Pub Date : 2024-11-15DOI: 10.1016/j.nahs.2024.101555
João Pedro Silvestre , Pedro Casau , Paulo Oliveira
In this paper, a quaternion-based attitude tracking controller is presented, which is robust to measurement noise and adaptable to modeling errors and external disturbances. By constructing the controller using the theory of hybrid systems and employing the backstepping technique an adaptive controller that globally asymptotically stabilizes the null tracking error set for the closed-loop system is obtained. Furthermore, two estimators are explicitly derived to account for slowly time-varying or constant disturbances and moment of inertia errors. All the stability and convergence properties are carefully proven using Lyapunov stability theory for hybrid systems. Simulation results are shown to assess the resulting closed-loop system performance.
{"title":"Adaptive hybrid global attitude tracking controller","authors":"João Pedro Silvestre , Pedro Casau , Paulo Oliveira","doi":"10.1016/j.nahs.2024.101555","DOIUrl":"10.1016/j.nahs.2024.101555","url":null,"abstract":"<div><div>In this paper, a quaternion-based attitude tracking controller is presented, which is robust to measurement noise and adaptable to modeling errors and external disturbances. By constructing the controller using the theory of hybrid systems and employing the backstepping technique an adaptive controller that globally asymptotically stabilizes the null tracking error set for the closed-loop system is obtained. Furthermore, two estimators are explicitly derived to account for slowly time-varying or constant disturbances and moment of inertia errors. All the stability and convergence properties are carefully proven using Lyapunov stability theory for hybrid systems. Simulation results are shown to assess the resulting closed-loop system performance.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"55 ","pages":"Article 101555"},"PeriodicalIF":3.7,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142657487","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 : 2024-11-14DOI: 10.1016/j.nahs.2024.101554
Ibon Gracia , Dimitris Boskos , Morteza Lahijanian , Luca Laurenti , Manuel Mazo Jr.
We introduce a framework for the control of discrete-time switched stochastic systems with uncertain distributions. In particular, we consider stochastic dynamics with additive noise whose distribution lies in an ambiguity set of distributions that are close, in the Wasserstein distance sense, to a nominal one. We propose algorithms for the efficient synthesis of distributionally robust control strategies that maximize the satisfaction probability of reach-avoid specifications with either a given or an arbitrary (not specified) time horizon, i.e., unbounded-time reachability. The framework consists of two main steps: finite abstraction and control synthesis. First, we construct a finite abstraction of the switched stochastic system as a robust Markov decision process (robust MDP) that encompasses both the stochasticity of the system and the uncertainty in the noise distribution. Then, we synthesize a strategy that is robust to the distributional uncertainty on the resulting robust MDP. We employ techniques from optimal transport and stochastic programming to reduce the strategy synthesis problem to a set of linear programs, and propose a tailored and efficient algorithm to solve them. The resulting strategies are correctly refined into switching strategies for the original stochastic system. We illustrate the efficacy of our framework on various case studies comprising both linear and non-linear switched stochastic systems.
{"title":"Efficient strategy synthesis for switched stochastic systems with distributional uncertainty","authors":"Ibon Gracia , Dimitris Boskos , Morteza Lahijanian , Luca Laurenti , Manuel Mazo Jr.","doi":"10.1016/j.nahs.2024.101554","DOIUrl":"10.1016/j.nahs.2024.101554","url":null,"abstract":"<div><div>We introduce a framework for the control of discrete-time switched stochastic systems with uncertain distributions. In particular, we consider stochastic dynamics with additive noise whose distribution lies in an ambiguity set of distributions that are <span><math><mrow><mi>ɛ</mi><mo>−</mo></mrow></math></span>close, in the Wasserstein distance sense, to a nominal one. We propose algorithms for the efficient synthesis of distributionally robust control strategies that maximize the satisfaction probability of reach-avoid specifications with either a given or an arbitrary (not specified) time horizon, i.e., unbounded-time reachability. The framework consists of two main steps: finite abstraction and control synthesis. First, we construct a finite abstraction of the switched stochastic system as a <em>robust Markov decision process</em> (robust MDP) that encompasses both the stochasticity of the system and the uncertainty in the noise distribution. Then, we synthesize a strategy that is robust to the distributional uncertainty on the resulting robust MDP. We employ techniques from optimal transport and stochastic programming to reduce the strategy synthesis problem to a set of linear programs, and propose a tailored and efficient algorithm to solve them. The resulting strategies are correctly refined into switching strategies for the original stochastic system. We illustrate the efficacy of our framework on various case studies comprising both linear and non-linear switched stochastic systems.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"55 ","pages":"Article 101554"},"PeriodicalIF":3.7,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142657488","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 : 2024-11-12DOI: 10.1016/j.nahs.2024.101553
Yilun Wu, Anna Tur, Peichen Ye
Switching phenomena are ubiquitous in real-world applications. An -player hybrid pollution-control problem is considered with switching behavior and uncertain game duration. The payoff functional with a random duration is converted to a payoff functional in the infinite horizon, which is discounted by a heterogeneous discounting function. By applying Pontryagin’s maximum principle and analyzing the structure of the adjoint variable, the sustainable equilibria in cooperative and noncooperative games are uniquely determined. The convergence of the corresponding state variable in cooperative and noncooperative games is proved. Furthermore, a unique state trajectory represented by a hybrid limit cycle is found to compute the players’ payoffs in cooperative and noncooperative scenarios. Finally, a reasonable, cooperative solution that employs the Shapley value as a single-point solution is proposed. All results are derived analytically and demonstrated with a numerical example.
切换现象在实际应用中无处不在。本文考虑了一个 n 人混合污染控制问题，该问题具有切换行为和不确定的博弈持续时间。随机持续时间的报酬函数被转换为无限视界的报酬函数，并通过异质贴现函数进行贴现。通过应用庞特里亚金最大原则和分析邻接变量的结构，唯一确定了合作博弈和非合作博弈中的可持续均衡。证明了合作博弈和非合作博弈中相应状态变量的收敛性。此外，还找到了一个由混合极限循环代表的唯一状态轨迹，用于计算合作和非合作情况下博弈者的报酬。最后，还提出了一种合理的合作解，它采用夏普利值作为单点解。所有结果都是通过分析得出的，并通过一个数值示例进行了演示。
{"title":"Sustainable solution for hybrid differential game with regime shifts and random duration","authors":"Yilun Wu, Anna Tur, Peichen Ye","doi":"10.1016/j.nahs.2024.101553","DOIUrl":"10.1016/j.nahs.2024.101553","url":null,"abstract":"<div><div>Switching phenomena are ubiquitous in real-world applications. An <span><math><mi>n</mi></math></span>-player hybrid pollution-control problem is considered with switching behavior and uncertain game duration. The payoff functional with a random duration is converted to a payoff functional in the infinite horizon, which is discounted by a heterogeneous discounting function. By applying Pontryagin’s maximum principle and analyzing the structure of the adjoint variable, the sustainable equilibria in cooperative and noncooperative games are uniquely determined. The convergence of the corresponding state variable in cooperative and noncooperative games is proved. Furthermore, a unique state trajectory represented by a hybrid limit cycle is found to compute the players’ payoffs in cooperative and noncooperative scenarios. Finally, a reasonable, cooperative solution that employs the Shapley value as a single-point solution is proposed. All results are derived analytically and demonstrated with a numerical example.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"55 ","pages":"Article 101553"},"PeriodicalIF":3.7,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142657595","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 : 2024-11-09DOI: 10.1016/j.nahs.2024.101552
Yong Wang , Bowen Li , Qinyao Pan , Jie Zhong , Ning Li
This paper addresses the delay output synchronization in a coupled system of a Boolean network and a probabilistic Boolean network with state delays. We model the system as a Markov chain-based augmented system, simplifying the synchronization problem to a delay set stability issue. Analysis of the Markov chain’s transition matrix through positive recurrent closed sets yields synchronization criteria, both in probability and in probability one, based on Boolean matrix characteristics and matrix splitting techniques. These methods avoid the cumulative multiplication of high-dimensional matrices and reduce the complexity of the computation. Besides, the study progresses to explore asymptotic output synchronization, employing these methods. To demonstrate the practicality and effectiveness of the proposed methodology, several illustrative examples are provided.
{"title":"Asymptotic synchronization in coupled Boolean and probabilistic Boolean networks with delays","authors":"Yong Wang , Bowen Li , Qinyao Pan , Jie Zhong , Ning Li","doi":"10.1016/j.nahs.2024.101552","DOIUrl":"10.1016/j.nahs.2024.101552","url":null,"abstract":"<div><div>This paper addresses the delay output synchronization in a coupled system of a Boolean network and a probabilistic Boolean network with state delays. We model the system as a Markov chain-based augmented system, simplifying the synchronization problem to a delay set stability issue. Analysis of the Markov chain’s transition matrix through positive recurrent closed sets yields synchronization criteria, both in probability and in probability one, based on Boolean matrix characteristics and matrix splitting techniques. These methods avoid the cumulative multiplication of high-dimensional matrices and reduce the complexity of the computation. Besides, the study progresses to explore asymptotic output synchronization, employing these methods. To demonstrate the practicality and effectiveness of the proposed methodology, several illustrative examples are provided.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"55 ","pages":"Article 101552"},"PeriodicalIF":3.7,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142657486","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 : 2024-11-01DOI: 10.1016/j.nahs.2024.101550
Hui Zhou , Jingheng Feng , Ju H. Park , Wenxue Li
The article researches the synchronization issue of delayed multilink complex dynamical networks with Lévy noise (DMCNL) via asynchronously intermittent sampled-data decentralized control (AISDC). Asynchronous intermittent decentralized control, compared to synchronous intermittent control, is a policy that enables individual node-system to operate with distinct work and rest periods, thereby offering a higher degree of adaptability. Considering that continuous sampling in the control segment may result in resource wastage, a novel policy called AISDC is proposed by integrating the policy above and intermittent sampled-data control. Then, an auxiliary timer is designed for every node-system to make a compromise between regulating work intervals and controlling the rest interval. Moreover, graph theory and the Lyapunov method are combined to establish several synchronization criteria. Finally, numerical examples on a second-order Kuramoto model verify the feasibility of the proposed results.
{"title":"Asynchronous intermittent sampled-data control for delayed complex dynamical networks with Lévy noise","authors":"Hui Zhou , Jingheng Feng , Ju H. Park , Wenxue Li","doi":"10.1016/j.nahs.2024.101550","DOIUrl":"10.1016/j.nahs.2024.101550","url":null,"abstract":"<div><div>The article researches the synchronization issue of delayed multilink complex dynamical networks with Lévy noise (DMCNL) via asynchronously intermittent sampled-data decentralized control (AISDC). Asynchronous intermittent decentralized control, compared to synchronous intermittent control, is a policy that enables individual node-system to operate with distinct work and rest periods, thereby offering a higher degree of adaptability. Considering that continuous sampling in the control segment may result in resource wastage, a novel policy called AISDC is proposed by integrating the policy above and intermittent sampled-data control. Then, an auxiliary timer is designed for every node-system to make a compromise between regulating work intervals and controlling the rest interval. Moreover, graph theory and the Lyapunov method are combined to establish several synchronization criteria. Finally, numerical examples on a second-order Kuramoto model verify the feasibility of the proposed results.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"55 ","pages":"Article 101550"},"PeriodicalIF":3.7,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572380","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 : 2024-10-31DOI: 10.1016/j.nahs.2024.101551
Yacine Chitour , Hussein Obeid , Salah Laghrouche , Leonid Fridman
In this paper, two classes of continuous higher order adaptive sliding mode controllers based on barrier functions are developed for a perturbed chain of integrators with perturbations bounded by unknown functions. Both classes provide finite-time convergence of the state of the system to a predefined domain using a continuous control signal. The first class of adaptive controllers require few assumptions about the perturbation. However, it can provide unbounded control gains in general. To ensure bounded control gains in the case of a Lipschitz perturbation, a second class of adaptive controllers, called the adaptive higher order Super-Twisting (HOST) algorithm, is developed. The effectiveness of the proposed adaptive controllers is specifically assessed for a cart-pendulum system. Simulation results illustrate high performance in achieving stabilization, even in cases where the disturbance upper bound and its derivative are unknown.
{"title":"Barrier function-based adaptive continuous higher-order sliding mode controllers","authors":"Yacine Chitour , Hussein Obeid , Salah Laghrouche , Leonid Fridman","doi":"10.1016/j.nahs.2024.101551","DOIUrl":"10.1016/j.nahs.2024.101551","url":null,"abstract":"<div><div>In this paper, two classes of continuous higher order adaptive sliding mode controllers based on barrier functions are developed for a perturbed chain of integrators with perturbations bounded by unknown functions. Both classes provide finite-time convergence of the state of the system to a predefined domain using a continuous control signal. The first class of adaptive controllers require few assumptions about the perturbation. However, it can provide unbounded control gains in general. To ensure bounded control gains in the case of a Lipschitz perturbation, a second class of adaptive controllers, called the adaptive higher order Super-Twisting (HOST) algorithm, is developed. The effectiveness of the proposed adaptive controllers is specifically assessed for a cart-pendulum system. Simulation results illustrate high performance in achieving stabilization, even in cases where the disturbance upper bound and its derivative are unknown.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"55 ","pages":"Article 101551"},"PeriodicalIF":3.7,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142560722","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 : 2024-10-23DOI: 10.1016/j.nahs.2024.101549
Do Duc Thuan
In this paper, the problem of positivity and stability for linear time-invariant implicit dynamic equations is generally studied. We provide necessary and sufficient conditions for positivity of these equations. This characterization can be considered as a unification and generalization for some previous results. On the other hand, we study the exponential stability of positive implicit dynamic equations. Previously, this issue was not completely addressed. By using Krein–Rutman theorem, we show that a positive implicit dynamic equation on a time scale is uniformly exponentially stable if and only if the characteristic polynomial of the matrix pair defining the equation has all its coefficients of the same sign.
{"title":"Exponential stability of positive implicit dynamic equations with constant coefficients","authors":"Do Duc Thuan","doi":"10.1016/j.nahs.2024.101549","DOIUrl":"10.1016/j.nahs.2024.101549","url":null,"abstract":"<div><div>In this paper, the problem of positivity and stability for linear time-invariant implicit dynamic equations is generally studied. We provide necessary and sufficient conditions for positivity of these equations. This characterization can be considered as a unification and generalization for some previous results. On the other hand, we study the exponential stability of positive implicit dynamic equations. Previously, this issue was not completely addressed. By using Krein–Rutman theorem, we show that a positive implicit dynamic equation on a time scale is uniformly exponentially stable if and only if the characteristic polynomial of the matrix pair defining the equation has all its coefficients of the same sign.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"55 ","pages":"Article 101549"},"PeriodicalIF":3.7,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530119","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 : 2024-10-21DOI: 10.1016/j.nahs.2024.101548
Shaohua Long , Mei Huang , Shouming Zhong
In this paper, we focus on the finite-time stability problem of singular Markovian jump systems with time-varying delay. Firstly, this paper presents some new inequalities which are very important to the finite-time stability problem of the considered systems. Secondly, by employing these new inequalities and the Lyapunov–Krasovskii functional approach, this paper derives some sufficient conditions that guarantee the considered systems to be regular, impulse-free and finite-time stable. Finally, three numerical examples are given to illustrate the effectiveness and advantage of the proposed methods.
{"title":"New results on finite-time stability of singular Markovian jump systems with time-varying delay","authors":"Shaohua Long , Mei Huang , Shouming Zhong","doi":"10.1016/j.nahs.2024.101548","DOIUrl":"10.1016/j.nahs.2024.101548","url":null,"abstract":"<div><div>In this paper, we focus on the finite-time stability problem of singular Markovian jump systems with time-varying delay. Firstly, this paper presents some new inequalities which are very important to the finite-time stability problem of the considered systems. Secondly, by employing these new inequalities and the Lyapunov–Krasovskii functional approach, this paper derives some sufficient conditions that guarantee the considered systems to be regular, impulse-free and finite-time stable. Finally, three numerical examples are given to illustrate the effectiveness and advantage of the proposed methods.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"55 ","pages":"Article 101548"},"PeriodicalIF":3.7,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530118","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 : 2024-09-25DOI: 10.1016/j.nahs.2024.101547
Haifeng Wu , Shuai Liu , Licheng Wang
In this paper, the cluster synchronization pinning control problem is investigated for the continuous-time-directed complex dynamic networks under the bit rate constraint. Firstly, a node selection scheme based on differences in node degrees is proposed to achieve cluster synchronization. Subsequently, a coding–decoding scheme is designed during data transmission through digital communication channels where only a limited number of encoded signal sequences are sent to the controller side. Further, regarding the unreliability of the channel, the phenomenon of packet dropouts is considered during the encoding process, which is modeled by using a series of independent Bernoulli distributed random variables. The pinning controller is then designed based on the received decoding information. By means of the convex optimization method, a sufficient condition is established to ensure that the cluster synchronization error is ultimately bounded and the desired controller gain is determined based on the solution to matrix inequalities. Finally, the effectiveness of the obtained results is validated through a simulation example.
{"title":"Cluster synchronization of complex dynamic networks under pinning control via a limited capacity communication channel","authors":"Haifeng Wu , Shuai Liu , Licheng Wang","doi":"10.1016/j.nahs.2024.101547","DOIUrl":"10.1016/j.nahs.2024.101547","url":null,"abstract":"<div><div>In this paper, the cluster synchronization pinning control problem is investigated for the continuous-time-directed complex dynamic networks under the bit rate constraint. Firstly, a node selection scheme based on differences in node degrees is proposed to achieve cluster synchronization. Subsequently, a coding–decoding scheme is designed during data transmission through digital communication channels where only a limited number of encoded signal sequences are sent to the controller side. Further, regarding the unreliability of the channel, the phenomenon of packet dropouts is considered during the encoding process, which is modeled by using a series of independent Bernoulli distributed random variables. The pinning controller is then designed based on the received decoding information. By means of the convex optimization method, a sufficient condition is established to ensure that the cluster synchronization error is ultimately bounded and the desired controller gain is determined based on the solution to matrix inequalities. Finally, the effectiveness of the obtained results is validated through a simulation example.</div></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"55 ","pages":"Article 101547"},"PeriodicalIF":3.7,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142319164","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 : 2024-09-13DOI: 10.1016/j.nahs.2024.101546
T. Sântejudean , Ş. Ungur , R. Herzal , I.-C. Morărescu , V.S. Varma , L. Buşoniu
Consider a mobile robot that must navigate as quickly as possible to the global maxima of a function (e.g. density of seabed litter, pollutant concentration, wireless signal strength) defined over its operating area. This objective function is initially unknown and is assumed to be Lipschitz continuous. The limited velocity of the robot restricts the next samples to neighboring positions, and to avoid wasting time and energy, the robot’s path must be adapted as new information becomes available. The paper proposes two methods that use an upper bound on the objective to iteratively change the position targeted by the robot as new samples are acquired. The first method is FTW, which Turns When the best value seen so far of the objective Function is larger than the bound of the current target position. The second is FTWD, an extension of FTW that takes into account the Distance to the target. Convergence guarantees are provided for both methods, and a convergence rate is proven to characterize how fast the FTW suboptimality decreases as the number of samples grows. In a numerical study, FTWD greatly improves performance compared to FTW, outperforms two representative source-seeking baselines, and obtains results similar to a much more computationally intensive method that does not guarantee convergence. The relationship between FTW and FTWD is also confirmed in real-robot experiments, where a TurtleBot3 seeks the darkest point on a 2D grayscale map.
{"title":"Globally convergent path-aware optimization with mobile robots","authors":"T. Sântejudean , Ş. Ungur , R. Herzal , I.-C. Morărescu , V.S. Varma , L. Buşoniu","doi":"10.1016/j.nahs.2024.101546","DOIUrl":"10.1016/j.nahs.2024.101546","url":null,"abstract":"<div><p>Consider a mobile robot that must navigate as quickly as possible to the global maxima of a function (e.g. density of seabed litter, pollutant concentration, wireless signal strength) defined over its operating area. This objective function is initially unknown and is assumed to be Lipschitz continuous. The limited velocity of the robot restricts the next samples to neighboring positions, and to avoid wasting time and energy, the robot’s path must be adapted as new information becomes available. The paper proposes two methods that use an upper bound on the objective to iteratively change the position targeted by the robot as new samples are acquired. The first method is FTW, which Turns When the best value seen so far of the objective Function is larger than the bound of the current target position. The second is FTWD, an extension of FTW that takes into account the Distance to the target. Convergence guarantees are provided for both methods, and a convergence rate is proven to characterize how fast the FTW suboptimality decreases as the number of samples grows. In a numerical study, FTWD greatly improves performance compared to FTW, outperforms two representative source-seeking baselines, and obtains results similar to a much more computationally intensive method that does not guarantee convergence. The relationship between FTW and FTWD is also confirmed in real-robot experiments, where a TurtleBot3 seeks the darkest point on a 2D grayscale map.</p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":"55 ","pages":"Article 101546"},"PeriodicalIF":3.7,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1751570X24000839/pdfft?md5=fa25eec126f2b4af5ecf2f2391974551&pid=1-s2.0-S1751570X24000839-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142229352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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