RS Stochastic Optimal Control With Gravity Compensation Applied to an Actuated Robot

In this paper the Risk-Sensitive (RS) Optimal Control Equations are obtained for Polynomial Stochastic Systems of first degree, starting from Hamilton Jacobi Bellman equation (HJBE). In these RS control equations the diffusion parameter $\epsilon$ gets involved into the gain equations. A comparison with RS optimal control equations is made, where the gain of the control does not contain the diffusion parameter $\epsilon$. In both approaches the RS control equations are the same, but the gain equations aren’t. Both systems of RS control equations are applied to the simple pendulum system, getting best results for the gain equations without $\epsilon$, comparing error values and exponential quadratic cost criterion in final time.