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Optimal Control for Partially Observed Nonlinear Interval Systems.

¹Department of Electrical Engineering, Higher Technological Institute, P.O. Box 228, Ramadan 10th City, Sharkia K1N-6NP, Egypt

Journal of Dynamic Systems, Measurement, and Control

|January 13, 2021

Summary

This summary is machine-generated.

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This study introduces a novel method for optimal control of nonlinear systems with interval differential equations. The approach transforms interval problems into ordinary differential equations, simplifying analysis and enabling effective control strategies.

Area of Science:

Control Theory
Differential Equations
Interval Analysis

Background:

Optimal control problems often involve complex systems, including those described by nonlinear, time-varying, and partially observed interval differential equations.
Existing methods may require specialized interval mathematics, posing computational challenges.

Purpose of the Study:

To develop a method for solving optimal control problems for nonlinear time-varying partially observed interval differential equations.
To transform interval control problems into equivalent ordinary control problems, avoiding complex interval mathematics.

Main Methods:

Utilizing the bounds of state, observation, and control processes to derive ordinary differential equations governing these bounds.
Transforming the interval control problem into an equivalent ordinary control problem.

Keywords:

interval differential equations interval systems optimal control variational calculus

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Applying variational arguments to derive necessary conditions of optimality for the transformed problem.

Main Results:

A novel set of ordinary differential equations describing the bounds of the system processes was developed.
The interval control problem was successfully transformed into an equivalent ordinary control problem.
Necessary conditions for optimality were derived for the transformed problem.

Conclusions:

The proposed method effectively transforms complex interval control problems into tractable ordinary control problems.
The approach simplifies the analysis and solution of optimal control for systems described by interval differential equations.
Numerical simulations demonstrate the effectiveness of the proposed control scheme.