A Hybrid Optimization Method for Constrained Optimal Control Problem

Forming a method for determining the coordinates of sound anomalies based on data from a computerized microphone system

“…Thanks to such property as analyticity, it is relatively simple to build an algorithm of calculating coordinates of a sound anomaly. The difference between the current results and the results obtained in [27][28][29] can be explained by the proposed elimination of irrationality from the model composition in the course of its formation, departure from the methods of [30,31] and application of the recurrent approximation method (RAM) [33][34][35] for the solution. The data of numerical experiments given in Tables 1 and 2 also demonstrate stable algorithm operation and good enough convergence.…”

“…The advantage of these results over those obtained by direct and indirect numerical methods [30][31][32] based on the Newton-Kantorovich method includes the advantages of the RAM itself. This method eliminates the main problem of optimization when gradient drops when approaching the optimum point leading to a step-like growth in the algorithm of root search.…”

“…Search for and implementation of design solutions that realize the binaural effect [29] requires prediction of the event direction which cannot be predicted for civilian tasks. Under these conditions, the problem of determining the coor dinate of sound anomaly is usually reduced to a problem of either minimizing the functional [30] or solving the system of nonlinear algebraic equations [31].…”

“…Theoretical generalizations of the studies devoted to the use of direct and indirect methods of solving the problem of determining coordinates of existing models are presented in [32]. Analysis of the studies [30][31][32] shows that the operation of square-rooting both for indirect gradient methods [30] and the methods of quadratic programming with constraints [31] causes ambiguity. A comparison of the results for direct and indirect methods presented in the applied mathematics study [32] just confirmed the assumption of non-singularity.…”

“…Further development of systems for management of emergencies, traffic on highways, etc., requires joint application of geoinformation systems and mapping tools which was substantiated and presented in [16] as a field of the current study. The contradiction between mapping systems that work with a continuous scale and the numerical methods of finding coordinates [30][31][32] using finite increments is about averaging of the first and second derivatives. The continuity requirement creates the need for interpolation and as a consequence generates an error.…”