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Stabilization and Tracking of the Trajectory of a Linear System with Jump Drift

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Abstract

For a controlled linear stochastic differential system, we consider the problem of tracking the jumping state of an additive input action determining the current stabilization direction (drift). The tracking objective, which is to stabilize the system near the varying drift, is formalized by a quadratic performance functional. The input action defines a continuous-time Markov chain. The problem is considered in the cases of complete and incomplete information. Dynamic programming is used to solve it in both cases. The solution of the Bellman equation in the first case is obtained based on the properties of a finite-dimensional chain, and in the second case, based on the principle of separation of control and state estimation problems provided by the Wonham filter estimate and the properties of the quadratic performance criterion. A numerical experiment uses an applied model describing the position of a simple mechanical drive. The results of calculations confirming the applicability of the solutions obtained, as well as ways to overcome the difficulties of their numerical implementation, are presented and discussed in detail.

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Funding

The work was supported by project no. 075-15-2020-799 of the Ministry of Science and Higher Education of the Russian Federation. The work was carried out using the infrastructure of the Shared Use Center “High-Performance Computing and Big Data” (SUC “Computer Science” of the Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences).

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  1. Federal Research Center “Computer Science and Control,” Russian Academy of Sciences, Moscow, 119333, Russia

    A. V. Bosov

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  1. A. V. Bosov
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Correspondence to A. V. Bosov.

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Translated by V. Potapchouck

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Bosov, A.V. Stabilization and Tracking of the Trajectory of a Linear System with Jump Drift. Autom Remote Control 83, 520–535 (2022). https://doi.org/10.1134/S0005117922040026

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