Abstract
As mentioned in the preface, the stability theory of SDEs was developed mainly to meet the needs of stabilization of moving systems subjected to random perturbations. In this chapter we shall consider some problems concerning the stabilization of controlled stochastic systems. The results achieved to date in this field are rather sparse, despite the fact that the basic formulations of the problems and the fundamental equations have been known for some time. The only results of any significance are those pertaining to linear systems and employing quadratic control criteria. We devote to them the exposition which now follows, based on the material of Chaps. 5 through 7.
This chapter was written jointly with M.B. Nevelson.
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Notes
- 1.
In the literature this type of control is known as Markov control, or control employing the feedback principle.
References
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Khasminskii, R. (2012). Stabilization of Controlled Stochastic Systems. In: Stochastic Stability of Differential Equations. Stochastic Modelling and Applied Probability, vol 66. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23280-0_8
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DOI: https://doi.org/10.1007/978-3-642-23280-0_8
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