Infinite networks and quadratic optimal control

Abstract

A discrete-time quadratic optimal control problem is shown to be equivalent to an infinite cascade ofn-port electrical networks. Both problems can be expressed as a generalized Schur complement (or shorted operator) of a block tridiagonal operator. Using Maxwell's principle for resistive networks, a variational formulation of the cascade limit ofn-port networks is given. For one special case a formula for the solution of the quadratic control problem is given in terms of the geometric mean of operators.