scholarly journals PARAOPT: A Parareal Algorithm for Optimality Systems

2020 ◽  
Vol 42 (5) ◽  
pp. A2773-A2802
Author(s):  
Martin J. Gander ◽  
Felix Kwok ◽  
Julien Salomon
Keyword(s):  
Optimality Systems

Modeling and control through leadership of a refined flocking system

2014 ◽  
Vol 25 (02) ◽  
pp. 255-282 ◽  
Author(s):  
Alfio Borzì ◽  
Suttida Wongkaew
Keyword(s):  
Predictive Control ◽  
Control Strategy ◽  
Social Systems ◽  
Open Loop ◽  
Modeling And Control ◽  
Control Scheme ◽  
Nonlinear Conjugate Gradient ◽  
Optimality Systems ◽  
And Control ◽  
Conjugate Gradient Solver

A new refined flocking model that includes self-propelling, friction, attraction and repulsion, and alignment features is presented. This model takes into account various behavioral phenomena observed in biological and social systems. In addition, the presence of a leader is included in the system in order to develop a control strategy for the flocking model to accomplish desired objectives. Specifically, a model predictive control scheme is proposed that requires the solution of a sequence of open-loop optimality systems. An accurate Runge–Kutta scheme to discretize the optimality systems and a nonlinear conjugate gradient solver are implemented and discussed. Numerical experiments are performed that investigate the properties of the refined flocking model and demonstrate the ability of the control strategy to drive the flocking system to attain a desired target configuration and to follow a given trajectory.

A Goal-Oriented Adaptive Moreau-Yosida Algorithm for Control- and State-Constrained Elliptic Control Problems

2016 ◽  
Vol 8 (3) ◽  
pp. 426-448 ◽  
Author(s):  
Andreas Günther ◽  
Moulay Hicham Tber
Keyword(s):  
Piecewise Linear ◽  
Adaptive Mesh ◽  
Control Problems ◽  
Local Error ◽  
Error Estimators ◽  
Variational Discretization ◽  
Elliptic Control Problems ◽  
Optimality Systems ◽  
Elliptic Optimal Control ◽  
And Control

AbstractIn this work, we develop an adaptive algorithm for solving elliptic optimal control problems with simultaneously appearing state and control constraints. The algorithm combines a Moreau-Yosida technique for handling state constraints with a semi-smooth Newton method for solving the optimality systems of the regularized sub-problems. The state and adjoint variables are discretized using continuous piecewise linear finite elements while a variational discretization concept is applied for the control. To perform the adaptive mesh refinements cycle we derive local error estimators which extend the goal-oriented error approach to our setting. The performance of the overall adaptive solver is assessed by numerical examples.

scholarly journals Seeking Best-Balanced Patch-Injecting Strategies through Optimal Control Approach

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Kaifan Huang ◽  
Pengdeng Li ◽  
Lu-Xing Yang ◽  
Xiaofan Yang ◽  
Yuan Yan Tang
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Negative Impact ◽  
Cost Effective ◽  
Control Approach ◽  
Novel Virus ◽  
Optimality Systems ◽  
Objective Functional ◽  
Optimal Control Approach

To restrain escalating computer viruses, new virus patches must be constantly injected into networks. In this scenario, the patch-developing cost should be balanced against the negative impact of virus. This article focuses on seeking best-balanced patch-injecting strategies. First, based on a novel virus-patch interactive model, the original problem is reduced to an optimal control problem, in which (a) each admissible control stands for a feasible patch-injecting strategy and (b) the objective functional measures the balance of a feasible patch-injecting strategy. Second, the solvability of the optimal control problem is proved, and the optimality system for solving the problem is derived. Next, a few best-balanced patch-injecting strategies are presented by solving the corresponding optimality systems. Finally, the effects of some factors on the best balance of a patch-injecting strategy are examined. Our results will be helpful in defending against virus attacks in a cost-effective way.

Optimal control problem in an epidemic disease SIS model with stages and delays

2016 ◽  
Vol 09 (05) ◽  
pp. 1650072 ◽  
Author(s):  
Yongzhen Pei ◽  
Miaomiao Chen ◽  
Xiyin Liang ◽  
Zhumei Xia ◽  
Yunfei Lv ◽  
...  
Keyword(s):  
Optimal Control ◽  
Stage Structure ◽  
Infectious Period ◽  
Optimal Controls ◽  
Epidemic Disease ◽  
Sis Model ◽  
Terminal Time ◽  
Optimality Systems ◽  
Infectious Burden ◽  
Maximal Effort

Based on literature [J. Q. Li, Z. E. Ma and F. Q. Zhang, Stability analysis for an epidemic model with stage structure, J. Appl. Math. Comput. 9 (2008) 1672–1679], incorporating the recovery of the infected population with the length of the infectious periods, a modified epidemic disease SIS model with delay and stage was investigated. First, the criteria keeping stability with delay were given. Next, in order to lower the level of the infected individuals and minimize the cost of treatment, mixed, early and late therapeutic strategies were introduced into our model, respectively. Then we investigated the existence and uniqueness of optimal controls. And then, we expressed the unique optimal control in terms of the solution of the optimality systems. Finally, by numerical simulations, several important results were acquired: (1) The terminal time influenced the early optimal control largely. In detail, for a shorter terminal time it was optimal to initiate treatment with maximal effort at the start of the epidemic and continue treatment with maximal effort until the switch time was arrived. But for a longer terminal time, the maximal treatment effort need not be a prerequisite at the start or end of the epidemic but it was obligatory at the metaphase of the epidemic. (2) For our SIS model, minimizing the total infectious burden of the disease can be achieved by only early optimal treatment tactics. (3) For a disease with a shorter infectious period time, more cost would be spent to control the disease in order to achieve the optimal control objective. Otherwise, a relative lower cost would be to control the disease with a longer infectious period.

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