Precise integration method for finite horizon H∞ generalized regulator problem

The controllers for H_∞ generalized regulator problem exist if and only if two given Riccati equations have solutions and the product of the solutions meets the restrictive condition of spectral radius. Then the controllers can be generated with these data. Up to now, the existing algorithms could only be used to solve Riccati algebraic equations and compute the corresponding optimal H_∞ -norm, which arise from the infinite horizon H_∞ control problem. The precise integration method, which is developed on the basis of the theory of analogy between structural mechanics and optimal control, can be employed to solve both Riccati differential and algebraic equations. Therefore, the finite and infinite horizon H_∞ regulator problems can be solved using the same method. The paper presents the procedure of solving the Riccati differential equations and computing the optimal H_∞-norm combined with the extended W-W algorithm. It is the essential step in synthesizing controllers for the finite horizon H _∞ generalized regulator problem