Design of the Risk Sensitive Optimal Control Equations with Damping and its Application to a Wheeled Mobile Robot on an Inclined Plane

Abstract

In this work risk-sensitive stochastic equations with damping are designed and applied to a mobile system on an inclined plane. Stochastic term is added to the model in both states: displacement and velocity of the mobile on an inclined plane. The objective is that the mobile has a displacement and it be in the position in certain point. For this it is need add to the risk-sensitive optimal stochastic control input a term of damping, according to this system. In other hand, it is designed a PID equations for this system. Exponential quadratic criterion to be minimized (J) is evaluated with both controllers and results are presented in tables. In simulation, efficiency of risk-sensitive optimal control with damping is demonstrated respect to PID, thought the error values and values of exponential quadratic cost criterion J.