Precise integration method for finite horizon H/sub /spl infin// generalized regulator problem

The controllers for H/sub /spl infin// 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/sub /spl infin//-norm, which arise from the infinite horizon H/sub /spl infin// 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/sub /spl infin// 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/sub /spl infin//-norm combined with the extended W-W algorithm. It is the essential step in synthesizing controllers for the finite horizon H/sub /spl infin// generalized regulator problem.