{"title":"A numerical method for ℋ2$$ {mathscr{H}}_2 $$ control of linear delay systems","authors":"Renhong Hu, Jie Mei, G. Ma","doi":"10.1002/oca.3027","DOIUrl":"https://doi.org/10.1002/oca.3027","url":null,"abstract":"This paper is concerned with the output feedback stabilization of linear delay systems with exogenous disturbances. Based on the ℋ2$$ {mathscr{H}}_2 $$ norm, an optimization problem is formulated for the suppression of exogenous disturbances in the linear delay systems. The effectiveness of the presented approach is demonstrated via several numerical examples.","PeriodicalId":105945,"journal":{"name":"Optimal Control Applications and Methods","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124312406","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}
Lingwei Li, Bing Xiao, S. Su, Haichao Zhang, Xiwei Wu, Yiming Guo
{"title":"Attack‐defense differential game to strength allocation strategies generation","authors":"Lingwei Li, Bing Xiao, S. Su, Haichao Zhang, Xiwei Wu, Yiming Guo","doi":"10.1002/oca.3035","DOIUrl":"https://doi.org/10.1002/oca.3035","url":null,"abstract":"This paper addresses a difficult problem of strength allocation strategies generation with various adversaries and complex factors. Firstly, to investigate the strength allocation strategies generation problem, an attack‐defense differential game problem is formulated based on an improved Lanchester equation. Secondly, a numerical method, multi‐intervals simultaneous orthogonal collocation decomposition (MISOCD) method, is proposed to obtain the strength allocation strategies from the constructed model. Compared with the analytical method, MISOCD does not need to derive the necessary conditions. Thirdly, this study designs an approximated solution generation strategy based on adaptive learning pigeon‐inspired optimization algorithm to pregenerate the approximated strength allocation strategies in order to solve the initial value sensitivity problem. The approximated strategies are then used as the initial value guess of MISOCD method to generate optimal strength allocation strategies. Finally, two attack‐defense numerical simulations verify the effectiveness of strength allocation strategies generated by the proposed approach. Our proposed results provide a theoretical guide for both making attack‐defense strength allocation strategies and assessing confrontation actions.","PeriodicalId":105945,"journal":{"name":"Optimal Control Applications and Methods","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125894634","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}
{"title":"Adaptive event‐triggering mechanism‐based N‐step predictive load frequency control for power systems with cyber attack","authors":"Yuehua Wu, Xiaoming Tang, Jialiang Wang, Hongchun Qu","doi":"10.1002/oca.3033","DOIUrl":"https://doi.org/10.1002/oca.3033","url":null,"abstract":"Although there have already been many works on the model predictive control (MPC) for load frequency control (LFC) of modern power systems, limited works can be found in the literature related to the output feedback MPC. This article studies an N‐step synthesis approach of output feedback MPC for LFC systems considering the problems of communication efficiency and network security. First, to improve the communication efficiency, an adaptive event‐triggering (AET) scheme involving two adaptive laws is designed to reduce the number of transmitted data packages which offers more flexible compared with existing event‐triggering schemes; Second, to handle the network security, a new model of LFC power system combining the AET scheme and random deception attack under an unified framework is established; Moreover, a synthesis approach of output feedback MPC with N‐step strategy is addressed for LFC of power system by parameterizing the infinite control moves into a series of output feedback laws. Compared with the existing predictive load frequency control methods, the present technique is shown as an useful way to improve the control performance since more degrees freedom is introduced by the N‐step strategy. Finally, the simulation experiment is carried out to verify our technique.","PeriodicalId":105945,"journal":{"name":"Optimal Control Applications and Methods","volume":"96 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124944058","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}
{"title":"Space−time spectral approximations of a parabolic optimal control problem with an L2‐norm control constraint","authors":"Zhenzhen Tao, Bing Sun","doi":"10.1002/oca.3022","DOIUrl":"https://doi.org/10.1002/oca.3022","url":null,"abstract":"This article deals with the spectral approximation of an optimal control problem governed by a parabolic partial differential equation (PDE) with an L2$$ {L}^2 $$ ‐norm control constraint. The investigations employ the space−time spectral method, which is, more precisely, a dual Petrov‐Galerkin spectral method in time and a spectral method in space to discrete the continuous system. As a global method, it uses the global polynomials as the trial functions for discretization of PDEs. After obtaining the optimality condition of the continuous system and that of its spectral discrete surrogate, we establish a priori and a posteriori error estimates for the spectral approximation in detail. Three numerical examples in different spatial dimensions then confirm the theoretical results and also show the efficiency as well as a good precision of the adopted space−time spectral method.","PeriodicalId":105945,"journal":{"name":"Optimal Control Applications and Methods","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117033286","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}
{"title":"The numerical treatment of fractal‐fractional 2D optimal control problems by Müntz–Legendre polynomials","authors":"P. Rahimkhani, Y. Ordokhani, S. Sedaghat","doi":"10.1002/oca.3024","DOIUrl":"https://doi.org/10.1002/oca.3024","url":null,"abstract":"In this work, we introduce a method based on the Müntz–Legendre polynomials (M‐LPs) for solving fractal‐fractional 2D optimal control problems that the fractal‐fractional derivative is described in Atangana‐Riemann‐Liouville's sense. First, we obtain operational matrices of fractal‐fractional‐order derivative, integer‐order integration, and derivative of the M‐LPs. Second, the under study problem is converted into an equivalent variational problem. Then, by applying the M‐LPs, their operational matrices and Gauss–Legendre integration, the mentioned problem is converted to a system of algebraic equations. Finally, this system is solved by Newton's iterative method. Also, we introduce an error bound for the described method. Two examples are included to test the applicability and validity of the present scheme.","PeriodicalId":105945,"journal":{"name":"Optimal Control Applications and Methods","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125210228","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}
{"title":"Optimal allocation of distributed generation for power flow enhancement in distribution network","authors":"Srividhya Jayaraman Panneerselvam, Yogitha Krishnamoorthi, Suresh Ramamoorthy, Jaisiva Selvaraj","doi":"10.1002/oca.3031","DOIUrl":"https://doi.org/10.1002/oca.3031","url":null,"abstract":"This article articulates the enhancement of voltage profiles in transmission systems by reducing the voltage deviation and system power losses. Electric power flows uniformly throughout Regional Distribution Networks in the power grid station, resulting in low voltage consistency, significant voltage dips and power losses in the distribution network, highlighting high R/X ratios even with a heavy load or power failure issues, despite installing distributed generation in the radial distribution system for enhancing voltage profile in the grid network. The meta‐heuristic optimization algorithm plays a vital role in determining optimal location of DG for attaining the objective of research. In the practical network, a single objective optimization strategy cannot be employed to solve of power system optimization problems of all kinds. Hence multi‐objective function needs to be addressed. The prime task of this research is to investigate and allocate an optimal location to connect the Distributed Generation, with evaluation of the best DG configuration, with minimized power losses and improved voltage profile of the distribution network using the Hummingbird Optimization Algorithm. A standard IEEE 37‐bus Radial Distribution system is employed as the test bus system to test the performance and effectiveness of the optimization technique. To show the stiffness of the proposed algorithm the results are compared with various optimization approaches that employ similar objective functions.","PeriodicalId":105945,"journal":{"name":"Optimal Control Applications and Methods","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121515973","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}
{"title":"Solvability of general fully coupled forward–backward stochastic difference equations with delay and applications","authors":"Teng Song","doi":"10.1002/oca.3023","DOIUrl":"https://doi.org/10.1002/oca.3023","url":null,"abstract":"A class of fully coupled forward–backward stochastic difference equations with delay (FBSDDEs) over infinite horizon are considered in this article. By establishing a non‐homogeneous explicit relation between the forward and backward equations in terms of Riccati‐like difference equations, we derive the unique solution to the FBSDDEs under certain conditions. Then, we deduce that the FBSDDEs are solvable if and only if the corresponding stochastic delayed system is β$$ beta $$ ‐degree open‐loop mean‐square exponentially stabilizable. Finally, as an application, the FBSDDEs are employed to demonstrate the maximum principle of the stochastic LQ optimal control problem.","PeriodicalId":105945,"journal":{"name":"Optimal Control Applications and Methods","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116811341","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}
{"title":"A modified reptile search algorithm for parametric estimation of fractional order model of lithium battery","authors":"Jie Ding, Shimeng Huang, Yuefei Hao, Min Xiao","doi":"10.1002/oca.3034","DOIUrl":"https://doi.org/10.1002/oca.3034","url":null,"abstract":"In this paper, a Levy reptile search algorithm (LRSA) is proposed to improve the global search capability and convergence speed of reptile search algorithm which has advantages in solving single‐modal, multi‐modal and composite problems. Firstly, circle chaotic mapping is introduced to make the initial distribution of population more uniform and diversified. Secondly, Levy flight strategy is employed in the global search, which can improve the accuracy and convergence speed. In order to test and verify the optimization performance of the LRSA, 12 benchmark functions are tested and compared with four other intelligent optimization algorithms. It can be seen that LRSA is effective and advantageous in average convergence speed. In addition, the proposed LRSA is applied to a fractional order model identification of lithium battery with a very small error (less than 2%). The experimental results show that the LRSA can effectively estimate the parameters of the fractional order model and aid to state of charge and state of health estimation.","PeriodicalId":105945,"journal":{"name":"Optimal Control Applications and Methods","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116682387","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}
Gabriel A. Salcedo‐Varela, F. Peñuñuri, D. González‐Sánchez, Saúl Díaz-Infante
{"title":"Synchronizing lockdown and vaccination policies for COVID‐19: An optimal control approach based on piecewise constant strategies","authors":"Gabriel A. Salcedo‐Varela, F. Peñuñuri, D. González‐Sánchez, Saúl Díaz-Infante","doi":"10.1002/oca.3032","DOIUrl":"https://doi.org/10.1002/oca.3032","url":null,"abstract":"","PeriodicalId":105945,"journal":{"name":"Optimal Control Applications and Methods","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127796446","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}
{"title":"Model‐free optimal tracking over finite horizon using adaptive dynamic programming","authors":"M. Jha, D. Theilliol, P. Weber","doi":"10.1002/oca.3028","DOIUrl":"https://doi.org/10.1002/oca.3028","url":null,"abstract":"Adaptive dynamic programming (ADP) based approaches are effective for solving nonlinear Hamilton–Jacobi–Bellman (HJB) in an approximative sense. This paper develops a novel ADP‐based approach, in that the focus is on minimizing the consecutive changes in control inputs over a finite horizon to solve the optimal tracking problem for completely unknown discrete time systems. To that end, the cost function considers within its arguments: tracking performance, energy consumption and as a novelty, consecutive changes in the control inputs. Through suitable system transformation, the optimal tracking problem is transformed to a regulation problem with respect to state tracking error. The latter leads to a novel performance index function over finite horizon and corresponding nonlinear HJB equation that is solved in an approximative iterative sense using a novel iterative ADP‐based algorithm. A suitable Neural network‐based structure is proposed to learn the initial admissible one step zero control law. The proposed iterative ADP is implemented using heuristic dynamic programming technique based on actor‐critic Neural Network structure. Finally, simulation studies are presented to illustrate the effectiveness of the proposed algorithm.","PeriodicalId":105945,"journal":{"name":"Optimal Control Applications and Methods","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133716334","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}