{'fraction_non_alphanumeric': 0.010796221322537112, 'fraction_numerical': 0.0, 'mean_word_length': 5.3418803418803416, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
METHOD OF DECOMPOSITION AND ITS APPLICATIONS TO UNCERTAIN DYNAMICAL SYSTEMS

Abstract A nonlinear dynamical system described by Lagrange's equations is considered. The system is subjected to uncertain external forces and controls bounded by geometric constraints. A feedback control that satisfies the imposed conditions and brings the system to a prescribed terminal state in a finite time is proposed. The control is based on the decomposition of the system and uses ideas of optimal control and differential games. Explicit formulas for the feedback control are presented. Applications to control of robots and underactuated systems are discussed. Computer simulation of motions of a double pendulum controlled by one torque is presented.