观测后被探测到。从另一个角度来看，T- i可探测性意味着在延迟T个时间单位后可以确定初始状态。在假定TIA中的每个周期都有严格正权的前提下，我们建立了TIA是t - i可检测的当且仅当它满足i可检测的条件。最后，我们引入了一种代数方法来计算在i可检测的TIA中确定初始状态所需时间的上界。
{"title":"Timed initial-state detectability of discrete-event systems by algebraic method","authors":"Shaowen Miao , Aiwen Lai , Jan Komenda , Sébastien Lahaye","doi":"10.1016/j.nahs.2025.101633","DOIUrl":"10.1016/j.nahs.2025.101633","url":null,"abstract":"<div><div>In this paper, we address the problem of initial-state detectability (I-detectability) for timed discrete-event systems modeled by time-interval automata (TIAs). An I-observer, defined over a timed event set, is developed to check both strong and weak I-detectability. Additionally, an I-detector structure is designed as an alternative method for verifying strong I-detectability, which is more efficient than the I-observer in certain cases. In addition, we are the first to formally define the concepts of strong and weak timed initial-state detectability (<span><math><mi>T</mi></math></span>-I-detectability) within the framework of timed discrete-event systems. Specifically, I-detectability necessitates that the initial state of a system can be detected after a finite number of observations. From another perspective, <span><math><mi>T</mi></math></span>-I-detectability entails that the initial state can be ascertained after a delay of <span><math><mi>T</mi></math></span> time units. Under the assumption that every cycle in the TIA has strictly positive weight, we establish that a TIA is <span><math><mi>T</mi></math></span>-I-detectable if and only if it satisfies the condition of being I-detectable. Finally, we introduce an algebraic method to compute the upper bound of time that needs to elapse before the initial state can be determined in an I-detectable TIA.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"59 ","pages":"Article 101633"},"PeriodicalIF":3.7,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145027221","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 : 2025-09-09DOI: 10.1016/j.nahs.2025.101630
Vishnu Murali, Ashutosh Trivedi, Majid Zamani
A barrier certificate, defined over the states of a dynamical system, is a real-valued function whose zero level set characterizes an inductively verifiable state invariant separating reachable states from unsafe ones. When combined with powerful decision procedures — such as sum-of-squares programming (SOS) or satisfiability-modulo-theory solvers (SMT) — barrier certificates enable an automated deductive verification approach to safety. The barrier certificate approach has been extended to refute LTL and -regular specifications by separating consecutive transitions of corresponding -automata in the hope of denying all accepting runs. Unsurprisingly, such tactics are bound to be conservative as refutation of recurrence properties requires reasoning about ranking functions to prove liveness as well. This paper introduces the notion of closure certificates as a natural extension of barrier certificates from state invariants to transition invariants. We show how one may use ranking function arguments over such certificates to verify discrete-time dynamical systems against Linear Temporal logic formulae. We augment these definitions with SOS and SMT based characterization for automating the search of closure certificates and demonstrate their effectiveness over some case studies.
{"title":"Closure certificates","authors":"Vishnu Murali, Ashutosh Trivedi, Majid Zamani","doi":"10.1016/j.nahs.2025.101630","DOIUrl":"10.1016/j.nahs.2025.101630","url":null,"abstract":"<div><div>A <em>barrier certificate</em>, defined over the states of a dynamical system, is a real-valued function whose zero level set characterizes an inductively verifiable <em>state invariant</em> separating reachable states from unsafe ones. When combined with powerful decision procedures — such as sum-of-squares programming (SOS) or satisfiability-modulo-theory solvers (SMT) — barrier certificates enable an automated deductive verification approach to safety. The barrier certificate approach has been extended to refute LTL and <span><math><mi>ω</mi></math></span>-regular specifications by separating consecutive transitions of corresponding <span><math><mi>ω</mi></math></span>-automata in the hope of denying all accepting runs. Unsurprisingly, such tactics are bound to be conservative as refutation of <em>recurrence properties</em> requires reasoning about ranking functions to prove liveness as well. This paper introduces the notion of <em>closure certificates</em> as a natural extension of barrier certificates from state invariants to transition invariants. We show how one may use ranking function arguments over such certificates to verify discrete-time dynamical systems against Linear Temporal logic formulae. We augment these definitions with SOS and SMT based characterization for automating the search of closure certificates and demonstrate their effectiveness over some case studies.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"59 ","pages":"Article 101630"},"PeriodicalIF":3.7,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020290","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 : 2025-09-04DOI: 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}
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