Non-linear Optimal Filter and Control with Tracking vs Pid Applied to an Electric Resistance System

Optimal Risk-Sensitive control equations with tracking for first degree polynomial stochastic systems have been obtained and applied to heater system where the actuator is the electrical resistance, achieving the optimal values of the state, for different values of the parameter epsilon which multiplies the white noise in the state equation, which is non linear. Exponential quadratic criterion function to be minimized values are obtained in final time, for some values of the parameter . PID simulation was realized for this heater system. Values of the errors for both (Risk-Sensitive with tracking and PID) are presented in tables showing advantages the Risk-Sensitive control. In addition, in this paper is present the optimal Risk-Sensitive filtering equations applied to the heater system, with both controls and exponential quadratic criterion to be minimized, which contain the quadratic error, for some values of the parameter . Advantage for the system conformed by optimal non linear Risk-Sensitive stochastic control with tracking and non linear stochastic Risk-Sensitive filtering equations is observed through tables.