A discretized algorithm for the solution of a constrained, continuous quadratic control problem

Olorunsola, SA; Olotu, O.

doi:10.4314/jonamp.v8i1.40017

Cited by 3 publications

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“…In [1,2] , the scheme establishing the solution of optimal control problems constrained by evolution equation of the delay type with matrix coefficients was presented, without addressing the geometric convergence ratio profile. Here, a class of optimal control problems constrained by ordinary differential equation with matrix coefficients is considered.…”

Section: Introductionmentioning

confidence: 99%

Convergence Ratio Profile for Optimal Control Problems Governed by Ordinary Differential Equations with Matrix Coefficients

Olotu¹,

Olorunsola²

2008

American J. of Applied Sciences

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The geometric convergence ratio, the main focus of a discretized scheme for constrained quadratic control problem was examined. In order to allow for the numerical applications of the developed scheme, discretizing the time interval and using Eulers scheme for its differential constraint obtained a finite dimensional approximation. Applying the penalty function method, an unconstrained problem was obtained on function minimization with bilinear form expression. This finally led to the construction of an operator. The Scheme was applied to a sampled problem and it exhibited geometric convergence ratio, α, in the open interval (0, 1) as depicted in column 6 of Table 1

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Section: Introductionmentioning

confidence: 99%

Convergence Ratio Profile for Optimal Control Problems Governed by Ordinary Differential Equations with Matrix Coefficients

Olotu¹,

Olorunsola²

2008

American J. of Applied Sciences

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Quadratic Convergence Ratio of Constrained Optimal Control Problems

Olotu¹

2010

Journal of Mathematics and Statistics

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Problem statement: Earlier Researchers developed algorithms for solving quadratic control problems, but did not address the quadratic convergence ratio profile. Approach: Hence, the objective of this work is using our developed scheme, Discretized Continuous Algorithm (DCA), to examine both convergence profile and quadratic ratio profile demonstrating the effectiveness and efficiency of the scheme. Methodologically, we obtained generalized unconstrained formulation of the constrained problem. Using Conjugate Gradient Method (CGM) and linear ratio of the deviation of the generated iterates from the exact solution, we obtained respectively the objective values and the quadratic ratio values. Results: If these quadratic ratio values fall within the interval [1, ∞], then the convergence is quadratically convergent. Two examples were examined and satisfied the condition for quadratic convergence. Conclusion: Thus, we can conclude that the algorithm is optimally effective and efficient

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Modified Gradient Flow Method for Solving One-Dimensional Optimal Control Problem Governed by Linear Equality Constraint

Olotu

Dawodu

2022

J. Nig. Soc. Phys. Sci.

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This study presents a computational technique developed for solving linearly constraint optimal control problems using the Gradient Flow Method. This proposed method, called the Modified Gradient Flow Method (MGFM), is based on the continuous gradient flow reformulation of constrained optimization problem with three-level implicit time discretization scheme. The three-level splitting parameters for the discretization of the gradient flow equations are such that the sum of the parameters equal to one (\theta1 + \theta2 +\theta3=1). The Linear and quadratic convergence of the scheme were analyzed and were shown to have first order scheme when each parameter exist in the domain [0, 1] and second order when the third parameter equal to one. Numerical experiments were carried out and the results showed that the approach is very effective for handling this class of constrained optimal control problems. It also compared favorably with the analytical solutions and performed better than the existing schemes in terms of convergence and accuracy

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A discretized algorithm for the solution of a constrained, continuous quadratic control problem

Cited by 3 publications

References 0 publications

Convergence Ratio Profile for Optimal Control Problems Governed by Ordinary Differential Equations with Matrix Coefficients

Convergence Ratio Profile for Optimal Control Problems Governed by Ordinary Differential Equations with Matrix Coefficients

Quadratic Convergence Ratio of Constrained Optimal Control Problems

Modified Gradient Flow Method for Solving One-Dimensional Optimal Control Problem Governed by Linear Equality Constraint

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