No 4 (2022)

This paper is devoted to constructing nonelementary linear regressions consisting of explanatory variables and all possible combinations of their pairs transformed using binary minimum and maximum operations. Such models are formalized through a 0-1 mixed integer linear programming problem. By adjusting the constraints on binary variables, we control the structural specification of a nonelementary linear regression, namely, the number of regressors, their types, and the composition of explanatory variables. In this case, the model parameters are approximately estimated using the ordinary least squares method. The formulated problem has advantages: the number of constraints does not depend on the sample size, and the signs of the estimates for the explanatory variables are consistent with the signs of their correlation coefficients with the dependent variable. Regressors are eliminated at the initial stage to reduce the time for solving the problem and make the model quite interpretable. A nonelementary linear regression of rail freight in Irkutsk oblast is constructed, and its interpretation is given.

We propose a simple upper bound on trajectory deviations for an affine family of discrete-time systems under nonzero initial conditions subjected to bounded exogenous disturbances. It involves the design of a parametric quadratic Lyapunov function for the system. The apparatus of linear matrix inequalities and the method of invariant ellipsoids are used as technical tools. The original problem is reduced to a parametric semidefinite programming problem, which is easily solved numerically. Numerical simulation results demonstrate the relatively low conservatism of the upper bound. This paper continues the series of our previous publications on estimating trajectory deviations for linear continuous- and discrete-time systems with parametric uncertainty and exogenous disturbances. The results presented below can be extended to various robust formulations of the original problem and also the problem of minimizing trajectory deviations for an affine family of discrete-time control systems under exogenous disturbances via linear feedback.

The types of rock destruction at the bottom hole under different loads on the drilling bit are considered, and well-known domestic and foreign models of the penetration rate are analyzed. As shown, they have no optima as power-type functions, being unsuitable for drilling optimization. In addition, they can be used for quick drilling control by adjusting only one parameter (the load on the bit). A mathematical model based on a sinusoid curve is constructed. This model allows the simultaneous control of three drilling mode parameters, namely, the axial load on the bit, its rotation frequency, and the mud flow rate for flushing the well. The adequacy of the model to the drilling process is verified, and its software implementation is performed. This model automatically recognizes the rock at the bottom hole during drilling, adapts to it, and calculates the optimal control parameters for destructing the traversed rock. The model is intended for an intelligent optimal adaptive control system for oil and gas well drilling.

Forming optimal motion control laws for unmanned vehicles (UVs) by analyzing sensory data about the choice environment is an integral part of designing their situational control systems. The weakly predictable variability of the UV operating environment and the imperfection of measuring means reduce the possibility of obtaining comprehensive information about the environment state. Therefore, routing to minimize travel time and the probability of an accident is performed under uncertainty. An effective way to solve this problem is using logical-probabilistic and logical-linguistic models and algorithms. This paper is intended to develop new optimal routing methods for UVs with estimating the probability of an accident based on the logical-linguistic classification of route segments. For this purpose, the rows of parameters and characteristics of reference route segments are created and compared with the logical-probabilistic and logical-linguistic parameters and characteristics of classified route segments considering their significance for routing. After processing sensory and statistical data, the proposed logical-probabilistic and logical-linguistic methods are used to estimate the probabilities of accidents and minimize a performance criterion. As a consequence, the accuracy and speed of optimal routing for UVs are both increased. The results of this research can be used in the central nervous system of intelligent robots to classify route segments obtained by analyzing sensory and statistical data, which will improve the quality of motion control in an uncertain environment.