Decentralized H₂ Control for Discrete-Time Networked Systems With Positivity Constraint

Area of Science:

• Control Theory
• Systems Engineering
• Networked Systems

Background:

• Decentralized H2 state-feedback control for networked discrete-time systems with positivity constraints is a complex problem.
• Existing methods often provide only sufficient conditions, potentially leading to suboptimal solutions.
• The inherent nonconvexity of the problem for single positive systems presents significant challenges.

Purpose of the Study:

• To investigate the decentralized H2 state-feedback control problem for networked discrete-time positive systems.
• To develop necessary and sufficient synthesis conditions, overcoming limitations of existing approaches.
• To propose a primal-dual iterative algorithm that guarantees convergence to the global minimum.

Main Methods:

• Utilizing a primal-dual scheme to derive control synthesis conditions.
• Formulating equivalent conditions for networked positive systems.
• Developing a primal-dual iterative algorithm for solving the control problem.
• Employing simulation examples for validation.

Main Results:

• Established necessary and sufficient conditions for decentralized H2 state-feedback control in networked positive systems.
• Developed a primal-dual iterative algorithm that avoids local minima.
• Demonstrated the effectiveness of the proposed method through two simulation examples.

Conclusions:

• The primal-dual scheme offers a robust framework for solving the challenging decentralized H2 state-feedback control problem.
• The proposed algorithm ensures convergence to optimal solutions, unlike methods relying solely on sufficient conditions.
• The findings advance the theory and practice of control for networked positive systems.