Overlapping state-input-output decomposition of complex systems with guaranteed structural observability and...

Area of Science:

• Control Systems Engineering
• Systems Theory
• Optimization

Background:

• Complex dynamic systems present significant analytical and control challenges.
• Decomposition into lower-order subsystems is a key strategy to manage complexity.
• Existing methods may not effectively handle overlapping subsystem structures.

Purpose of the Study:

• To propose an overlapping ϵ-decomposition method for complex dynamic systems.
• To guarantee structural observability and controllability of the decomposed subsystems.
• To systematically detect both disjoint and overlapping structures within dynamic systems.

Main Methods:

• Formulation of a single optimization problem for system decomposition.
• Development of an approach based on optimization and graph theory.
• Extension of decomposition to ensure structural observability and controllability.

Main Results:

• A novel overlapping ϵ-decomposition technique is presented.
• The method effectively decomposes systems into weakly coupled subsystems with potential overlaps.
• Simulations demonstrate the approach's effectiveness on ship boiler and power system case studies.

Conclusions:

• The proposed optimization-based decomposition systematically identifies system structures.
• The method ensures essential properties like structural observability and controllability.
• This approach offers a robust tool for analyzing and controlling complex dynamic systems.