A class of Markov processes with non-linear, bounded generators

Bounded Parameter Markov Decision Processes Bounded Parameter Markov Decision Processes

In this paper, we introduce the notion of a bounded parameter Markov decision process as a generalization of the traditional exact MDP. A bounded parameter MDP is a set of exact MDPs speciied by giving upper and lower bounds on transition probabilities and rewards (all the MDPs in the set share the same state and action space). Bounded parameter MDPs can be used to represent variation or uncert...

Bounded generators of linear spaces

Local stabilization for a class of nonlinear impulsive switched system with non-vanishing uncertainties under a norm-bounded control input

Stability and stabilization of impulsive switched system have been considered in recent decades, but there are some issues that are not yet fully addressed such as actuator saturation. This paper deals with expo-nential stabilization for a class of nonlinear impulsive switched systems with different types of non-vanishing uncertainties under the norm-bounded control input. Due to the constraine...

Comparison of Markov processes via infinitesimal generators

We derive comparison results for Markov processes with respect to stochastic orderings induced by function classes. Our main result states that stochastic monotonicity of one process and comparability of the infinitesimal generators implies ordering of the processes. Unlike in previous work no boundedness assumptions on the function classes are needed anymore. We also present an integral versio...

Bounded Parameter Markov Decision Processes

In this paper, we introduce the notion of a bounded-parameter Markov decision process (BMDP) as a generalization of the familiar exact MDP. A bounded-parameter MDP is a set of exact MDPs specified by giving upper and lower bounds on transition probabilities and rewards (all the MDPs in the set share the same state and action space). BMDPs form an efficiently solvable special case of the already...