Abstract
The algorithms for the optimal filter and control have been obtained for polynomial systems of first grade. For the filter, two cases are presented: systems with disturbances in L2 and systems with Brownian motion and parameter ∈ multiplying the diffusion term, in state and observations equations. The performance of this algorithms is verified and compared with the optimal Kalman-Bucy filter through an example. Besides the solution to the optimal control Risk-Sensitive problem for stochastic system, taking quadratic value function as solution of PDE HJB is obtained. These Risk-Sensitive control algorithms are compared with the L-Q control algorithms through a numerical example, using quadratic-exponential cost function to be minimized. The optimal risk-sensitive filter and control algorithms show better performance for large values of the parameter ∈.
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