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This study introduces a distributed optimization method for solving continuous-time algebraic Riccati inequalities (ARIs). The novel algorithm efficiently determines ARI feasibility and converges to a solution when one exists, even with distributed matrix information.

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Area of Science:

Control Systems Engineering
Distributed Optimization
Matrix Inequalities

Background:

Continuous-time algebraic Riccati inequalities (ARIs) present computational challenges due to nonlinearity and coupled information structures.
Existing methods often require centralized information, limiting applicability in distributed systems.

Purpose of the Study:

To develop a distributed optimization design for computing continuous-time algebraic Riccati inequalities (ARIs).
To address the inherent nonlinearity, inequality constraints, and coupled information structures in ARI computation.
To enable distributed verification of ARI feasibility.

Main Methods:

A novel design procedure is proposed to handle the complexities of ARIs.
A distributed algorithm based on optimization principles is developed.
Convergence properties of the distributed algorithm are rigorously analyzed.

Main Results:

The proposed distributed algorithm can determine the feasibility of ARIs.
The algorithm converges to a valid solution for feasible ARIs, irrespective of the initial conditions.
The method effectively manages distributed matrix information among agents.

Conclusions:

The developed distributed optimization approach provides an effective solution for computing continuous-time algebraic Riccati inequalities.
This method enhances the capability of distributed systems to solve complex control problems involving inequalities.
The algorithm's convergence guarantees ensure reliable solutions in decentralized settings.