Optimization of Communication Network Topology in Distributed Control Systems Subject to Prescribed Decay Rate.

Area of Science:

• Control Systems Engineering
• Optimization Theory
• Network Science

Background:

• Distributed control systems require efficient network topologies for optimal performance.
• Ensuring a specific decay rate in transient responses is crucial but challenging.
• Eigenvalue optimization for parametric matrices is a complex, nonconvex problem.

Purpose of the Study:

• To develop a cohesive framework for finding optimal directed control network topologies.
• To minimize the number of links in the control network while satisfying decay rate constraints.
• To address the nonconvex optimization problem arising from eigenvalue constraints.

Main Methods:

• Formulating a convex equivalent optimization problem for eigenvalue constraints.
• Integrating sparsity-promoting optimal control with the convex problem.
• Employing the alternating direction method of multipliers (ADMM) for decomposition.
• Developing a framework that balances control network topology and system decay rate.

Main Results:

• A convex equivalent optimization problem was derived, simplifying eigenvalue optimization.
• The proposed method yields a state-feedback matrix for faster decay rates with considered input costs.
• ADMM decomposed the combinatorial optimization problem into solvable subproblems.
• Simulation results demonstrated the framework's effectiveness in optimizing network topology and decay rates.

Conclusions:

• The proposed framework effectively designs optimal directed control network topologies.
• It successfully minimizes network links while guaranteeing prescribed decay rates.
• The method provides a practical approach to complex eigenvalue optimization problems in control systems.