Optimal Risk Sensitive Controller Design Applied to a Stochastic Dynamics of a Simple Pendulum Robot

In this paper the Risk-Sensitive (RS) Optimal Controller Equations for Polynomial Stochastic Systems of first degree with tuning in the real states are applied to the of simple pendulum model. This RS controller contains the RS optimal control equations and the RS filtering equations connecting the control into the estimate RS equations. The dynamic of the state contains a parameter ϵ, as attenuation of the noise and parameter γ which permits adjustment to the gain control values to obtain solution in R. Values of the exponential quadratic cost criterion function are obtained for some values of parameter ϵ, which are selected according to the real tolerance of the motor of the pendulum. Results (errors values, exponential quadratic cost criterion values) presented in a table show the feasibility of this proposal.