Related Experiment Video
Updated: Jul 15, 2026
11:53
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).
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.
Related Concept Videos
01:30Lagrange Multipliers: Problem Solving
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...
01:29Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
01:30Gaussian Elimination: Problem Solving
Systems of linear equations in several variables are pivotal in modeling complex scenarios involving multiple unknowns and constraints. Such systems are widely used in various fields to represent relationships where several conditions must be simultaneously satisfied. Each variable in the system corresponds to an unknown quantity, while each equation imposes a linear constraint, leading to a structured approach for analyzing and solving real-world problems.A system of three equations with three...
01:21Differential Equations: Problem Solving
When analyzing the motion of falling objects, it is essential to consider not only the force of gravity but also the opposing force of air resistance. A practical example involves releasing a heavy test weight during a safety check on a ship. As the weight falls from rest, gravity accelerates it downward while air resistance exerts an upward force that increases with velocity. This dynamic interplay of forces is well described by differential equations, which provide a mathematical framework...
01:28Lagrange Multipliers: Two Constraints
The method of Lagrange multipliers with two constraints is used to optimize a function subject to two independent constraints. In many applications, the objective function represents a quantity to be maximized or minimized, such as cost, area, distance, or energy. The two constraints represent requirements that the solution must satisfy, such as fixed volume, limited resources, or prescribed dimensions.For a function of three variables, each constraint forms a surface in three-dimensional space.
01:29Mathematical Modeling: Problem Solving
Mathematical modeling transforms real-world scenarios into mathematical expressions, allowing for structured problem-solving and analysis. This process involves defining the situation, assigning variables to measurable quantities, selecting an appropriate model, and solving the resulting equation. Such models are invaluable in finance, providing precise methods to evaluate investments, loans, and repayment structures.A widely used example is the calculation of fixed monthly payments on a loan,...