The cascade limit, the shorted operator and quadratic optimal control.

*(English)*Zbl 0675.93020Linear circuits, systems and signal processing, Sel. Pap. 8th Int. Symp. Math. Theory Networks Syst., Phoenix/Ariz. 1987, 3-7 (1988).

Summary: [For the entire collection see Zbl 0672.00017.]

It is shown that the solution of a discrete quaratic optimal control problem can be written in terms of the shorted operator of a tridiagonal matrix. Additionally, the solution of the control problem may be expressed as the infinite cascade limit of an n-port resistive network. Since the cascade limit has a variational formulation in terms of partitioned matrices, the solution of the optimal control problem also has such a variational formulation.