Trajectory optimization by a direct descent process

Abstract

The problem considered is that of trajectory optimization using step-bystep descent to minimum cost along the direction of the cost gradient with respect to the control. Using a hybrid computer, the gradient is computed directly as the response to nearly impulsive control perturbations. A method is presented for computing the gradient when several terminal constraints are enforced. Examples of application of t h e method are presented. It is concluded that the direct gradient computation method has some significant ~ I advantages over other methods.

Applied Mathematics

“…Papers have been published dealing with time-optimal control (81), various types of delays (31,141,241,271,311,651,661,981), singular control (41,741,851), suboptimal control (21,171,541,581,681,921), and stochastic control (51,461,521,771,891,971). Other papers have dealt with the synthesis of control ( 101), the computational aspects of control (161,211,341,371), control in Banach space ( 221), the connection of game theory to control ( 231), a survey of incorrect problems in control (361), a general theory of extremals ( 561), the inclusion of constraints (471,571,901), the use of singular perturbations (701), the application of the sweep method ( 721), the pursuit problem (801), the connection to programming techniques (201,911), and the discrete maximum principle (291).…”

Discussion: “Plastic Failure of Fiber-Reinforced Materials” (Prager, W., 1969, ASME J. Appl. Mech., 36, pp. 770–773)

“…There are in existence several relatively complete nonlinear mathematical models of the automobile crash victim in a longitudinal collision [2,3] which could be applied in optimization studies with techniques that operate externally of the mathematical model, on the inputs and outputs (e.g., the method described in reference [4]). However, limitations on practical belt material properties and on achievable vehicle deceleration waveforms make the benefits of such a theoretical optimization rather doubtful.…”

“…W. Morlcmd. 4 This paper makes a preliminaiy investigation of viscoelastic creep (relaxation) as a feature of seatbelt design. The model adopted is a point mass attached to the midpoint of a tension supporting belt fixed at both ends, and assumes small displacement and infinitesimal strain in the belt during the motion caused by a suddenly imparted velocity (change) to the mass.…”

Plastic Failure of Fiber-Reinforced Materials

“…L. W. Morlcmd. 4 This paper makes a preliminaiy investigation of viscoelastic creep (relaxation) as a feature of seatbelt design. The model adopted is a point mass attached to the midpoint of a tension supporting belt fixed at both ends, and assumes small displacement and infinitesimal strain in the belt during the motion caused by a suddenly imparted velocity (change) to the mass.…”