Sequential supporting solutions method in the linear oscillating objects control problems optimized by processing speed

Abstract

In connection with control and regulations means massive transfer from analog to digital hardware, that is a necessary step towards automated management systems upgrading, and of great interest are the optimum control principles where the exclusive place is given to the limit processing speed. Despite advances in the optimum control theory and practice, there are still a lot of unresolved relevant and complex problems related to the development of applied numerical methods adapted to the specificity of tasks that will enable the optimal control theory practical use. The choice of the initial (zero) approximation, which would guarantee the iterative process convergence, presents a substantial difficulty arising with numerical solution of the two-point boundary-value problem. The concerned sequential supporting solutions method, that implements a focused search of unknown values (conjugate variables or durations of control intervals) zero approximation, allows one to overcome this difficulty. The recommendations for this method application for the linear oscillating objects estimation control are considered. The oscillatory links optimized by the processing speed are of a particular interest. The propositions are stated allowing to overcome difficulties associated with the number of control intervals determination for q-objects consisting of oscillating links for which there is no an upper bound on the control switches number when translated from the arbitrary initial state in origin of coordinates.