Elliptic partial differential equation and optimal control

AbstractThe theory of optimal control and the semianalytical method of elliptic partial differential equation (PDE) in a prismatic domain are mutually simulated issues. The simulation of discrete‐time linear quadratic (LQ) control with the substructural chain problem in static structural analysis is given first. From the minimum potential energy variational principle of substructural chain, the generalized variational principle with two kinds of variables and the dual equations are derived. The simulation relation is then recognized by comparing the variational principle and dual equations of the LQ control theory. The simulation between elliptic PDE in the prismatic domain and continuous‐time LQ control is established in the same way, and the interval energy is naturally introduced, as in the case of substructural chain. The assembling and condensation equations can help one to derive the differential equations of the submatrices of potential energy and mixed energy. The well known Riccati equation is one of them. The interval assembling and condensation algorithm can be used to solve the Riccati equation. Some numerical examples are given to illustrate the method.