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Lagrange Multipliers: Problem Solving

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A silo with a cylindrical base, flat bottom, and hemispherical roof is a common design in agricultural and industrial storage due to its structural efficiency and ease of construction. Optimizing its dimensions to maximize storage capacity for a given amount of material—i.e., a fixed surface area—is a classic problem in applied calculus and engineering design. The key parameters are the radius r of the base and the height h of the cylindrical section.The total volume of the silo is obtained by...

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Updated: Jul 15, 2026

The Modular Design and Production of an Intelligent Robot Based on a Closed-Loop Control Strategy

The Modular Design and Production of an Intelligent Robot Based on a Closed-Loop Control Strategy

Published on: October 14, 2017

Solution of nonlinear optimal control problems using a semi-exhaustive search.

¹Department of Process Engineering and Applied Science, Dalhousie University, Halifax, NS, Canada. yash.gupta@dal.ca

ISA Transactions

|April 5, 2007

Summary

A novel semi-exhaustive search method efficiently solves complex nonlinear optimal control problems. This approach offers smooth convergence and significantly reduces computation time compared to Iterative Dynamic Programming (IDP).

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Last Updated: Jul 15, 2026

The Modular Design and Production of an Intelligent Robot Based on a Closed-Loop Control Strategy

The Modular Design and Production of an Intelligent Robot Based on a Closed-Loop Control Strategy

Published on: October 14, 2017

Area of Science:

Engineering
Computer Science
Applied Mathematics

Background:

Solving nonlinear optimal control problems is computationally intensive.
Current methods often require extensive computational resources and time.
Comparing different algorithms is crucial for identifying efficient solutions.

Purpose of the Study:

To evaluate the performance of a semi-exhaustive search method for nonlinear optimal control.
To compare this new method against the established Iterative Dynamic Programming (IDP) algorithm.
To demonstrate the effectiveness and efficiency of the proposed semi-exhaustive search.

Main Methods:

A semi-exhaustive search algorithm was developed and implemented.
The algorithm was tested on five distinct nonlinear optimal control problems.
Performance was benchmarked against the Iterative Dynamic Programming (IDP) algorithm, measuring convergence and computational time.

Main Results:

The semi-exhaustive search method demonstrated smooth convergence to optimal solutions.
This method required significantly less computational time compared to the IDP algorithm.
Consistent performance was observed across all five test problems.

Conclusions:

The semi-exhaustive search method is a viable and efficient alternative for solving nonlinear optimal control problems.
This approach offers advantages in terms of computational efficiency and convergence behavior.
Further research can explore its application to more complex and larger-scale control problems.