Olga Granichina

Randomized Algorithm for UAVs Group Flight Optimization

Abstract The problem of small UAVs flight optimization is considered. To solve this problem thermal updrafts are used. For the precise detection of the thermal updrafts center the simultaneous perturbation stochastic approximation (SPSA) type algorithm is proposed. If UAVs use thermal updrafts so they can save the energy during the flight. Therefore the flight time will be vary for different UAVs. In order to optimize the area monitoring, the consensus approach has been proposed.

Multi-agent Stochastic Systems with Switched Topology and Noise

In this paper the approximate consensus problem in multi-agent stochastic systems with noisy information about the current state of the nodes and randomly switched topology for agents with nonlinear dynamics is considered. The control is formed by the local voting protocol with step size not tending to zero. To analyze closed loop system we propose to use method of continuous models (ODE approach or Derevitskii-Fradkov-Ljung (DFL)-scheme). The usage of this method allows one to reduce the computation load. The bounds of the mean proximity of trajectories of the discrete stochastic system to its continuous deterministic model are obtained. Based on those bounds the conditions for achieving mean square ε-consensus are established. The method is applied to the load balancing problem in decentralized stochastic dynamic network with incomplete information about the current state of nodes and changing set of communication links is considered. The load balancing problem is reformulated as consensus problem in noisy model with switched topology. The conditions to achieve the optimal level of nodes load are obtained. The performance of the system is evaluated both analytically and by simulation. Obtained results are important for control of production networks, multiprocessor or multicomputer networks, etc.

Differentiated consensuses in decentralized load balancing problem with randomized topology, noise, and delays

In this paper, a new consensus problem, termed differentiated consensuses, is studied. This consensus problem is that, in a system with multiple classes, consensus is targeted for each class, which may be different among classes. Specifically, we investigate differentiated consensuses in a distributed stochastic network system of nodes (or agents), where tasks, classified with different priorities, are serviced. The network system is assumed to have switched topology, noise and delay in measurement, and cost on the topology. The goal is to reach/maintain balanced (equal) load, i.e. consensus, across the network and at the same time to meet the topology cost constraint, both for every priority class. A control protocol is proposed. We prove that the proposed control protocol is able to meet the topology cost constraint and achieve approximate consensus for each of the priority classes in the network.

Detection of abrupt changes in autonomous system fault analysis using spatial adaptive estimation of nonparametric regression

The paper deals with the detection of abrupt changes in autonomous systems. We consider this problem in the presence of Gaussian noise and solve it in two steps. At first, spatial adaptive estimation of nonparametric regression is used to estimate the observable data. Then Filtered Derivative Algorithm is used to detect abrupt changes in the obtained data using an adaptive threshold. The estimation of this adaptive threshold is presented. This approach is then applied to demonstrate the slowdown detection of a small autonomous vehicle.

Two procedures with randomized controls for the parameters' confidence region of linear plant under external arbitrary noise

In this paper we join the previous results about asymptotic properties of a randomized control strategy with new one based on a non-asymptotic approach of LSCR (Leave-out Sign-dominant Correlation Regions) methods. Our consideration is focused on problems of the identification or adaptive optimal control for the linear plant with unknown parameters and dynamics disturbed by an external noise. The assumptions about the noise are reduced to a minimum: it can virtually be arbitrary, but, independently of it, the user must be able to add test perturbations through the input channel. The theoretical results are illustrated by simulations.

Combined procedure with randomized controls for the parameters' confidence region of linear plant under external arbitrary noise

The new algorithm is proposed for the estimating of linear plants unknown parameters in the case of observations with arbitrary external noises. It is based on adding of randomized inputs (test perturbations) through the feedback channel. The assumptions about the noise are reduced to a minimum: it can virtually be arbitrary but independently of it the user must be able to add test perturbations. We combine the previous result about asymptotic properties of randomized control strategy with the new one which is followed by a non-asymptotic approach of LSCR (Leave-out Sign-dominant Correlation Regions) method. The new algorithm gives confidence regions for series of finite sets of observations. These regions shrink to the true values of an unknown parameters when number of observations tents to infinity while the algorithm complexity does not increases.

Local voting protocol for the adaptation of airplane's “feathers” in a turbulence flow

The traditional detailed mathematical description of the motion of complicated complex systems with many transducers/sensors and actuators often leads to a very hard problems involving an extremely high-dimensional state space. However, multi-agent technology can effectively solve many of such problems by replacing the general model of interactions in a complex system with a set of local models and their aggregation (clustering). In this paper we apply the results of the synchronization and consensus achievement within the network control to the flight control tasks when a vast array of sensors and actuators (“feathers”) is distributed over the surface of an airplane. The usage possibilities of Local Voting Protocol for the adaptation of airplanes “feathers” in a turbulence flow are examined.

Control of Educational Processes Using SPSA

In this paper we consider a possible application of simultaneous perturbation stochastic approximation (SPSA) method to problems of control of educational processes. SPSA is an efficient tool for optimization problems and uncertain parameters estimation. What is more important, such SPSA procedures actually work under arbitrary external observation noise, while most other optimization methods work only with Gaussian noises. The illustrative example is also presented.

Information and mathematical models for evaluation of the effectiveness and quality of the university

Possible approaches to building the information and mathematical models to evaluate of the effectiveness and quality of the University are discussed in this paper. We characterize cycle of university management, determine the factors affecting the performance activity of universities, identify indicators of assessment of effectiveness and quality, formulate the problem of university management through the organization of control by this indicators. Proposes and explains the concept of integrated distributed information space and state the main problems that must be overcome in its implementation. Discusses the choice of the mathematical model of the organization of control of the effectiveness and quality of the University as a basis for making management decisions. Examines the complexity of the task of assessment of quality at the University, posit that the decision this problems by standard methods is very difficult. For the particular case of the solution of this task provides an example of using the randomized algorithm of stochastic optimization.

Spectral profiling of writing process

This paper discusses a novel methodology for dynamic modeling of writing process. Sequent sub-documents of a given document are described through occurrences of the suitably selected N-grams. The Mean Dependence similarity measures the association between a present sub-document and numerous preceding ones and transforms a document into a time series, which is supposed to be weak stationary if the document is created using the same writing style. A periodogram of this signal estimates its Power Spectral Density providing a spectral attribute of the style. Numerical experiments demonstrate high ability of the proposed method in authorship identification and the reveal of writing style evolution.