Abstract
AbstractThe theory of optimal control and the theory of a substructural chain in static structural analysis are mutually simulated issues. From the minimum potential energy variational principle of the substructural chain, the generalized variational principle with two kinds of variables is derived first. By comparing that generalized variational principle with the variational principle in LQ control theory, the simulation relation is established. Based on that relation, the potential energy and mixed energy formulation of the algebraic Riccati equations are derived, then iterative algorithms are proposed which give the upper and lower bounds to the solution matrix. By using the solutions of the positive and negative co‐ordinate algebraic Riccati equations, the canonical transformation matrices for the eigenproblems of the substructural chain and LQ control are constructed respectively, which reduce the eigenproblem to half‐size. The properties of the solutions are analysed, which establishes the basis for expansion solutions.
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