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

Abstract 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 associated with 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 standard 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.