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Related Experiment Video

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Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

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Solutions of nonlinear constrained optimal control problems using quasilinearization and variational pseudospectral

Mingwu Li¹, Haijun Peng¹

¹Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, 116024 Dalian, People׳s Republic of China.

ISA Transactions

|February 27, 2016

Summary

This study introduces a novel method for nonlinear optimal control problems, transforming them into solvable linear complementary problems. This approach offers high precision and efficiency for complex control tasks.

Keywords:

Hamiltonian boundary value problems Optimal control problems Pesudospectral methods Quasilinearization Variational principles

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Area of Science:

Control Theory
Applied Mathematics
Numerical Analysis

Background:

Nonlinear constrained optimal control problems present significant computational challenges.
Existing methods often require complex formulations or extensive computational resources.

Purpose of the Study:

To develop an efficient and accurate alternative method for solving nonlinear constrained optimal control problems.
To transform these complex problems into more tractable forms for numerical solution.

Main Methods:

Quasilinearization is employed to convert nonlinear optimal control problems into a sequence of linear quadratic (LQ) optimal control problems.
A variational pseudospectral method, utilizing dual variational principles and pseudospectral approximations, transforms the LQ problem into linear complementary problems (LCPs).

Main Results:

The proposed method demonstrates high efficiency due to quasilinearization and the properties of variational principles.
High-precision solutions are achievable with fewer time nodes, and boundary conditions can be prescribed due to pseudospectral approximations.
The method avoids the need for extra costate estimations by construction using dual variational principles.

Conclusions:

The developed method provides an effective and advantageous approach for nonlinear constrained optimal control.
It offers a computationally efficient and accurate alternative to existing techniques for solving complex control problems.