Context. In this article, a generalized parametric identification procedure for linear nonstationary systems is proposed, which uses spline functions and orthogonal expansion in a series according to the Walsh function system, which makes it possible to find estimates of the desired parameters by minimizing the integral quadratic criterion of discrepancy based on solving a system of linear algebraic equations for a wide class of linear dynamical systems. The accuracy of parameter estimation is ensured by constructing a spline with a given accuracy and choosing the number of terms of the Walsh series expansion when solving systems of linear algebraic equations by the A. N. Tikhonov regularization method. To improve the accuracy of the assessment, an algorithm for adaptive partitioning of the observation interval is proposed. The partitioning criterion is the weighted square of the discrepancy between the state variables of the control object and the state variables of the model. The choice of the number of terms of the expansion into the Walsh series is carried out on the basis of adaptive approximation of non-stationary parameters in the observation interval, based on the specified accuracy of their estimates. The quality of the management of objects with variable parameters is largely determined by the accuracy of the evaluation of their parameters. Hence, obtaining reliable information about the actual nature of parameter changes is undoubtedly an urgent task. Objective. Improving the accuracy of parameter estimation of a wide class of linear dynamical systems through the joint use of spline functions and Walsh functions. Method. A generalized parametric identification procedure for a wide class of linear dynamical systems is proposed. The choice of the number of terms of the expansion into the Walsh series is made on the basis of the proposed algorithm for adaptive partitioning of the observation interval. Results. The results of modeling of specific linear non-stationary systems confirm the effectiveness of using the proposed approaches to estimating non-stationary parameters. Conclusions. The joint use of spline functions and Walsh functions makes it possible, based on the proposed generalized parametric identification procedure, to obtain analytically estimated parameters, which is very convenient for subsequent use in the synthesis of optimal controls of real technical objects. This procedure is applicable to a wide class of linear dynamical systems with concentrated and distributed parameters.
This paper considers the problem of optimal fuel consumption damping of sudden deviations of angular velocities of an axisymmetric spacecraft with a constant speed of rotation around the main axis of symmetry. This assumption has some practical significance and may be due to the creation of artificial gravity on the spacecraft. The idea of artificial gravity due to the rotation of an axisymmetric cylindrical spacecraft is based on the principle of equivalence of the force of gravity and the force of inertia. The urgency of the fuel consumption optimization problem is due to the presence of its limited stock onboard the spacecraft. The optimization problem is solved based on the maximum principle and the phase plane method. The authors of the article determine the structure of optimal fuel consumption processes with three levels of control, and the number of their switches depends on the initial conditions. Synthesized on the phase plane, the optimal switching curves divide the phase plane into eight curvilinear quadrants, which uniquely determine the values of the optimal control effects by the current values of the deviations of the angular velocities of the spacecraft. The problem of the possible presence of a delay in the control loop is proposed to be solved based on the Bess compensation method. To do this, the corresponding optimal curves of switching and disabling the controls are built as geometric locations of points remoted for the time of delay from the found curves of switching and the beginning of coordinates accordingly. It allows us to avoid the emergence of steady self-oscillations in a control contour and to provide a condition of keeping the spacecraft in a given final state after the completion of the stabilization process. Depending on the technical equipment of the spacecraft, two variants of the optimal damping algorithm are offered, namely: an autonomous device in the onboard control system of the spacecraft in the absence of a sufficiently powerful onboard computer, or the optimal damping algorithm, implemented entirely in the onboard computer of the spacecraft in case of its sufficient power.
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