The Dynamic Finite Element and Nonlinear Programming Method in Control of Transient Differential Systems

Abstract

By combining the finite element method with dynamic programming, the dynamic finite element & nonlinear programming method (the dynamic FE&NLP method, i.e. the finite element & dynamic programming method (the FE&DP method) is developed and systematized in order to control transient differential equation systems with both equality or inequality constraints and a nonlinear objective function. Such systems are frequently encountered in various engineering and scientific problems of control and optimal design. The dynamic FE&NLP method (the FE&DP method) is applied to optimal control in thermal diffusion phenomena. The tractability in the initial or final condition, the boundary conditions and the equality or inequality constraints makes sure that the method becomes a powerful technique for several new types of boundary value problems with nonlinear objective function.