A study of nonlinear optimal control

The major objective of this study is to compile a detailed comparison of the methods available for the solution of nonlinear optimal control problems (OCPs). Special emphasis is placed on the solution of OCPs with a large number of state and/or control variables. In addition, the design sensitivity analysis (DSA) of dynamic response constraints and the solution of large scale nonlinear programming (NLP) problems are studied.;To simplify the comparison of optimal control methods, each method is classified into one of three general categories. The state variable elimination (SVE) category assumes that the state variables are dependent on the control variables and eliminated from the optimization process. The simultaneous simulation and control (SSC) category assumes that both the state and control variables are the unknowns of the optimization process and dynamic programming category contains methods that are based upon the Hamilton-Jacobi-Bellman equation.;With the SVE approach, DSA techniques are used to determine the total derivatives of all functions with respect to the control variables. In previous studies the DSA for dynamic response constraints was determined to dominate the total computational effort. However, new results presented in this study demonstrate that DSA can be implemented much more efficiently.;For one method in the SSC category, the state and control variables are approximated with a finite number of parameters. This results in the solution of a large, sparse NLP problem. Two methods based on the sequential quadratic programming method are developed to solve this problem efficiently. One method based upon a dual approach showed very poor performance. However, a method based on a primal approach showed some promise for the solution of large scale OCPs.;From the results presented in this study the differential dynamic programming method is suggested for the solution of small, unconstrained OCPs. Methods based on the SVE approach are suggested for more generally constrained OCPs and for the solution of large scale OCPs. SSC methods based on a primal approach may also prove to be effective for the solution of large scale OCPs, however additional research is required.