H-Infinity Control Design and Entropy Minimization for Second Order Systems

A modified Newton-Kleinman method is introduced to solve the algebraic Riccati equations present in the H-infinity controller synthesis problem. The new method utilizes the inherent properties of the mass, stiffness and damping matrices present in second order systems to efficiently compute the solutions to the algebraic Riccati equations for large systems, with an analytical proof of convergence. This allows for efficient H-infinity controller synthesis as compared to traditional methods such as the Hamiltonian approach and the Newton-Kleinnman method when applied to the same systems. The entropy formulation of the H-infinity controller synthesis problem is then utilized in conjunction with the new algorithms to develop a data-driven controller that balances the total entropy and the quadratic cost functional associated with the problem.