Fuzzy time-optimal controller (FTOC) for second order nonlinear systems

Area of Science:

• Control Systems Engineering
• Fuzzy Logic Applications
• Non-linear System Dynamics

Background:

• Classical optimal control often involves solving complex two-point boundary value problems (TPBVPs) using Pontryagin's Minimum Principle (PMP).
• Existing fuzzy controllers may not always provide near-optimal performance for non-linear systems.
• There is a need for alternative methods to achieve optimal control without analytical problem-solving.

Purpose of the Study:

• To develop a new fuzzy time-optimal controller as an alternative to classical methods for non-linear systems.
• To design a controller that approximates the performance of traditional time-optimal controllers.
• To investigate online tuning of membership functions for improved control output.

Main Methods:

• A novel fuzzy time-optimal controller with two inputs and a bang-bang output is proposed.
• Input membership functions are tuned online to optimize the controller's time-optimal output.
• Controller rules are designed to ensure stability and optimality conditions.
• A sliding mode controller is used for benchmarking and comparison.

Main Results:

• The proposed fuzzy controller closely approximates the output of classical time-optimal controllers.
• The controller demonstrates optimal behavior for second-order non-linear systems.
• Simulations on three non-linear examples show promising results, validating the controller's effectiveness.

Conclusions:

• The developed fuzzy time-optimal controller offers a viable alternative for controlling non-linear systems.
• Online tuning of membership functions enhances the controller's ability to achieve time-optimal performance.
• This research is expected to stimulate further interest in fuzzy controller design for optimal control applications.