In this paper we study a bilinear optimal control problem for a diffusive Lotka-Volterra competition model with chemo-repulsion in a bounded domain of ℝ^(ℕ),N=2,3.This model describes the competition of two species in...In this paper we study a bilinear optimal control problem for a diffusive Lotka-Volterra competition model with chemo-repulsion in a bounded domain of ℝ^(ℕ),N=2,3.This model describes the competition of two species in which one of them avoid encounters with rivals through a chemo-repulsion mechanism.We prove the existence and uniqueness of weak-strong solutions,and then we analyze the existence of a global optimal solution for a related bilinear optimal control problem,where the control is acting on the chemical signal.Posteriorly,we derive first-order optimality conditions for local optimal solutions using the Lagrange multipliers theory.Finally,we propose a discrete approximation scheme of the optimality system based on the gradient method,which is validated with some computational experiments.展开更多
A bicubic B-spline finite element method is proposed to solve optimal control problems governed by fourth-order semilinear parabolic partial differential equations.Its key feature is the selection of bicubic B-splines...A bicubic B-spline finite element method is proposed to solve optimal control problems governed by fourth-order semilinear parabolic partial differential equations.Its key feature is the selection of bicubic B-splines as trial functions to approximate the state and costate variables in two space dimensions.A Crank-Nicolson difference scheme is constructed for time discretization.The resulting numerical solutions belong to C2in space,and the order of the coefficient matrix is low.Moreover,the Bogner-Fox-Schmit element is considered for comparison.Two numerical experiments demonstrate the feasibility and effectiveness of the proposed method.展开更多
文摘本文针对一种新型遥控无人潜水器(Remote Operated Vehicle,ROV)拖曳采集装置(Mining Robot,MRT)的路径跟踪问题,提出一种路径跟踪控制方法。首先建立简化的ROV型深海采集装置的运动模型,随后提出一种基于线性模型预测控制算法(Linear Model Predictive Control,LMPC)和非线性模型预测控制器(Nonlinear Model Predictive Control,NMPC)的路径跟踪算法。与传统的模型预测控制器(Model Predictive Control,MPC)不同,本文提出的双层模型预测控制算法(Double Model Predictive Control,DMPC)由两部分组成:(1)由MRT的LMPC控制器计算得到MRT的速度控制律,用于快速收敛MRT的跟踪误差;(2)由ROV的NMPC控制器计算得到ROV的控制输入,用于响应MRT的速度控制律。在DMPC的设计中,有效考虑状态量和控制量约束,其中为了保证ROV控制输入的平顺性,引入ROV的控制量增量约束。最后,设计仿真实验用于验证MRT的路径跟踪效果,数值仿真结果证明了该算法的有效性。
基金supported by Vicerrectoría de Investigación y Extensión of Universidad Industrial de Santander,Colombia,project 3704.
文摘In this paper we study a bilinear optimal control problem for a diffusive Lotka-Volterra competition model with chemo-repulsion in a bounded domain of ℝ^(ℕ),N=2,3.This model describes the competition of two species in which one of them avoid encounters with rivals through a chemo-repulsion mechanism.We prove the existence and uniqueness of weak-strong solutions,and then we analyze the existence of a global optimal solution for a related bilinear optimal control problem,where the control is acting on the chemical signal.Posteriorly,we derive first-order optimality conditions for local optimal solutions using the Lagrange multipliers theory.Finally,we propose a discrete approximation scheme of the optimality system based on the gradient method,which is validated with some computational experiments.
基金supported by the National Natural Science Foundation of China(11871312,12131014)the Natural Science Foundation of Shandong Province,China(ZR2023MA086)。
文摘A bicubic B-spline finite element method is proposed to solve optimal control problems governed by fourth-order semilinear parabolic partial differential equations.Its key feature is the selection of bicubic B-splines as trial functions to approximate the state and costate variables in two space dimensions.A Crank-Nicolson difference scheme is constructed for time discretization.The resulting numerical solutions belong to C2in space,and the order of the coefficient matrix is low.Moreover,the Bogner-Fox-Schmit element is considered for comparison.Two numerical experiments demonstrate the feasibility and effectiveness of the proposed method.
