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 Estimates in Various Spaces to the Control Function of the Extremum Problem for Parabolic Equation

For the minimization problem with pointwise observation governed by a one-dimensional parabolic equation with a free convection term and a depletion potential, we formulate a result on the existence and uniqueness of a minimizer from a prescribed set. We use a weight quadratic cost functional showing the temperature deviation. We obtain estimates for the norm of control functions in terms of the value of the quality functional in different functional spaces. It gives us a possibility to estimate the required internal energy of the system. To prove these results we establish the positivity principle.

Quadratic Cost Minimax Optimal Control Problems for a Semilinear Viscoelastic Equation with Long Memory

In this paper, we study the quadratic cost minimax optimal control problems for a semilinear viscoelastic equation with long memory. A global well-posedness theorem regarding the solutions to its Cauchy problem is given. We formulate the minimax control problem with bilinear control inputs and corresponding disturbances. Under some assumptions, we prove the existence of optimal pairs and give necessary optimality conditions for optimal pairs in some observation cases.

Analysis of an SQEIAR epidemic model with media coverage and asymptomatic infection

<abstract><p>An SQEIAR model with media coverage and asymptomatic infection is proposed for populations with a certain level of immunity. Firstly, we discuss the extinction and persistence for the diseases of the model by using basic reproduction number $ \mathcal{R}_C $. Then the parameter threshold is analyzed and the effect of parameters on the basic reproduction number is discussed. Furthermore, the optimal media coverage strategy and quarantine strategy for optimal problems under quadratic cost function are derived by applying Pontryagin's Maximum Principle.</p></abstract>