Pseudospectral （PS） computational methods for nonlinear constrained optimal control have been applied to many industrial-strength problems,notably,the recent zero-propellant-maneuvering of the international space st...Pseudospectral （PS） computational methods for nonlinear constrained optimal control have been applied to many industrial-strength problems,notably,the recent zero-propellant-maneuvering of the international space station performed by NASA.In this paper,we prove a theorem on the rate of convergence for the optimal cost computed using a Legendre PS method.In addition to the high-order convergence rate,two theorems are proved for the existence and convergence of the approximate solutions.Relative to existing work on PS optimal control as well as some other direct computational methods,the proofs do not use necessary conditions of optimal control.Furthermore,we do not make coercivity type of assumptions.As a result,the theory does not require the local uniqueness of optimal solutions.In addition,a restrictive assumption on the cluster points of discrete solutions made in existing convergence theorems is removed.展开更多
基金supported by the Air Force Office of Scientific Research(No.F1ATA0-90-4-3G001)and Air Force Research Laboratory
文摘Pseudospectral （PS） computational methods for nonlinear constrained optimal control have been applied to many industrial-strength problems,notably,the recent zero-propellant-maneuvering of the international space station performed by NASA.In this paper,we prove a theorem on the rate of convergence for the optimal cost computed using a Legendre PS method.In addition to the high-order convergence rate,two theorems are proved for the existence and convergence of the approximate solutions.Relative to existing work on PS optimal control as well as some other direct computational methods,the proofs do not use necessary conditions of optimal control.Furthermore,we do not make coercivity type of assumptions.As a result,the theory does not require the local uniqueness of optimal solutions.In addition,a restrictive assumption on the cluster points of discrete solutions made in existing convergence theorems is removed.
