Optimization of nonlinear dynamic systems without Lagrange multipliers
Pana Claewplodtook · OhioLink ETD Center (Ohio Library and Information Network) · 1996
This thesis presents a new procedure for finding globally optimal trajectories of multi-degree-of-freedom open-chain mechanical systems, consisting of as many controlled inputs as the number of degrees-of-freedom.For an n degree-of-freedom system, conventional approaches using Lagrange multipliers require solving 4n firstorder nonlinear differential equations in joint variables and Lagrange multiplier variables along with 4n boundary conditions split between the initial time and the final time.Numerical solutions to this problem are highly computation-intensive, since Lagrange multiplier values are unknown at the two end-times.In this thesis, a new technique is proposed for solving the optimal control problem without using Lagrange multipliers.The optimal solution now satisfies n fourth-order differential equations along with 4n boundary conditions split between the two end-times.With the absence of Lagrange multipliers, the two-point boundaryvalue problem can be solved efficiently by using classical weighted residual methods. Appendix D Derivation of Optimality Equations 71.....