Hierarchical controller synthesis using ( γ , δ )-Similarity.

Area of Science:

• Control Theory
• Computer Science
• Systems Engineering

Background:

• Scalability issues hinder controller synthesis for complex non-deterministic systems.
• Existing methods struggle with large-scale control problems.
• Hierarchical approaches offer potential solutions for managing complexity.

Purpose of the Study:

• To develop a hierarchical control scheme for synthesizing controllers for non-deterministic systems.
• To address scalability limitations in traditional controller synthesis.
• To enable the creation of effective controllers for complex systems.

Main Methods:

• Developed a hierarchical control scheme based on (gamma, delta)-similarity.
• Introduced and characterized (gamma, delta)-abstraction using L2 approximation metric.
• Proposed a step-by-step procedure for constructing an interface between abstract and concrete systems.
• Synthesized an abstract controller and refined it into a concrete controller.

Main Results:

• Successfully demonstrated a hierarchical approach to controller synthesis.
• Quantified the behavioral similarity between concrete systems and their abstractions.
• Provided a method for interface construction to bridge abstraction levels.
• Enabled the synthesis of controllers for non-deterministic systems overcoming scalability challenges.

Conclusions:

• The proposed hierarchical control scheme effectively compensates for scalability issues.
• (gamma, delta)-abstraction provides a robust framework for controller synthesis.
• The method facilitates the design of controllers for complex non-deterministic systems.