Multi-dimensional stochastic optimization plays an important role in analysis and control of many technical systems. To solve the challenging multidimensional problems of nonstationary optimization, it is suggested to use a stochastic approximation algorithm (like SPSA) with perturbed input and constant step-size which has simple form. We get a finite bound of residual between estimates and time-varying unknown parameters when observations are made under an unknown but bounded noise. Applications of the algorithm are considered for a random walk, an optimization of UAV's flight, and a load balancing problem.

We consider a setup where a distributed set of sensors working cooperatively can estimate an unknown signal of interest, whereas any individual sensor cannot fulfil the task due to lack of necessary information diversity. This paper deals with these kinds of estimation and tracking problems and focuses on a class of simultaneous perturbation stochastic approximation (SPSA)-based consensus algorithms for the cases when the corrupted observations of sensors are transmitted between sensors with communication noise and the communication protocol has to satisfy a prespecified cost constraints on the network topology. Sufficient conditions are introduced to guarantee the stability of estimates obtained in this way, without resorting to commonly used but stringent conventional statistical assumptions about the observation noise such as randomness, independence, and zero mean. We derive an upper bound of the mean square error of the estimates in the problem of unknown time-varying parameters tracking under unknown but bounded observation errors and noisy communication channels. The result is illustrated by a practical application to the multi-sensor multi-target tracking problem.

This paper presents a new algorithm for maximizing the flight duration of a single UAV (Uninhabited Air Vehicle) and UAVs group using the thermal model developed by Allen at NASA Dryden. As a first step, we suggest a new algorithm based on Simultaneous Perturbation Stochastic Approximation for quick and precise detection of the center of a thermal updraft where the vertical velocity of the air stream is the highest. The method takes into account the unstable behavior of the updraft dynamics and the drift of its center in time. Then, a multi-agent system for joint flight of multiple UAVs is presented. A protocol for UAV communication providing effective information exchange on updrafts locations is proposed. A sufficient condition for the protocol to be effective is deduced theoretically. We show that the energy consumption of each UAV can be significantly reduced using the multi-agent approach.

Consideration was given to the randomized stochastic approximation algorithm with simultaneous trial input perturbation and two measurements used to optimize the unconstrained nonstationary...

In this paper application of the stochastic approximation algorithm with randomized differences to the minimum tracking problem for the non-constrained optimization is considered. The upper bound of mean-squared estimation error is derived in the case of once differentiable functional and almost arbitrary observation noise. Numerical simulation of the estimates stabilization for the multidimensional optimization with unknown but bounded deterministic noise is provided. Stabilization bound has sufficiently small level comparing to significant level of noise.