Abstract
The second variation of the performance index is derived for optimal control problems which include state-variable-inequality constraints. Necessary conditions for a neighboring-optimal trajectory are then obtained through formulation of an accessory minimization problem which minimizes the second variation of the performance index. These necessary conditions are utilized with a backward-sweep method to develop a neighboring-optimal feedback control law. Detailed procedures for implementation of the feedback control law are developed for problems in which the control is discontinuous at juncture points between constrained and unconstrained arcs and for problems in which the control is continuous. Feasibility of the continuous-control procedure is demonstrated through application to two classical optimization problems.
Hymas, Carl Eugene (1972). Neighboring optimal feedback control for dynamic systems with state-variable-inequality constraints. Texas A&M University. Texas A&M University. Libraries. Available electronically from
https : / /hdl .handle .net /1969 .1 /DISSERTATIONS -184651.