LINEAR OPTIMAL CONTROL MODEL FOR FELLING THE OIL PALM TREES

2017 ◽  
Vol 79 (4) ◽  
Author(s):  
Noryanti Nasir ◽  
Mohd Ismail Abd Aziz ◽  
Akbar Banitalebi
Keyword(s):  
Optimal Control ◽  
Palm Oil ◽  
Oil Palm ◽  
Minimum Cost ◽  
Real Data ◽  
Control Model ◽  
Optimal Feedback Control ◽  
State Variables ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control

The increases of operational felling cost have prompted the oil palm industry to look at the current practices. The felling activity is considered as the main aspects to improve and maintain palm oil production through the provision of effective and agronomic practices. To support this success and achieve minimum cost of operation, this study aims to develop a time-invariant linear quadratic optimal control model for controlling the felling and harvest rate of the oil palm plantation. The proposed model involves two state variables which are biomass and crude oil. The optimal parameters for the model are estimated using a set of real data collected from Malaysian Palm Oil Board (MPOB). The study analyzes the solution of the resulting control problem within a limited time frame of 30 years and the results provide an optimal feedback control for the felling and harvest rates.

scholarly journals The Optimal Felling Rate in the Palm Oil Plantation System

MATEMATIKA ◽  
2019 ◽  
Vol 35 (1) ◽  
pp. 95-104
Author(s):  
Mohd Ismail Abd Aziz ◽  
Noryanti Nasir ◽  
Akbar Banitalebi
Keyword(s):  
Optimal Control ◽  
Palm Oil ◽  
Oil Palm ◽  
Oil Production ◽  
Real Data ◽  
Palm Trees ◽  
Environmental Friendly ◽  
Proposed Model ◽  
Carbon Absorption ◽  
Plantation System

Successful palm oil plantation should have high returns profit, clean and environmental friendly. Since oil palm trees have a long life and it takes years to be fully grown, controlling the felling rate of the palm oil trees is a fundamental challenge. It needs to be addressed in order to maximize oil production. However, a good arrangement of the felling palm oil trees may still affect the amount of carbon absorption. The objective of this study is to develop an optimal felling model of the palm oil plantation system taking into account both oil production and carbon absorption. The model facilitates in providing the optimal control of felling rate that results in maximizing both oil production and carbon absorption. With this aim, the model is formulated considering palm oil biomass, carbon absorption rate, oil production rate and the average prices of carbon and oil palm. A set of real data is used to estimate the parameters of the model and numerical simulation is conducted to highlight the application of the proposed model. The resulting parameter estimation is solved that leads to an optimal control of felling rate problem.

scholarly journals A New Approach for Solving Optimal Nonlinear Control Problems Using Decriminalization and Rationalized Haar Functions

2011 ◽  
Vol 1 ◽  
pp. 387-394 ◽  
Author(s):  
Zhen Yu Han ◽  
Shu Rong Li
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Nonlinear Optimal Control ◽  
Control Problems ◽  
State Variables ◽  
Linear Quadratic ◽  
Control Variables ◽  
Linear Quadratic Optimal Control ◽  
Haar Functions ◽  
And Control

This paper presents a numerical method based on quasilinearization and rationalized Haar functions for solving nonlinear optimal control problems including terminal state constraints, state and control inequality constraints. The optimal control problem is converted into a sequence of quadratic programming problems. The rationalized Haar functions with unknown coefficients are used to approximate the control variables and the derivative of the state variables. By adding artificial controls, the number of state and control variables is equal. Then the quasilinearization method is used to change the nonlinear optimal control problems with a sequence of constrained linear-quadratic optimal control problems. To show the effectiveness of the proposed method, the simulation results of two constrained nonlinear optimal control problems are presented.

scholarly journals Stochastic linear quadratic optimal control problems for mean-field stochastic evolution equations

2020 ◽  
Vol 26 ◽  
pp. 127
Author(s):  
Qi Lü
Keyword(s):  
Optimal Control ◽  
Regular Solution ◽  
Mean Field ◽  
Riccati Equations ◽  
Optimal Feedback Control ◽  
Stochastic Evolution ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Optimal Feedback ◽  
Quadratic Optimal Control

We study a linear quadratic optimal control problem for mean-field stochastic evolution equation with the assumption that all the coefficients concerned in the problem are deterministic. We show that the existence of optimal feedback operators is equivalent to that of regular solution to the system which is coupled by two Riccati equations and an explicit formula of the optimal feedback control operator is given via the regular solution. We also show that the mentioned Riccati equations admit a unique strongly regular solution when the cost functional is uniformly convex.

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.

scholarly journals Convergence results for an averaged LQR problem with applications to reinforcement learning

2021 ◽  
Author(s):  
Andrea Pesare ◽  
Michele Palladino ◽  
Maurizio Falcone
Keyword(s):  
Optimal Control ◽  
Reinforcement Learning ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Current System ◽  
Numerical Test ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Lqr Problem ◽  
Quadratic Optimal Control

AbstractIn this paper, we will deal with a linear quadratic optimal control problem with unknown dynamics. As a modeling assumption, we will suppose that the knowledge that an agent has on the current system is represented by a probability distribution $$\pi $$ π on the space of matrices. Furthermore, we will assume that such a probability measure is opportunely updated to take into account the increased experience that the agent obtains while exploring the environment, approximating with increasing accuracy the underlying dynamics. Under these assumptions, we will show that the optimal control obtained by solving the “average” linear quadratic optimal control problem with respect to a certain $$\pi $$ π converges to the optimal control driven related to the linear quadratic optimal control problem governed by the actual, underlying dynamics. This approach is closely related to model-based reinforcement learning algorithms where prior and posterior probability distributions describing the knowledge on the uncertain system are recursively updated. In the last section, we will show a numerical test that confirms the theoretical results.

scholarly journals Two Inverse Problems Solution by Feedback Tracking Control

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 137
Author(s):  
Vladimir Turetsky
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Feedback Linearization ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Linear Quadratic Tracking ◽  
Ill Posed ◽  
Quadratic Optimal Control ◽  
Quadratic Tracking

Two inverse ill-posed problems are considered. The first problem is an input restoration of a linear system. The second one is a restoration of time-dependent coefficients of a linear ordinary differential equation. Both problems are reformulated as auxiliary optimal control problems with regularizing cost functional. For the coefficients restoration problem, two control models are proposed. In the first model, the control coefficients are approximated by the output and the estimates of its derivatives. This model yields an approximating linear-quadratic optimal control problem having a known explicit solution. The derivatives are also obtained as auxiliary linear-quadratic tracking controls. The second control model is accurate and leads to a bilinear-quadratic optimal control problem. The latter is tackled in two ways: by an iterative procedure and by a feedback linearization. Simulation results show that a bilinear model provides more accurate coefficients estimates.

scholarly journals A Hida–Malliavin white noise calculus approach to optimal control

2018 ◽  
Vol 21 (03) ◽  
pp. 1850014
Author(s):  
Nacira Agram ◽  
Bernt Øksendal
Keyword(s):  
Optimal Control ◽  
Diffusion Coefficient ◽  
White Noise ◽  
Backward Stochastic Differential Equation ◽  
Second Order ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Alternative Approach ◽  
Quadratic Optimal Control ◽  
White Noise Calculus

The classical maximum principle for optimal stochastic control states that if a control [Formula: see text] is optimal, then the corresponding Hamiltonian has a maximum at [Formula: see text]. The first proofs for this result assumed that the control did not enter the diffusion coefficient. Moreover, it was assumed that there were no jumps in the system. Subsequently, it was discovered by Shige Peng (still assuming no jumps) that one could also allow the diffusion coefficient to depend on the control, provided that the corresponding adjoint backward stochastic differential equation (BSDE) for the first-order derivative was extended to include an extra BSDE for the second-order derivatives. In this paper, we present an alternative approach based on Hida–Malliavin calculus and white noise theory. This enables us to handle the general case with jumps, allowing both the diffusion coefficient and the jump coefficient to depend on the control, and we do not need the extra BSDE with second-order derivatives. The result is illustrated by an example of a constrained linear-quadratic optimal control.

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