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Class of affine nonlinear single-input single-output systems, where the relative degree of the equivalent form of the input-output is invariant to the presence of external, unmatched disturbances, is formalized. Methods of synthesis of a multifunctional tracking system in the conditions of parametric uncertainty of the control plant model and incomplete measurements are designed for this class of systems. The original method of synthesis of a low dimension observer for estimating mixed variables...

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 iterat...

The problem of minimizing the impact of bounded perturbations on certain classes of controlled nonlinear discrete systems is solved. The radius of the invariant set, an analog of variance for the perturbations of probabilistic nature, is taken as a measure of the impact. The cases of two-sided linear and nonlinear constraints that form multivalued mappings and also the case in which the nonlinear function has a given estimate of the norm are considered.

We propose an approach to construction of robust non-Euclidean iterative algorithms for convex composite stochastic optimization based on truncation of stochastic gradients. For such algorithms, we establish sub-Gaussian confidence bounds under weak assumptions about the tails of the noise distribution in convex and strongly convex settings. Robust estimates of the accuracy of general stochastic algorithms are also proposed.

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...

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 classificati...

The paper presents the evolution of discontinuous control systems starting from a relay with only two output constant values. The relay systems were widely used at the early stage of the feedback control system history. The analysis and design methods for them were developed by Ya. Tsypkin and discussed in his monograph “Theory of relay control systems,” published in 1956. It is shown how a relay function is modified in the so-called variable structure systems, when the relay output cab be equal...

Synthesis of Anisotropic Suboptimal PID Controller for Linear Discrete Time-Invariant System with Scalar Control Input and Measured Output

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 subopti...

The behavior of trajectories of multidimensional linear discrete-time systems with nonzero initial conditions is considered in two cases as follows. The first case is the systems with infinite degree of stability (the processes of a finite duration); the second case is the stable systems with a spectral radius close to 1. It is demonstrated that in both cases, large deviations of the trajectories from the equilibrium may occur. These results are applied to accelerated unconstrained optimization ...

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.

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