This paper focuses on optimizing project investments in oil and gas companies. It proposes a multi-objective method for investing in oil and gas assets, considering factors such as scale and efficiency. The model takes into account the presence of nonlinear equations and integer constraints, and establishes a nonlinear multi-objective mixed integer programming portfolio model for oil and gas. The weights of multiple objectives are determined using support vector machines. The optimization model incorporates the displacement transfer concept of particle swarm optimizer and the mutation operation of genetic algorithm using the transfer strategy of Gaussian particle swarm. The effectiveness of the model and algorithm is demonstrated through two examples.
{"title":"Modeling and solving a multi-objective optimal portfolio of upstream oil and gas assets","authors":"Wei Yan","doi":"10.1002/oca.3095","DOIUrl":"https://doi.org/10.1002/oca.3095","url":null,"abstract":"This paper focuses on optimizing project investments in oil and gas companies. It proposes a multi-objective method for investing in oil and gas assets, considering factors such as scale and efficiency. The model takes into account the presence of nonlinear equations and integer constraints, and establishes a nonlinear multi-objective mixed integer programming portfolio model for oil and gas. The weights of multiple objectives are determined using support vector machines. The optimization model incorporates the displacement transfer concept of particle swarm optimizer and the mutation operation of genetic algorithm using the transfer strategy of Gaussian particle swarm. The effectiveness of the model and algorithm is demonstrated through two examples.","PeriodicalId":501055,"journal":{"name":"Optimal Control Applications and Methods","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139068216","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 paper is concerned with the optimal control problem governed by linear parabolic equation with box constraints on control variables. We employ the Fenchel duality scheme to derive an unconstrained dual problem. Compared with the primal problem, the objective functional of the dual problem includes a projection onto the box constraints. We prove the existence and uniqueness of solutions to the dual problem and derive the first-order optimality conditions. Furthermore, we investigate the saddle point property between the solutions of the primal problem and the solutions of the dual problem. To solve the dual problem, we design two implementable methods: the conjugate gradient method and the semi-smooth Newton method. The solutions of the primal problem can be easily obtained through the solutions of the dual problem. We demonstrate the effectiveness and accuracy of the proposed methods by solving three example problems.
{"title":"A duality-based approach for linear parabolic optimal control problems","authors":"Hailing Wang, Di Wu, Changjun Yu, Kok Lay Teo","doi":"10.1002/oca.3094","DOIUrl":"https://doi.org/10.1002/oca.3094","url":null,"abstract":"This paper is concerned with the optimal control problem governed by linear parabolic equation with box constraints on control variables. We employ the Fenchel duality scheme to derive an unconstrained dual problem. Compared with the primal problem, the objective functional of the dual problem includes a projection onto the box constraints. We prove the existence and uniqueness of solutions to the dual problem and derive the first-order optimality conditions. Furthermore, we investigate the saddle point property between the solutions of the primal problem and the solutions of the dual problem. To solve the dual problem, we design two implementable methods: the conjugate gradient method and the semi-smooth Newton method. The solutions of the primal problem can be easily obtained through the solutions of the dual problem. We demonstrate the effectiveness and accuracy of the proposed methods by solving three example problems.","PeriodicalId":501055,"journal":{"name":"Optimal Control Applications and Methods","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139056412","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 paper deals with the second-order necessary optimality conditions for discrete-time stochastic optimal control problems under weakened convexity assumptions. Using a special variation of the control, and by virtue of a new discrete-time backward stochastic equation, we establish a more general and constructive first-order necessary optimality condition in the form of a global stochastic maximum principle. Moreover, by introducing a new discrete-time backward stochastic matrix equation, the second-order multipoint necessary optimality conditions of singular controls are derived, which covers and improves the classical second-order necessary optimality conditions of discrete-time stochastic systems.
{"title":"Second-order necessary optimality conditions for discrete-time stochastic systems","authors":"Teng Song, Yong Yao","doi":"10.1002/oca.3073","DOIUrl":"https://doi.org/10.1002/oca.3073","url":null,"abstract":"This paper deals with the second-order necessary optimality conditions for discrete-time stochastic optimal control problems under weakened convexity assumptions. Using a special variation of the control, and by virtue of a new discrete-time backward stochastic equation, we establish a more general and constructive first-order necessary optimality condition in the form of a global stochastic maximum principle. Moreover, by introducing a new discrete-time backward stochastic matrix equation, the second-order multipoint necessary optimality conditions of singular controls are derived, which covers and improves the classical second-order necessary optimality conditions of discrete-time stochastic systems.","PeriodicalId":501055,"journal":{"name":"Optimal Control Applications and Methods","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138825056","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}
Yong-Ki Ma, K. Kavitha, Anurag Shukla, V. Vijayakumar, Kottakkaran Sooppy Nisar
The existence and uniqueness of solutions to Hilfer fractional neutral delay integro-differential equations subject to nonlocal conditions are discussed in this study. The main results of this study are based in part on the fixed point techniques of Banach contraction and Krasnoselskii's fixed point theorem from calculus theory. First, we determine whether or not the fractional system has a mild solution. The uniqueness of the mild solution is further illustrated by expanding our results. The optimal control problems are governed by a new class of neutral delay integro-differential equations in Banach spaces, and we also develop sufficient conditions for the approximate controllability of a nonlinear fractional system. An example is given at the end to strengthen the compatibility of the results.
{"title":"An analysis on the optimal control and approximate controllability for Hilfer fractional neutral integro-differential systems with finite delay","authors":"Yong-Ki Ma, K. Kavitha, Anurag Shukla, V. Vijayakumar, Kottakkaran Sooppy Nisar","doi":"10.1002/oca.3090","DOIUrl":"https://doi.org/10.1002/oca.3090","url":null,"abstract":"The existence and uniqueness of solutions to Hilfer fractional neutral delay integro-differential equations subject to nonlocal conditions are discussed in this study. The main results of this study are based in part on the fixed point techniques of Banach contraction and Krasnoselskii's fixed point theorem from calculus theory. First, we determine whether or not the fractional system has a mild solution. The uniqueness of the mild solution is further illustrated by expanding our results. The optimal control problems are governed by a new class of neutral delay integro-differential equations in Banach spaces, and we also develop sufficient conditions for the approximate controllability of a nonlinear fractional system. An example is given at the end to strengthen the compatibility of the results.","PeriodicalId":501055,"journal":{"name":"Optimal Control Applications and Methods","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138716163","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}
The article investigated the stability of a two-lane car-following model with lateral friction on the basis of cluster synchronization theory of complex network. By using the Lyapunov stability theory and designing the appropriate controller, the two-lane car-following model with lateral friction is quickly stabilized and the stability condition of the model is obtained. Besides, based on the adaptive cluster synchronization theory for complex networks with external disturbances, the stability of two-lane car-following model with lateral friction is studied when the vehicles is subjected to random external disturbance. Finally, the numerical simulation is carried out by using Matlab simulation technology, the results show that the two-lane car-following model with lateral friction is rapidly stabilizing and congestion phenomenon is effectively alleviated under the controller designed.
{"title":"Stability control of a two-lane car-following model based on cluster synchronization of complex network","authors":"Wenju Du, Yinzhen Li, Jiangang Zhang","doi":"10.1002/oca.3088","DOIUrl":"https://doi.org/10.1002/oca.3088","url":null,"abstract":"The article investigated the stability of a two-lane car-following model with lateral friction on the basis of cluster synchronization theory of complex network. By using the Lyapunov stability theory and designing the appropriate controller, the two-lane car-following model with lateral friction is quickly stabilized and the stability condition of the model is obtained. Besides, based on the adaptive <mjx-container aria-label=\"upper H Subscript normal infinity\" ctxtmenu_counter=\"0\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/oca3088-math-0001.png\"><mjx-semantics><mjx-mrow><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"upper H Subscript normal infinity\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em; margin-left: -0.057em;\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\" size=\"s\"><mjx-c></mjx-c></mjx-mi></mjx-script></mjx-msub></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml aria-hidden=\"true\" display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:01432087:media:oca3088:oca3088-math-0001\" display=\"inline\" location=\"graphic/oca3088-math-0001.png\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><msub data-semantic-=\"\" data-semantic-children=\"0,1\" data-semantic-role=\"latinletter\" data-semantic-speech=\"upper H Subscript normal infinity\" data-semantic-type=\"subscript\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">H</mi><mi data-semantic-=\"\" data-semantic-font=\"normal\" data-semantic-parent=\"2\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\" mathvariant=\"normal\">∞</mi></msub></mrow>$$ {H}_{infty } $$</annotation></semantics></math></mjx-assistive-mml></mjx-container> cluster synchronization theory for complex networks with external disturbances, the stability of two-lane car-following model with lateral friction is studied when the vehicles is subjected to random external disturbance. Finally, the numerical simulation is carried out by using Matlab simulation technology, the results show that the two-lane car-following model with lateral friction is rapidly stabilizing and congestion phenomenon is effectively alleviated under the controller designed.","PeriodicalId":501055,"journal":{"name":"Optimal Control Applications and Methods","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138689512","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 explores the development of dynamic observer (HDO) for discrete-time nonlinear systems (DTNLS) with time-varying delay (TVD) and disturbances. The approach is to construct an augmented Lyapunov–Krasovskii function (LKF) with double summation terms, using the generalized reciprocally convex matrix inequality (GRCMI), as well as the Jensen-based inequality (JBI) and the Wirtinger-based inequality (WBI). These lead to less conservative time-dependent conditions, represented as a set of linear matrix inequalities (LMIs) that can be efficiently solved using the LMI or YALMIP toolboxes. In addition, the proposed observer includes the widely used proportional observer (PO) and proportional integral observer (PIO) as specific cases. Two examples are presented to demonstrate the validity and effectiveness of the results.
{"title":"H∞ dynamic observer design for a class of Lipschitz nonlinear discrete-time systems with time varying delays","authors":"Ghali Naami, Mohamed Ouahi","doi":"10.1002/oca.3081","DOIUrl":"https://doi.org/10.1002/oca.3081","url":null,"abstract":"This study explores the development of <mjx-container aria-label=\"Menu available. Press control and space , or space\" ctxtmenu_counter=\"0\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/oca3081-math-0003.png\"><mjx-semantics><mjx-mrow><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"upper H Subscript infinity\" data-semantic-type=\"subscript\"><mjx-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-mrow><mjx-script style=\"vertical-align: -0.15em; margin-left: -0.057em;\"><mjx-mrow size=\"s\"><mjx-mi data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-script></mjx-msub></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml aria-hidden=\"true\" display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:oca:media:oca3081:oca3081-math-0003\" display=\"inline\" location=\"graphic/oca3081-math-0003.png\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><msub data-semantic-=\"\" data-semantic-children=\"0,1\" data-semantic-role=\"latinletter\" data-semantic-speech=\"upper H Subscript infinity\" data-semantic-type=\"subscript\"><mrow><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">H</mi></mrow><mrow><mi data-semantic-=\"\" data-semantic-parent=\"2\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\">∞</mi></mrow></msub></mrow>$$ {H}_{infty } $$</annotation></semantics></math></mjx-assistive-mml></mjx-container> dynamic observer (HDO) for discrete-time nonlinear systems (DTNLS) with time-varying delay (TVD) and disturbances. The approach is to construct an augmented Lyapunov–Krasovskii function (LKF) with double summation terms, using the generalized reciprocally convex matrix inequality (GRCMI), as well as the Jensen-based inequality (JBI) and the Wirtinger-based inequality (WBI). These lead to less conservative time-dependent conditions, represented as a set of linear matrix inequalities (LMIs) that can be efficiently solved using the LMI or YALMIP toolboxes. In addition, the proposed observer includes the widely used proportional observer (PO) and proportional integral observer (PIO) as specific cases. Two examples are presented to demonstrate the validity and effectiveness of the results.","PeriodicalId":501055,"journal":{"name":"Optimal Control Applications and Methods","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138628624","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}
Jens Göbel, Paulo Renato Da Costa Mendes, Andreas Wirsen, Tobias Damm
We present a straightforward way to solve a model predictive control problem for a power network system given as a nonlinear differential-algebraic equation (DAE) in a distributed way using the consensus alternating directions method of multipliers (consensus ADMM) algorithm. While no convergence- or stability results are available for fully nonlinear DAE models, this gives unprecedented experimental evidence that power network systems of the presented structure allow to be controlled in this way, unlocking the numerous combined advantages of distributed and predictive control schemes in the context of energy distribution networks, as well as broadening the field of use for the consensus ADMM algorithm to nonlinear DAE models.
{"title":"Distributed model predictive control based on the alternating directions method of multipliers applied to voltage and frequency control in power systems","authors":"Jens Göbel, Paulo Renato Da Costa Mendes, Andreas Wirsen, Tobias Damm","doi":"10.1002/oca.3083","DOIUrl":"https://doi.org/10.1002/oca.3083","url":null,"abstract":"We present a straightforward way to solve a model predictive control problem for a power network system given as a nonlinear differential-algebraic equation (DAE) in a distributed way using the consensus alternating directions method of multipliers (consensus ADMM) algorithm. While no convergence- or stability results are available for fully nonlinear DAE models, this gives unprecedented experimental evidence that power network systems of the presented structure allow to be controlled in this way, unlocking the numerous combined advantages of distributed and predictive control schemes in the context of energy distribution networks, as well as broadening the field of use for the consensus ADMM algorithm to nonlinear DAE models.","PeriodicalId":501055,"journal":{"name":"Optimal Control Applications and Methods","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138628699","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 paper, the problem of state estimation for a fractional-order neural networks system with uncertainties is studied by a sampled-data controller. First, considering the convenience of digital field, such as anti-interference, not affected by noise, a novel sampled-data controller is designed for the fractional-order neural network system of uncertainties with changeable sampling time. In the light of the input delay approach, the sampled-data control system of fractional-order is simulated by the delay system. The main purpose of the presented method is to obtain a sampled-data controller gain to estimate the state of neurons, which can guarantee the asymptotic stability of the closed-loop fractional-order system. Then, the fractional-order Razumishin theorem and linear matrix inequalities (LMIs) are utilized to derive the stable conditions. Improved delay-dependent and order-dependent stability conditions are given in the form of LMIs. Furthermore, the sampled-data controller can be acquired to promise the stability and stabilization for fractional-order system. Finally, two numerical examples are proposed to demonstrate the effectiveness and advantages of the provided method.
本文利用采样数据控制器研究了一类具有不确定性的分数阶神经网络系统的状态估计问题。首先，考虑到数字领域的抗干扰性、不受噪声影响等方便性，针对采样时间可变的分数阶不确定神经网络系统设计了一种新的采样数据控制器。根据输入延迟方法，利用延迟系统对分数阶采样数据控制系统进行了仿真。该方法的主要目的是获得一个采样数据控制器增益K $$ K $$来估计神经元的状态，从而保证闭环分数阶系统的渐近稳定性。然后，利用分数阶Razumishin定理和线性矩阵不等式(lmi)推导出稳定条件。以lmi的形式给出了改进的时滞相关稳定条件和序相关稳定条件。此外，采样数据控制器可以保证分数阶系统的稳定性和镇定性。最后，给出了两个数值算例，验证了所提方法的有效性和优越性。
{"title":"Order-dependent sampling control for state estimation of uncertain fractional-order neural networks system","authors":"Chao Ge, Qi Zhang, Hong Wang, Lei Wang","doi":"10.1002/oca.3071","DOIUrl":"https://doi.org/10.1002/oca.3071","url":null,"abstract":"In this paper, the problem of state estimation for a fractional-order neural networks system with uncertainties is studied by a sampled-data controller. First, considering the convenience of digital field, such as anti-interference, not affected by noise, a novel sampled-data controller is designed for the fractional-order neural network system of uncertainties with changeable sampling time. In the light of the input delay approach, the sampled-data control system of fractional-order is simulated by the delay system. The main purpose of the presented method is to obtain a sampled-data controller gain <math altimg=\"urn:x-wiley:oca:media:oca3071:oca3071-math-0001\" display=\"inline\" location=\"graphic/oca3071-math-0001.png\" overflow=\"scroll\">\u0000<semantics>\u0000<mrow>\u0000<mi>K</mi>\u0000</mrow>\u0000$$ K $$</annotation>\u0000</semantics></math> to estimate the state of neurons, which can guarantee the asymptotic stability of the closed-loop fractional-order system. Then, the fractional-order Razumishin theorem and linear matrix inequalities (LMIs) are utilized to derive the stable conditions. Improved delay-dependent and order-dependent stability conditions are given in the form of LMIs. Furthermore, the sampled-data controller can be acquired to promise the stability and stabilization for fractional-order system. Finally, two numerical examples are proposed to demonstrate the effectiveness and advantages of the provided method.","PeriodicalId":501055,"journal":{"name":"Optimal Control Applications and Methods","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138493364","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 disturbance observer-based proportional–integral–derivative (PID) control protocol is investigated for synchronization of complex networks with probabilistic interval time-varying delays and multiple disturbances. For the sake of reducing conservatism, a method of probabilistic interval time-varying delay is proposed by introducing two certain intervals with known probability distributions. Moreover, two different disturbances are taken into account. One of the disturbances is produced by an exogenous system which acts through the input channel, while the other is usual norm-bounded disturbance. Simultaneously, a disturbance observer is designed to estimate and compensate the disturbance generated by the exogenous system. By constructing an appropriate Lyapunov–Krasovskii function, a sufficient criterion is obtained to ensure both the exponential synchronization and prescribed performance index. Finally, the simulation examples are employed to demonstrate the validity of the theoretical results.
{"title":"Disturbance observer-based PID synchronization control of complex networks with probabilistic interval time-varying delays and multiple disturbances","authors":"Yujing Shi, Hongyang Lv, Dongyan Chen","doi":"10.1002/oca.3084","DOIUrl":"https://doi.org/10.1002/oca.3084","url":null,"abstract":"In this article, the disturbance observer-based proportional–integral–derivative (PID) control protocol is investigated for synchronization of complex networks with probabilistic interval time-varying delays and multiple disturbances. For the sake of reducing conservatism, a method of probabilistic interval time-varying delay is proposed by introducing two certain intervals with known probability distributions. Moreover, two different disturbances are taken into account. One of the disturbances is produced by an exogenous system which acts through the input channel, while the other is usual norm-bounded disturbance. Simultaneously, a disturbance observer is designed to estimate and compensate the disturbance generated by the exogenous system. By constructing an appropriate Lyapunov–Krasovskii function, a sufficient criterion is obtained to ensure both the exponential synchronization and prescribed <math altimg=\"urn:x-wiley:oca:media:oca3084:oca3084-math-0002\" display=\"inline\" location=\"graphic/oca3084-math-0002.png\" overflow=\"scroll\">\u0000<semantics>\u0000<mrow>\u0000<msub>\u0000<mrow>\u0000<mi>H</mi>\u0000</mrow>\u0000<mrow>\u0000<mi>∞</mi>\u0000</mrow>\u0000</msub>\u0000</mrow>\u0000$$ {H}_{infty } $$</annotation>\u0000</semantics></math> performance index. Finally, the simulation examples are employed to demonstrate the validity of the theoretical results.","PeriodicalId":501055,"journal":{"name":"Optimal Control Applications and Methods","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138497052","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 paper addresses the optimal control problem with sparse controls of a Timoshenko beam, its numerical approximation using the finite element method, and the numerical solution via nonsmooth methods. Incorporating sparsity-promoting terms in the cost function is practically useful for beam vibration models and results in the localization of the control action that facilitates the placement of actuators or control devices. We consider two types of sparsity-inducing penalizers: the -norm and the -penalizer, which measures function support. We analyze discretized problems utilizing linear finite elements with a locking-free scheme to approximate the states and adjoint states. We confirm that this approximation has the looking-free property required to achieve a linear convergence linear order of approximation for control case and depending on the set of switching points in the controls. This is similar to the purely -norm penalized optimal control, where the order of approximation is independent of the thickness of the beam.
{"title":"Sparse optimal control of Timoshenko's beam using a locking-free finite element approximation","authors":"Erwin Hernández, Pedro Merino","doi":"10.1002/oca.3085","DOIUrl":"https://doi.org/10.1002/oca.3085","url":null,"abstract":"This paper addresses the optimal control problem with sparse controls of a Timoshenko beam, its numerical approximation using the finite element method, and the numerical solution via nonsmooth methods. Incorporating sparsity-promoting terms in the cost function is practically useful for beam vibration models and results in the localization of the control action that facilitates the placement of actuators or control devices. We consider two types of sparsity-inducing penalizers: the <math altimg=\"urn:x-wiley:oca:media:oca3085:oca3085-math-0001\" display=\"inline\" location=\"graphic/oca3085-math-0001.png\" overflow=\"scroll\">\u0000<semantics>\u0000<mrow>\u0000<msup>\u0000<mrow>\u0000<mi>L</mi>\u0000</mrow>\u0000<mrow>\u0000<mn>1</mn>\u0000</mrow>\u0000</msup>\u0000</mrow>\u0000$$ {L}^1 $$</annotation>\u0000</semantics></math>-norm and the <math altimg=\"urn:x-wiley:oca:media:oca3085:oca3085-math-0002\" display=\"inline\" location=\"graphic/oca3085-math-0002.png\" overflow=\"scroll\">\u0000<semantics>\u0000<mrow>\u0000<msup>\u0000<mrow>\u0000<mi>L</mi>\u0000</mrow>\u0000<mrow>\u0000<mn>0</mn>\u0000</mrow>\u0000</msup>\u0000</mrow>\u0000$$ {L}^0 $$</annotation>\u0000</semantics></math>-penalizer, which measures function support. We analyze discretized problems utilizing linear finite elements with a locking-free scheme to approximate the states and adjoint states. We confirm that this approximation has the looking-free property required to achieve a linear convergence linear order of approximation for <math altimg=\"urn:x-wiley:oca:media:oca3085:oca3085-math-0003\" display=\"inline\" location=\"graphic/oca3085-math-0003.png\" overflow=\"scroll\">\u0000<semantics>\u0000<mrow>\u0000<msup>\u0000<mrow>\u0000<mi>L</mi>\u0000</mrow>\u0000<mrow>\u0000<mn>1</mn>\u0000</mrow>\u0000</msup>\u0000</mrow>\u0000$$ {L}^1 $$</annotation>\u0000</semantics></math> control case and depending on the set of switching points in the <math altimg=\"urn:x-wiley:oca:media:oca3085:oca3085-math-0004\" display=\"inline\" location=\"graphic/oca3085-math-0004.png\" overflow=\"scroll\">\u0000<semantics>\u0000<mrow>\u0000<msup>\u0000<mrow>\u0000<mi>L</mi>\u0000</mrow>\u0000<mrow>\u0000<mn>0</mn>\u0000</mrow>\u0000</msup>\u0000</mrow>\u0000$$ {L}^0 $$</annotation>\u0000</semantics></math> controls. This is similar to the purely <math altimg=\"urn:x-wiley:oca:media:oca3085:oca3085-math-0005\" display=\"inline\" location=\"graphic/oca3085-math-0005.png\" overflow=\"scroll\">\u0000<semantics>\u0000<mrow>\u0000<msup>\u0000<mrow>\u0000<mi>L</mi>\u0000</mrow>\u0000<mrow>\u0000<mn>2</mn>\u0000</mrow>\u0000</msup>\u0000</mrow>\u0000$$ {L}^2 $$</annotation>\u0000</semantics></math>-norm penalized optimal control, where the order of approximation is independent of the thickness of the beam.","PeriodicalId":501055,"journal":{"name":"Optimal Control Applications and Methods","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138497055","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}
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