Mixed zero-one linear programming and optimal control problem
Nonlinear optimal control problems are considered. The control system is described by nonlinear differential equations with given boundary conditions. A performance index consisting of an integral function of the state and the control is to be minimized. The problem is transformed into a linear programming problem. Nonlinear functions are approximated by piecewise linear functions. The active interval is determined by \((0,1)\) variables. Therefore a mixed zero-one linear programming problem must be solved. The method is applied to a control system described by the diffusion equation and to variational problems. Computational results are presented for three numerical examples. The results are compared with known solutions. Finally, some comments on the feasibility of the problem formulation are made.
scientific article; zbMATH DE number 1346192