On stochastic optimality for a linear controller with attenuating disturbances

• Published in: Automation and remote control Vol. 74; no. 4; pp. 628 - 641
• Main Authors: Belkina, T. A., Palamarchuk, E. S.
• Format: Journal Article
• Language: English
• Published: Dordrecht SP MAIK Nauka/Interperiodica 01.04.2013
• Subjects: Asymptotic properties; Attenuation; CAE) and Design; Calculus of Variations and Optimal Control; Optimization; Computer-Aided Engineering (CAD; Control; Control systems; Disturbances; Mathematics; Mathematics and Statistics; Mechanical Engineering; Mechatronics; Optimal control; Optimization; Queueing Systems; Remote control; Robotics; Stochastic Systems; Stochasticity; Systems Theory; Admissible Control; Fundamental Matrix; Stochastic Optimality; Remote Control; Linear Controller
• ISSN: 0005-1179; 1608-3032
• DOI: 10.1134/S0005117913040061

For a linear stochastic control system with quadratic objective functional, we introduce various generalizations of the notions of optimality on average and stochastic optimality on an infinite time interval that take into account possible degeneration of the parameter of the disturbing process with time (attenuation of the disturbances) or the presence of a discount function in the objective functional. This lets us improve upon the quality estimate for a well known optimal control in this problem from the point of view of both asymptotic behavior of the functional’s expectation and its asymptotic probabilistic properties. In particular, in the considered case we have found an improvement for the well known logarithmic upper bound on the optimal control for a family of defect processes.