Optimal Control of Microalgae Growth in Artificially Lighted Photobioreactors : Case study: closed-loop solution for a bilocal optimization problem

Author(s):  
Viorel Minzu ◽  
George Adrian Ifrim
Sensors ◽  
2021 ◽  
Vol 21 (23) ◽  
pp. 8065
Author(s):  
Viorel Minzu ◽  
George Ifrim ◽  
Iulian Arama

A metaheuristic algorithm can be a realistic solution when optimal control problems require a significant computational effort. The problem stated in this work concerns the optimal control of microalgae growth in an artificially lighted photobioreactor working in batch mode. The process and the dynamic model are very well known and have been validated in previous papers. The control solution is a closed-loop structure whose controller generates predicted control sequences. An efficient way to make optimal predictions is to use a metaheuristic algorithm, the particle swarm optimization algorithm. Even if this metaheuristic is efficient in treating predictions with a very large prediction horizon, the main objective of this paper is to find a tool to reduce the controller’s computational complexity. We propose a soft sensor that gives information used to reduce the interval where the control input’s values are placed in each sampling period. The sensor is based on measurement of the biomass concentration and numerical integration of the process model. The returned information concerns the specific growth rate of microalgae and the biomass yield on light energy. Algorithms, which can be used in real-time implementation, are proposed for all modules involved in the simulation series. Details concerning the implementation of the closed loop, controller, and soft sensor are presented. The simulation results prove that the soft sensor leads to a significant decrease in computational complexity.


2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang

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.


2018 ◽  
Vol 2018 (7) ◽  
pp. 5417-5435
Author(s):  
Alison Nojima ◽  
Adam Ross ◽  
Ken Glotzbach ◽  
Todd Jordan ◽  
George Hanson
Keyword(s):  

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 738
Author(s):  
Muhammad Munir Butt

Optimal control problems governed by stochastic partial differential equations have become an important field in applied mathematics. In this article, we investigate one such important optimization problem, that is, the stochastic Stokes control problem with forcing term perturbed by noise. A multigrid scheme with three-factor coarsening to solve the corresponding discretized control problem is presented. On staggered grids, a three-factor coarsening strategy helps in simplifying the inter-grid transfer operators and reduction in computation (CPU time). For smoothing, a distributive Gauss–Seidel scheme with a line search strategy is employed. To validate the proposed multigrid staggered grid framework, numerical results are presented with white noise at the end.


Author(s):  
Daniel González-Arribas ◽  
Manuel Soler ◽  
Javier López-Leonés ◽  
Enrique Casado ◽  
Manuel Sanjurjo-Rivo

The future air traffic management system is to be built around the notion of trajectory-based operations. It will rely on automated tools related to trajectory prediction in order to define, share, revise, negotiate and update the trajectory of the aircraft before and during the flight, in some case, in near real time. This paper illustrates how existing standards on trajectory description such as the aircraft intent description language can be enhanced including optimisation capabilities based on numerical optimal control. The Aircraft Intent Description Language is a formal language that has been created in order to describe aircraft intent information in a rigorous, unambiguous and flexible manner. It has been implemented in a platform for a modular design of the trajectory generation process. A case study is presented to explore its effectiveness and identify the requirements and needs to generate optimised aircraft intents with higher automation and flexibility. Preliminary results show the suitability of numerical optimal control to design optimised aircraft intents based on the aircraft intent description language.


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