Optimal filtering and control for first degree polynomial systems: Risk-sensitive method

The algorithms for the optimal filter and control have been obtained for systems with polynomial first degree drift term in the state and observations equations. Two cases are presented: systems with disturbances in L² and systems with Brownian motion and parameter epsiv multiplying both in the state and observation equations. The algorithms of the optimal risk-sensitive filter are obtained in each case and their performance is verified and compared with the algorithms of the optimal Kalman-Bucy filter through an example. The solution to the optimal control risk-sensitive problem for stochastic system, and log-exp-quadratic cost function to be minimized is obtained. This algorithms are obtained using value function as solution of PDE HJB. These algorithms are compared with the traditional control algorithms through numerical example. The optimal risk-sensitive filter and control show better performance for large values of the parameter epsiv.