Том 80, № 9 (2019)

Linear control systems operating in a repetitive mode with a constant period and returning each time to the initial state are considered. The problem is to find a control law that will employ information about the output variable at the current and previous repetitions and also the estimates of state variables from an observer in order to guarantee the convergence of this variable to a reference trajectory under unlimited increasing the repetitions number. This type of control is known as iterative learning control. The problem is solved using the dissipativity of 2D models and the divergent method of vector Lyapunov functions. The final results are expressed in the form of linear matrix inequalities. An example is given.

System Identification is about estimating models of dynamical systems from measured input-output data. Its traditional foundation is basic statistical techniques, such as maximum likelihood estimation and asymptotic analysis of bias and variance and the like. Maximum likelihood estimation relies on minimization of criterion functions that typically are non-convex, and may cause numerical search problems and estimates trapped in local minima. Recent interest in identification algorithms has focused on techniques that are centered around convex formulations. This is partly the result of developments in semidefinite programming, machine learning and statistical learning theory. The development concerns issues of regular-ization for sparsity and for better tuned bias/variance trade-offs. It also involves the use of subspace methods as well as nuclear norms as proxies to rank constraints. A special approach is to look for difference-of-convex programming (DCP) formulations, in case a pure convex criterion is not found. Other techniques are based on Lagrangian relaxation and contraction theory. A quite different route to convexity is to use algebraic techniques to manipulate the model parameterizations. This article will illustrate all this recent development.

The paper represents the main ideas of Robust Identification Theory, which was initiated by Ya.Z. Tzypkin in 80s of the past century. Here we demonstrate that the parallel application of both the “Whitening Procedure” and the recurrent min-max version of the “Maximum Likelihood Method” (MLLM), guarantees the property of Asymptotic Consistency of this procedure. The information Cramér–Rao inequality is also obtained and it is shown that this combined procedure attains this information bound. This means that for wide class of regular observations of ARX (auto regression with exogenous input) models, there does not exist any other identification algorithm, estimating asymptotically unknown parameters “quicker” then the procedure discussed here, if the distribution of the white noise at the input of the forming filter is known exactly. The main specific feature of this method consists in the possible consideration of external non-Gaussian white noise (defined on the given class of admissible distributions) in the input of the forming filter, making the noise sequence, affecting the input of ARX-dynamics, non-Gaussian, and correlated. The almost sure convergence as well as the Asymptotic Normality of the estimation error are formulated. If the information on the input of the forming filter is uncertain, that is, when the distribution belongs to a given class, then the Huber’s approach is applied using the robust version of MLLM.

A new concept of machine learning based on the computer simulation of entropy-optimal randomized models is proposed. The procedures of randomized machine learning (RML) with “hard” and “soft” randomization are considered; the former imply the exact reproduction of empirical balances while the latter their rough reproduction with an accepted approximation criterion. RML algorithms are formulated as functional entropy-linear programming problems. Applications of RML procedures to text classification and the randomized forecasting of migratory interaction of regional systems are presented.

This paper considers the problem of synthesis of a proportional-integral-derivative control law (PID controller) for a linear discrete time-invariant system with scalar control input and measured output operating under influence of the stochastic disturbances with uncertainty described in terms of the mean anisotropy. The closed-loop system abilities to attenuate the disturbances are quantitatively characterized by the anisotropic norm. Sufficient existence conditions for the anisotropic suboptimal controller that stabilizes the closed-loop system and guarantees that its anisotropic norm is strictly bounded by a given threshold value are derived.

For the generalized stochastic network the concept of degree of parallelism is entered. The method of determination of this value is offered. It makes the choice of the minimum number of performers of the network at which there is no formation of queues for passing of arcs.

In this paper we propose the quaternion-based control system for quadrotor. Adaptive scheme for thrust coefficients identification, based on speed-gradient method, is designed. Proofs of stability are provided, as well the results of numerical simulations. In existing theoretical works, Euler angles are often used as coordinates for describing quadrotor’s coordinates. Equations using those coordinates, however, have a singularity, which prevents their use near certain points. We use quaternions instead, which have no such restrictions. The process of discovering PID-regulator coefficients is known to be tedious, error-prone and specific for each quadcopter. We propose a control scheme in which most of the parameters are physical values, and the rest do not depend on the quadcopter and can be found once for the whole class of the flying machines. An identification algorithm for obtaining physical parameters is also described. MATLAB modelling is used to test and confirm the performance of the proposed scheme.

The knapsack problem with indivisible items as agents is considered. Each agent has certain weight and utility and wants to be in a knapsack. Such situation is treated as a cooperative game with transferable utility. A characteristic function of this game generalizes the characteristic function associated with the bankruptcy problem but, in contrast to the latter case, it is not convex. Nevertheless, it turns out that the core of this game is non-empty. At the end of the paper some special cases of the knapsack problem are studied. For these cases, the Shapley value, the τ-value and also the nucleolus are found in the explicit form.