122,528 research outputs found
A Quantum Langevin Formulation of Risk-Sensitive Optimal Control
In this paper we formulate a risk-sensitive optimal control problem for
continuously monitored open quantum systems modelled by quantum Langevin
equations. The optimal controller is expressed in terms of a modified
conditional state, which we call a risk-sensitive state, that represents
measurement knowledge tempered by the control purpose. One of the two
components of the optimal controller is dynamic, a filter that computes the
risk-sensitive state.
The second component is an optimal control feedback function that is found by
solving the dynamic programming equation. The optimal controller can be
implemented using classical electronics.
The ideas are illustrated using an example of feedback control of a two-level
atom
Partially Observed Non-linear Risk-sensitive Optimal Stopping Control for Non-linear Discrete-time Systems
In this paper we introduce and solve the partially observed optimal stopping non-linear risk-sensitive stochastic control problem for discrete-time non-linear systems. The presented results are closely related to previous results for finite horizon partially observed risk-sensitive stochastic control problem. An information state approach is used and a new (three-way) separation principle established that leads to a forward dynamic programming equation and a backward dynamic programming inequality equation (both infinite dimensional). A verification theorem is given that establishes the optimal control and optimal stopping time. The risk-neutral optimal stopping stochastic control problem is also discussed
Controlled diffusion processes
This article gives an overview of the developments in controlled diffusion
processes, emphasizing key results regarding existence of optimal controls and
their characterization via dynamic programming for a variety of cost criteria
and structural assumptions. Stochastic maximum principle and control under
partial observations (equivalently, control of nonlinear filters) are also
discussed. Several other related topics are briefly sketched.Comment: Published at http://dx.doi.org/10.1214/154957805100000131 in the
Probability Surveys (http://www.i-journals.org/ps/) by the Institute of
Mathematical Statistics (http://www.imstat.org
- …