Sequential Supporting Solutions Method Convergence Research in Optimal Processing Speed Tasks

摘要

The current level of computing and microprocessor technology development allows us to implement any technical objects control principles. Of considerable interest are the optimum control principles where the exclusive place is taken by the extreme processing speed problem. 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 the numerical solution of the two-point boundary-value process. The concerned sequential supporting solutions method that implements a focused search of zero approximation for unknown values (conjugate variables or durations of control intervals) allows one to overcome this difficulty. The method comes down to a sequence of approximations construction which, under some assumptions, converges to the solution. Approval on the of iterative procedure convergence of the sequential reference solutions method is drafted. The theorem setting up a sufficient condition for convergence of the sequential supporting solutions method. It is shown that, while choosing the initial approximations of interval durations in accordance with the sequential supporting solutions method, the convergence of the Newton's method's iterative process at each stage of the method is provided. Hence, the sequential reference solutions method convergence is provided too.