¿-coupling method for near-optimum design of large-scale linear systems

The solution of an optimal state regulator problem for an nth-order linear system with quadratic performance index involves the solution of a matrix Riccati equation, consisting of n(n + l)/2 coupled nonlinear equations. In this paper, the notion of ¿-coupled systems is introduced, permitting the approximation of the Riccati-equation solution by a truncated Maclaurin series with special properties. The first term of this series is computed from decoupled low-order subsystem Riccati equations. The higher order terms are computed from decoupled linear equations. Furthermore, an mth order series for the Riccati matrix yields a (2m + l)th order approximation to the optimal performance. Thus this procedure results in significant savings in computation time for insignificant degradation of system performance. A 7th-order numerical example illustrates the procedure.