A comparison between steepest ascent and differential correction optimization methods in a problem of Bolza, with a method for obtaining starting values for the adjoint variables from a nominal path
McCue, William W.
Good, Robert C.
Faulkner, Frank D.
MetadataShow full item record
The problem of maximum range atmospheric reentry for an orbiting lifting glider was treated by Bryson and Denham by the method of "steepest ascent". The same problem is undertaken here by a method of differential corrections developed by Faulkner , This method makes use of a Newton-Raphson type iteration based on paths which satisfy the Euler-Lagrange equations, A comparison of results is made, showing large differences in control variable history, and longer range for the path obtained by differential corrections. The problem was characterized by a sharp "ridge" in the domain of the starting values of the adjoint variables and the effect of this on the convergence of both methods is discussed. Finally , the difficulty of choosing initial approximations for the starting values of the adjoint variables is discussed, and a method is presented for obtaining these from a nominal path as the first step in the computer routine.
RightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
Showing items related by title, author, creator and subject.
Bloxom, Edward Leon (Monterey, California. Naval Postgraduate School, 1972);Four techniques for the numerical solution of partial differential equations and eigenvalue problems were investigated. Typical problems considered were elliptic partial differential equations of the form Uxx + Uyy = f(x,y), ...
Application of the adjoint system of differential equations in the solution of the bang-bang control problem McCalla, Thomas Richard (Monterey, California. Naval Postgraduate School, 1961);Some problems in the optimum control of a linear dynamic system are investigated, particularly the problem of determining the minimum time required to drive a linear, constant coefficient dynamic system from an initial ...
Discretely exact derivatives for hyperbolic PDE-constrained optimization problems discretized by the discontinuous Galerkin method, Draft Wilcox, Lucas C.; Stadler, Georg; Bui-Thanh, Tan; Ghattas, Omar (2013);This paper discusses the computation of derivatives for optimization problems governed by linear hyperbolic systems of partial differential equations (PDEs) that are discretized by the discontinuous Galerkin (dG) method. ...