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Costate prediction based optimal control for non-linear hybrid systems.

Minghui Hu¹, Yongshan Wang, Huihe Shao

¹School of Electrionic, Information and Electrical Engineering, Shanghai Jiaotong University, Shanghai 200240, China. agile_hu@sjtu.edu.cn <agile_hu@sjtu.edu.cn>

ISA Transactions

|August 10, 2007

Summary

This study presents an iterative method for solving complex non-linear optimal control problems in discrete-continuous systems. The approach decomposes the global problem into manageable subsystems, ensuring accurate solutions even with model-reality discrepancies.

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Area of Science:

Control Theory
Applied Mathematics
Systems Engineering

Background:

Non-linear discrete-continuous systems present significant challenges in optimal control.
Existing methods may struggle with model-reality differences and computational complexity.

Purpose of the Study:

To develop an iterative algorithm for solving non-linear discrete-continuous systems optimal control problems.
To demonstrate a hierarchical decomposition approach for complex control systems.

Main Methods:

A mixed approach using discrete cost functions and continuous state variables.
Decomposition of the global problem into local subsystem problems with a coordinator.
Iterative solution using interconnected costate prediction to handle model-reality differences.

Main Results:

The proposed method effectively solves non-linear discrete-continuous optimal control problems.
The hierarchical framework allows for efficient decomposition and coordination of subsystems.
The iterative costate prediction ensures accurate solutions for real-world systems with model inaccuracies.

Conclusions:

The developed iterative algorithm provides an efficient and accurate solution for non-linear discrete-continuous optimal control.
The hierarchical decomposition strategy is effective for managing complex systems.
The method's convergence and efficiency are validated through simulation studies.