The control of large deviations in oscillatory systems with small random perturbations (Q2761356)

The author studies the dynamics of controlled system whose equations are represented in the standard form NEWLINE\[NEWLINE \begin{gathered} x' = \varepsilon F(t,x,u)+\varepsilon\sigma(t,x)w'(t),\\ x(t) = x\in G,\quad x(0) = x^*,\quad u\in U, \end{gathered}\tag{1} NEWLINE\]NEWLINE where \(\,G\subset R^n\,\) with the boundary \(\Gamma\), \(U\) is a compact in \(R^m\), \(w(t)\) is a standard Wiener process in \(R^l\). Discussed is the application of the principle of dynamical programming to system (1). As example a control is constructed for the quasiconservative system motion.