In this paper, the consensus control problem of leader‐following linear multi‐agent systems with the input delay is investigated. We first present a necessary and sufficient condition for the leader‐following consensus of linear multi‐agent systems with the input delay. Then by means of the state transition matrix of linear delay systems, the leader‐following consensus problem is transformed into a distributed nonconvex optimization problem. Furthermore, a numerical method based on the successive convex approximation (SCA) technique is proposed to solve the distributed nonconvex optimization problem. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.
{"title":"A numerical method for consensus control of leader‐following multi‐agent systems with the input delay","authors":"Kunlong Bao, Yuhao Cong, Renhong Hu","doi":"10.1002/oca.3163","DOIUrl":"https://doi.org/10.1002/oca.3163","url":null,"abstract":"In this paper, the consensus control problem of leader‐following linear multi‐agent systems with the input delay is investigated. We first present a necessary and sufficient condition for the leader‐following consensus of linear multi‐agent systems with the input delay. Then by means of the state transition matrix of linear delay systems, the leader‐following consensus problem is transformed into a distributed nonconvex optimization problem. Furthermore, a numerical method based on the successive convex approximation (SCA) technique is proposed to solve the distributed nonconvex optimization problem. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.","PeriodicalId":501055,"journal":{"name":"Optimal Control Applications and Methods","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study proposes an improved model predictive static programming (MPSP) based path‐following control method for unmanned surface vessel (USV) subject to input disturbances. The method addresses the challenges of accurate USV dynamics modeling, unpredictable maritime environments, and limited power and energy systems. A trajectory generator is designed to construct smooth reference trajectories, and the MPSP algorithm is adapted to handle path‐following problems while considering state and input constraints. An event‐triggered mechanism is introduced to reduce computational burden and conserve energy. Comparative simulations demonstrate the superiority of the proposed method over open‐loop tracking and the original MPSP approach in terms of tracking accuracy, disturbance rejection, and overall control performance. The improved MPSP‐based control method offers a robust and efficient solution for USV path‐following tasks, ensuring accurate tracking even in the presence of environmental disturbances and system uncertainties.
{"title":"An improved MPSP‐based path‐following control method for USV with input disturbances","authors":"Ao Li, Xiaoxiang Hu, Kejun Dong, Bing Xiao","doi":"10.1002/oca.3166","DOIUrl":"https://doi.org/10.1002/oca.3166","url":null,"abstract":"This study proposes an improved model predictive static programming (MPSP) based path‐following control method for unmanned surface vessel (USV) subject to input disturbances. The method addresses the challenges of accurate USV dynamics modeling, unpredictable maritime environments, and limited power and energy systems. A trajectory generator is designed to construct smooth reference trajectories, and the MPSP algorithm is adapted to handle path‐following problems while considering state and input constraints. An event‐triggered mechanism is introduced to reduce computational burden and conserve energy. Comparative simulations demonstrate the superiority of the proposed method over open‐loop tracking and the original MPSP approach in terms of tracking accuracy, disturbance rejection, and overall control performance. The improved MPSP‐based control method offers a robust and efficient solution for USV path‐following tasks, ensuring accurate tracking even in the presence of environmental disturbances and system uncertainties.","PeriodicalId":501055,"journal":{"name":"Optimal Control Applications and Methods","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141500875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article investigates the problems of coupled orbit and attitude dynamics modeling and control for an on‐orbit serving spacecraft that is going to dock with a target spacecraft. First, a coupled relative orbit and attitude dynamics model of the servicing spacecraft with respect to the target spacecraft is constructed, considering external disturbances and actuators faults. To deal with such effects, two iterative learning observers are then designed respectively for orbit dynamics and attitude dynamics, which are capable of estimating interferences and faults. Combining the estimation information, the final control law is proposed based on the back stepping method. Through the Lyapunov approach, the stability of the closed‐loop control system is analyzed. Finally, a numerical simulation is carried out to bear out the effectiveness of the proposed control scheme.
{"title":"Iterative learning observer‐based fault‐tolerant control for on‐orbit serving spacecraft with coupled orbit and attitude dynamics","authors":"Shiyi Li, Kerun Liu, Ming Liu","doi":"10.1002/oca.3165","DOIUrl":"https://doi.org/10.1002/oca.3165","url":null,"abstract":"This article investigates the problems of coupled orbit and attitude dynamics modeling and control for an on‐orbit serving spacecraft that is going to dock with a target spacecraft. First, a coupled relative orbit and attitude dynamics model of the servicing spacecraft with respect to the target spacecraft is constructed, considering external disturbances and actuators faults. To deal with such effects, two iterative learning observers are then designed respectively for orbit dynamics and attitude dynamics, which are capable of estimating interferences and faults. Combining the estimation information, the final control law is proposed based on the back stepping method. Through the Lyapunov approach, the stability of the closed‐loop control system is analyzed. Finally, a numerical simulation is carried out to bear out the effectiveness of the proposed control scheme.","PeriodicalId":501055,"journal":{"name":"Optimal Control Applications and Methods","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141500876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Bridge cranes are complex nonlinear dynamic systems with underactuated characteristics, making it challenging for controllers to man age the spatial swing of the load effectively. Additionally, uncertainties both within and outside the system adversely impact control performance. To address these issues, a Type‐II fuzzy sliding mode controller has proven effective in enhancing the anti‐swing control performance of the payload. However, due to the intricate parameter adjustment optimization problem and potential challenges in dealing with nonlinearity and uncertainty, especially in complex dynamic systems, this paper proposes a grey wolf algorithm based on a dynamic spiral hunting mechanism. This enhancement endows the algorithm with improved convergence speed and higher robustness, enabling more effective parameter tuning for the second‐order fractional‐order sliding mode controller (FSMC). The proposed algorithm demonstrates superior convergence speed and solution accuracy performance through testing and comparison. Finally, simulation verification under two conditions of the bridge crane system validates the effectiveness of the proposed approach.
{"title":"Parameter optimization of type II fuzzy sliding mode control for bridge crane systems based on improved grey wolf algorithm","authors":"Zhiqiang Sun, Zhe Sun, Xiangpeng Xie, Zhixin Sun","doi":"10.1002/oca.3141","DOIUrl":"https://doi.org/10.1002/oca.3141","url":null,"abstract":"Bridge cranes are complex nonlinear dynamic systems with underactuated characteristics, making it challenging for controllers to man age the spatial swing of the load effectively. Additionally, uncertainties both within and outside the system adversely impact control performance. To address these issues, a Type‐II fuzzy sliding mode controller has proven effective in enhancing the anti‐swing control performance of the payload. However, due to the intricate parameter adjustment optimization problem and potential challenges in dealing with nonlinearity and uncertainty, especially in complex dynamic systems, this paper proposes a grey wolf algorithm based on a dynamic spiral hunting mechanism. This enhancement endows the algorithm with improved convergence speed and higher robustness, enabling more effective parameter tuning for the second‐order fractional‐order sliding mode controller (FSMC). The proposed algorithm demonstrates superior convergence speed and solution accuracy performance through testing and comparison. Finally, simulation verification under two conditions of the bridge crane system validates the effectiveness of the proposed approach.","PeriodicalId":501055,"journal":{"name":"Optimal Control Applications and Methods","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141112494","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article addresses adaptive event‐triggered discrete‐time nonlinear Markov jump systems (MJs) with DoS attacks, where the introduced DoS attacks are considered as more general stochastic models with fixed trigger frequency and duration. To solve the optimal control problem, we use an adaptive dynamic programming (ADP) algorithm based on policy iteration (PI). The approximate process is as follows: the performance index function (PIF) is first updated by the iteration policy in advance, and the control policy is obtained from the PIF. Subsequently, an approximate estimation of the optimal PIF and the optimal control policy is made using the actor‐critic structure obtained through neural network techniques. In order to reduce the occupied communication resources required for control policy iteration, we introduce an adaptive event triggering mechanism with an adaptive triggering threshold, which reduces the conservatism of resource occupation by the PIF compared to the fixed‐threshold ETM. In addition, an observer identifying the unknown dynamics part of the system is designed. Finally, using the Lyapunov function, it is shown that the designed control policy ensures the stability and convergence of the MJS, and the designed observer is effective. Simulation examples are given to verify the feasibility of the controller and the observer.
本文探讨了具有 DoS 攻击的自适应事件触发离散时间非线性马尔可夫跃迁系统（MJ），其中引入的 DoS 攻击被视为具有固定触发频率和持续时间的更一般的随机模型。为了解决最优控制问题，我们使用了基于策略迭代（PI）的自适应动态编程（ADP）算法。其近似过程如下：首先根据迭代策略提前更新性能指标函数（PIF），然后根据 PIF 获取控制策略。随后，利用神经网络技术获得的行动者批判结构对最优 PIF 和最优控制政策进行近似估计。为了减少控制策略迭代所需的通信资源占用，我们引入了具有自适应触发阈值的自适应事件触发机制，与固定阈值的 ETM 相比，该机制减少了 PIF 对资源占用的保守性。此外，我们还设计了一个能识别系统未知动态部分的观测器。最后，利用 Lyapunov 函数证明了所设计的控制策略能确保 MJS 的稳定性和收敛性，并且所设计的观测器是有效的。仿真实例验证了控制器和观测器的可行性。
{"title":"Adaptive event‐triggered control and observer design for discrete‐time nonlinear Markov jump systems with DoS attacks using policy iteration‐based adaptive dynamic programming","authors":"Hongqian Lu, Haobo Xing, Wuneng Zhou","doi":"10.1002/oca.3142","DOIUrl":"https://doi.org/10.1002/oca.3142","url":null,"abstract":"This article addresses adaptive event‐triggered discrete‐time nonlinear Markov jump systems (MJs) with DoS attacks, where the introduced DoS attacks are considered as more general stochastic models with fixed trigger frequency and duration. To solve the optimal control problem, we use an adaptive dynamic programming (ADP) algorithm based on policy iteration (PI). The approximate process is as follows: the performance index function (PIF) is first updated by the iteration policy in advance, and the control policy is obtained from the PIF. Subsequently, an approximate estimation of the optimal PIF and the optimal control policy is made using the actor‐critic structure obtained through neural network techniques. In order to reduce the occupied communication resources required for control policy iteration, we introduce an adaptive event triggering mechanism with an adaptive triggering threshold, which reduces the conservatism of resource occupation by the PIF compared to the fixed‐threshold ETM. In addition, an observer identifying the unknown dynamics part of the system is designed. Finally, using the Lyapunov function, it is shown that the designed control policy ensures the stability and convergence of the MJS, and the designed observer is effective. Simulation examples are given to verify the feasibility of the controller and the observer.","PeriodicalId":501055,"journal":{"name":"Optimal Control Applications and Methods","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141123023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, the cluster synchronization control for a complex dynamic network (CDN) with mutually coupled nodes subsystem (NS) and connection relations subsystem is investigated. The process of cluster synchronization is segmented into three dynamic continuous stages: first, the free movement, then the task‐oriented clustering, and finally the cluster synchronization. The control scheme, founded on the clustering nodes of CDN, is proposed, such that the cluster synchronization arises when clustering all the nodes into two different sub‐networks (SNs). This approach originates from the flight motion for a group of autonomous aircrafts. At a certain moment, free flight is interrupted, and all the aircrafts split into two SNs according to the given clustering rules. Then the two controlled SNs are required to achieve cluster synchronization, that is, every SN converges to the same in speed. In order to split all the nodes into two different SNs, a clustering algorithm according to the “central nodes” is proposed. Based on Lyapunov stability theory, by designing the suitable inner cluster links, the adaptive controller of NS for each SN is synthesized to guarantee the stability of the error system. It is shown that the eventual inner topology of each SN is displayed in the pre‐given form when the cluster synchronization achieves. Finally, the merits and effectiveness of the proposed control scheme are verified by a simulation example.
本文研究了具有相互耦合的节点子系统（NS）和连接关系子系统的复杂动态网络（CDN）的集群同步控制。集群同步过程分为三个动态连续阶段：首先是自由移动，然后是面向任务的集群，最后是集群同步。基于 CDN 聚类节点的控制方案被提出，当所有节点聚类为两个不同的子网络（SN）时，聚类同步就产生了。这种方法源于一组自主飞行器的飞行运动。在某一时刻，自由飞行中断，所有飞机根据给定的聚类规则分成两个 SN。然后，要求两个受控 SN 实现集群同步，即每个 SN 的速度趋于一致。为了将所有节点分成两个不同的 SN，提出了一种基于 "中心节点 "的聚类算法。基于李雅普诺夫稳定性理论，通过设计合适的内部簇链接，合成每个 SN 的 NS 自适应控制器，以保证误差系统的稳定性。结果表明，当实现簇同步时，每个 SN 的最终内部拓扑都会以预先给定的形式显示出来。最后，通过一个仿真实例验证了所提控制方案的优点和有效性。
{"title":"Cluster synchronization control for the complex network with dynamic connection relations","authors":"Jinbiao Chen, Yinhe Wang, Yi Peng, Xiaoxi Wang","doi":"10.1002/oca.3143","DOIUrl":"https://doi.org/10.1002/oca.3143","url":null,"abstract":"In this article, the cluster synchronization control for a complex dynamic network (CDN) with mutually coupled nodes subsystem (NS) and connection relations subsystem is investigated. The process of cluster synchronization is segmented into three dynamic continuous stages: first, the free movement, then the task‐oriented clustering, and finally the cluster synchronization. The control scheme, founded on the clustering nodes of CDN, is proposed, such that the cluster synchronization arises when clustering all the nodes into two different sub‐networks (SNs). This approach originates from the flight motion for a group of autonomous aircrafts. At a certain moment, free flight is interrupted, and all the aircrafts split into two SNs according to the given clustering rules. Then the two controlled SNs are required to achieve cluster synchronization, that is, every SN converges to the same in speed. In order to split all the nodes into two different SNs, a clustering algorithm according to the “central nodes” is proposed. Based on Lyapunov stability theory, by designing the suitable inner cluster links, the adaptive controller of NS for each SN is synthesized to guarantee the stability of the error system. It is shown that the eventual inner topology of each SN is displayed in the pre‐given form when the cluster synchronization achieves. Finally, the merits and effectiveness of the proposed control scheme are verified by a simulation example.","PeriodicalId":501055,"journal":{"name":"Optimal Control Applications and Methods","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141122093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article focuses on the optimal control problems governed by fourth‐order linear elliptic equations with clamped boundary conditions in the framework of the Hessian discretization method (HDM). The HDM is an abstract framework that enables the convergence analysis of several numerical methods such as the conforming finite element methods, the Adini and Morley nonconforming finite element methods (ncFEMs), the method based on gradient recovery (GR) operators, and the finite volume methods (FVMs). Basic error estimates and superconvergence results are established for the state, adjoint, and control variables. A companion operator for the GR method with specific property is designed. The article concludes with numerical results that illustrate the theoretical convergence rates for GR method, Adini ncFEM, and FVM.
这篇文章在黑森离散化方法（HDM）的框架内，重点研究了具有箝位边界条件的四阶线性椭圆方程所控制的最优控制问题。HDM 是一个抽象框架，可以对多种数值方法进行收敛分析，如符合有限元方法、Adini 和 Morley 非符合有限元方法（ncFEMs）、基于梯度恢复（GR）算子的方法以及有限体积方法（FVMs）。为状态变量、邻接变量和控制变量建立了基本误差估计和超收敛结果。文章还设计了一个具有特定性质的 GR 方法辅助算子。文章最后以数值结果说明了 GR 方法、Adini ncFEM 和 FVM 的理论收敛率。
{"title":"Numerical analysis of optimal control problems governed by fourth‐order linear elliptic equations using the Hessian discretization method","authors":"Devika Shylaja","doi":"10.1002/oca.3135","DOIUrl":"https://doi.org/10.1002/oca.3135","url":null,"abstract":"This article focuses on the optimal control problems governed by fourth‐order linear elliptic equations with clamped boundary conditions in the framework of the Hessian discretization method (HDM). The HDM is an abstract framework that enables the convergence analysis of several numerical methods such as the conforming finite element methods, the Adini and Morley nonconforming finite element methods (ncFEMs), the method based on gradient recovery (GR) operators, and the finite volume methods (FVMs). Basic error estimates and superconvergence results are established for the state, adjoint, and control variables. A companion operator for the GR method with specific property is designed. The article concludes with numerical results that illustrate the theoretical convergence rates for GR method, Adini ncFEM, and FVM.","PeriodicalId":501055,"journal":{"name":"Optimal Control Applications and Methods","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060382","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A hybrid technique is proposed for the energy management (EM) of smart grid (SG) systems. The proposed method integrates the Wild Horse Optimization (WHO) and dwarf mongoose optimization (DMO) methods; hence, it is named the WHO–DMO approach. The Micro‐grid (MG)‐tied system is a combination of battery, micro turbine (MT), photovoltaic (PV), and Wind Turbine (WT). The key aim of the proposed approach is to manage the resources and power of the SG model and reduce the cost of electricity. The objective of the system is to improve load demand. The WHO method is enhanced by the DMO method, which minimizes the objective of the system. Access to power demand, state of charge (SOC), and renewable energy sources (RESs) for storing elements are considered constraints of the system. The unit of renewable power systems relies on batteries as energy sources to stabilize and sustain stable and consistent output power throughout the operation. The proposed technique is done in MATLAB platform and its implementation is calculated using the existing methods. From the simulation, the proposed method has less cost and higher power than the existing methods.
{"title":"A Hybrid Wild Horses Optimization (WHO) and Dwarf Mongoose Optimization (DMO) method for optimum energy management in SG system","authors":"P. Ganesan, S. Arockia Edwin Xavier","doi":"10.1002/oca.3131","DOIUrl":"https://doi.org/10.1002/oca.3131","url":null,"abstract":"A hybrid technique is proposed for the energy management (EM) of smart grid (SG) systems. The proposed method integrates the Wild Horse Optimization (WHO) and dwarf mongoose optimization (DMO) methods; hence, it is named the WHO–DMO approach. The Micro‐grid (MG)‐tied system is a combination of battery, micro turbine (MT), photovoltaic (PV), and Wind Turbine (WT). The key aim of the proposed approach is to manage the resources and power of the SG model and reduce the cost of electricity. The objective of the system is to improve load demand. The WHO method is enhanced by the DMO method, which minimizes the objective of the system. Access to power demand, state of charge (SOC), and renewable energy sources (RESs) for storing elements are considered constraints of the system. The unit of renewable power systems relies on batteries as energy sources to stabilize and sustain stable and consistent output power throughout the operation. The proposed technique is done in MATLAB platform and its implementation is calculated using the existing methods. From the simulation, the proposed method has less cost and higher power than the existing methods.","PeriodicalId":501055,"journal":{"name":"Optimal Control Applications and Methods","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article consider a class of generalized coupled Sylvester‐transpose matrix equations which play an important role in control and systems theory. Based on the Jacobi iterative algorithm, the full‐row rank accelerated Jacobi gradient based iterative (RRAJGI) algorithm and the full‐column rank accelerated Jacobi gradient based iterative (CRAJGI) algorithm are proposed. By using the Frobenius norm of matrix and the trace function of matrix, the convergence of the algorithms are proved. The results show that the new algorithms are convergent for arbitrary initial matrices under the convergence number satisfies appropriate conditions. Numerical examples show that RRAJGI algorithm and CRAJGI algorithm have the advantages of faster convergence speed and higher convergence accuracy than other existing algorithms. Finally, an application example for robust and minimum norm observer design of linear systems is given.
{"title":"Iterative algorithm to the generalized coupled Sylvester‐transpose matrix equations with application in robust and minimum norm observer design of linear systems","authors":"Rui Qi, Caiqin Song","doi":"10.1002/oca.3134","DOIUrl":"https://doi.org/10.1002/oca.3134","url":null,"abstract":"This article consider a class of generalized coupled Sylvester‐transpose matrix equations which play an important role in control and systems theory. Based on the Jacobi iterative algorithm, the full‐row rank accelerated Jacobi gradient based iterative (RRAJGI) algorithm and the full‐column rank accelerated Jacobi gradient based iterative (CRAJGI) algorithm are proposed. By using the Frobenius norm of matrix and the trace function of matrix, the convergence of the algorithms are proved. The results show that the new algorithms are convergent for arbitrary initial matrices under the convergence number satisfies appropriate conditions. Numerical examples show that RRAJGI algorithm and CRAJGI algorithm have the advantages of faster convergence speed and higher convergence accuracy than other existing algorithms. Finally, an application example for robust and minimum norm observer design of linear systems is given.","PeriodicalId":501055,"journal":{"name":"Optimal Control Applications and Methods","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the framework of a second‐order semilinear integro‐differential control system in Hilbert spaces, the paper provides sufficient conditions for proving the existence of optimal control. The Banach fixed point theorem is used to investigate the existence and uniqueness of mild solutions for the proposed problem. Additionally, it is shown that, under specific assumptions, there exists at least one optimal control pair for the Lagrange's problem as presented in the article. An example for validation is included in the paper to further support the theoretical findings.
{"title":"Optimal control results for second‐order semilinear integro‐differential systems via resolvent operators","authors":"Anugrah Pratap Singh, Udaya Pratap Singh, Anurag Shukla","doi":"10.1002/oca.3138","DOIUrl":"https://doi.org/10.1002/oca.3138","url":null,"abstract":"In the framework of a second‐order semilinear integro‐differential control system in Hilbert spaces, the paper provides sufficient conditions for proving the existence of optimal control. The Banach fixed point theorem is used to investigate the existence and uniqueness of mild solutions for the proposed problem. Additionally, it is shown that, under specific assumptions, there exists at least one optimal control pair for the Lagrange's problem as presented in the article. An example for validation is included in the paper to further support the theoretical findings.","PeriodicalId":501055,"journal":{"name":"Optimal Control Applications and Methods","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：