Remarks on Pontryagin's Maximum Principle applied to a structural optimisation problem

Extract

In a recent publication, Professor L. Dixon applied to a structural optimisation problem elements of the Pontryagin theory of optimal processes; well known in control systems. The problem considered was that of the minimum deflection of a cantilever beam under its own weight with constraints on the geometry. Digital and hybrid solutions of the two point boundary value problem arising from the optimisation problem were presented. Significant differences in the digital and hybrid solutions by the hill-climbing method were found. The present authors have examined the numerical methods for solving the optimisation equations, have developed a computing method which does not have the inherent convergence problem of the methods of Dixon, have re-examined the governing equation, and have noted a correction to these equations.