EFFECT OF RISK-SENSITIVE STOCHASTIC OPTIMAL CONTROL WITH TRACKING IN AN EVAPORATOR

This work presents an application of the Risk-Sensitive (R-S) control with tracking applied to a stochastic nonlinear system which models the operation of an electronic expansion valve (EEV) in a conventional evaporator. A novel dynamical stochastic equation represents the mathematical model of the evaporator system. The R-S stochastic optimal problem consists of the design of an optimal control u(t) such that the state reaches setpoint values (SP) and minimizes the exponential quadratic cost function. The presence of disturbances and errors in the sensor measurements is represented by Gauss white noise in the state equation, with the coefficient v(e/(2?^2 )) . One novel characteristic in this proposal is that the coefficient of the control into the state equation contains the state term. The error and exponential quadratic cost function show that the R-S control has a better performance versus the classical PID (Proportional, Integral Derivative) control. Key Words: Optimal Risk-Sensitive control with tracking, modelling of the evaporator.

On the policy improvement algorithm for ergodic risk-sensitive control

In this article we consider the ergodic risk-sensitive control problem for a large class of multidimensional controlled diffusions on the whole space. We study the minimization and maximization problems under either a blanket stability hypothesis, or a near-monotone assumption on the running cost. We establish the convergence of the policy improvement algorithm for these models. We also present a more general result concerning the region of attraction of the equilibrium of the algorithm.