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.
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Anderson, W.N., Morley, T.D. & Trapp, G.E. Infinite networks and quadratic optimal control. Circuits Systems and Signal Process 9, 229–238 (1990). https://doi.org/10.1007/BF01236455
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DOI: https://doi.org/10.1007/BF01236455