The purpose of this paper is to study an optimal stopping problem with constraints for a Markov chain with general state space by using the convex analytic approach. The costs are assumed to be nonnegative. Our model is not assumed to be transient or absorbing and the stopping time does not necessarily have a finite expectation. As a consequence, the occupation measure is not necessarily finite, which poses some difficulties in the analysis of the associated linear program. Under a very weak hypothesis, it is shown that the linear problem admits an optimal solution, guaranteeing the existence of an optimal stopping strategy for the optimal stopping problem with constraints.

The design and implementation of adaptive control for nonlinear unknown systems is extremely difficult. The nonlinear adaptive control for assembly robots performing a peg-in-hole insertion is one such an example. The recently intensively studied neural networks brings a new stage in the development of adaptive control, particularly for unknown nonlinear systems. The aim of this paper is to propose a new approach of hybrid force position control of an assembly robot based on artificial neural networks systems. An appropriate neural network is used to model the plant and is updated online. An artificial neural network controller is then directly evaluated using the updated neuro model. Two control structures are proposed and the stability analysis of the closed-loop system is investigated using the Lyapunov method. Experimental results demonstrate that the identification and control schemes suggested in this paper are efficient in practice.