A Review on the Direct and Indirect Methods for Solving Optimal Control Problems with Differential-Algebraic Constraints

2015 ◽  
pp. 91-105 ◽  
Author(s):  
Paweł Dra̧g ◽  
Krystyn Styczeń ◽  
Marlena Kwiatkowska ◽  
Andrzej Szczurek
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Indirect Methods ◽  
Algebraic Constraints ◽  
Direct And Indirect Methods

scholarly journals Comparison of direct and indirect methods for minimum lap time optimal control problems

2018 ◽  
Vol 57 (5) ◽  
pp. 665-696 ◽  
Author(s):  
Nicola Dal Bianco ◽  
Enrico Bertolazzi ◽  
Francesco Biral ◽  
Matteo Massaro
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Time Optimal Control ◽  
Control Problems ◽  
Indirect Methods ◽  
Time Optimal ◽  
Direct And Indirect Methods

scholarly journals BVPs Codes for Solving Optimal Control Problems

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2618
Author(s):  
Francesca Mazzia ◽  
Giuseppina Settanni
Keyword(s):  
Optimal Control ◽  
Numerical Methods ◽  
Boundary Value Problems ◽  
Optimal Control Problems ◽  
Boundary Value ◽  
Minimum Principle ◽  
General Purpose ◽  
Control Problems ◽  
Indirect Methods ◽  
Interesting Class

Optimal control problems arise in many applications and need suitable numerical methods to obtain a solution. The indirect methods are an interesting class of methods based on the Pontryagin’s minimum principle that generates Hamiltonian Boundary Value Problems (BVPs). In this paper, we review some general-purpose codes for the solution of BVPs and we show their efficiency in solving some challenging optimal control problems.

scholarly journals Optimal Control Applied to Vaccination and Testing Policies for COVID-19

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3100
Author(s):  
Alberto Olivares ◽  
Ernesto Staffetti
Keyword(s):  
Optimal Control ◽  
Disease Transmission ◽  
Optimal Control Problems ◽  
Vaccination Rate ◽  
Control Problems ◽  
Vaccination Programs ◽  
Infected People ◽  
Control Approach ◽  
Algebraic Constraints ◽  
The Cost

In this paper, several policies for controlling the spread of SARS-CoV-2 are determined under the assumption that a limited number of effective COVID-19 vaccines and tests are available. These policies are calculated for different vaccination scenarios representing vaccine supply and administration restrictions, plus their impacts on the disease transmission are analyzed. The policies are determined by solving optimal control problems of a compartmental epidemic model, in which the control variables are the vaccination rate and the testing rate for the detection of asymptomatic infected people. A combination of the proportion of threatened and deceased people together with the cost of vaccination of susceptible people, and detection of asymptomatic infected people, is taken as the objective functional to be minimized, whereas different types of algebraic constraints are considered to represent several vaccination scenarios. A direct transcription method is employed to solve these optimal control problems. More specifically, the Hermite–Simpson collocation technique is used. The results of the numerical experiments show that the optimal control approach offers healthcare system managers a helpful resource for designing vaccination programs and testing plans to prevent COVID-19 transmission.

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

Sweep Algorithm for Solving Discrete Optimal Control Problems with Three-point Boundary Conditions

2008 ◽  
Vol 40 (7) ◽  
pp. 48-58 ◽  
Author(s):  
Fikret Akhmed Ali Ogly Aliev ◽  
Rena Takhir kyzy Zulfugarova ◽  
Mutallim Mirzaakhmed ogly Mutallimov
Keyword(s):  
Optimal Control ◽  
Boundary Conditions ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Point Boundary ◽  
Discrete Optimal Control ◽  
Sweep Algorithm
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