Sufficient epsilon-optimality conditions for systems with random quantization period (Q2027499)

Consider an optimal stochastic control problem, where the underlying stochastic system is represented by a controlled stochastic differential equation having the additive terms \(\sigma(t)W(t)\) with a standard Wiener process and a stochastic differential \(dQ(t)\) with a stochastic process \(Q=Q(t)\), having piecewise constant trajectories, described by a certain combination of Poisson processes. The performance function is the sum of \(i)\) an integral over the time and state domain \([t_0,t_1] \times \mathbb{R}^n\) of a cost function depending, among others, on a partial feedback function, depending on a certain subvector \(x_1\) of the state vector \(x\), and \(ii)\) a terminal cost term, depending on a control vector to be taken at the final time \(t_1\). Sufficient conditions are then given for the existence and the representation of an \(\epsilon\)-optimal control for certain values of \(\epsilon >0\).