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Optimal Control for Partially Observed Nonlinear Interval Systems.

T E Dabbous1

  • 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
PubMed
Summary
This summary is machine-generated.

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.

Keywords:
interval differential equationsinterval systemsoptimal controlvariational calculus

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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.
  • 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.