Minimum Indirect Jerk of Nonlinear Dynamic Systems with Given Boundary Conditions on Control Inputs by Applying Direct and Indirect Jerk Equations

摘要

This paper deals with nonlinear dynamic systems with given boundary conditions on control inputs. The problem can be considered as ordinary dynamic optimization problem with defining control inputs as constraints on the boundaries. Then the problem can be solved by using direct or indirect numerical method. However, when the problem has constraints on the boundaries, the difficulty arises since the problem contains more boundary conditions compare with the highest order on the dynamic equations of motion (differential equations). Therefore, the problem is reconsidered by applying both direct and indirect jerk equations which allow assigning more ordinary boundary conditions since the highest order of the necessary conditions have been increased by the order of one. Both problems are solved in this paper by using direct numerical method and the comparisons have been made.