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FINITE-DIMENSIONAL CONTROLLERS FOR PARTIALLY OBSERVABLE

This paper introduces certain nonlinear partially observable stochastic optimal control problems which are equivalent to completely observable control problems with finite-dimensional state space. In some cases the optimal control laws are analogous to linear-exponential-quadraticGaussian and linear-quadratic-Gaussian tracking problems. The problems discussed allow nonlinearities to enter the unobservable dynamics as gradients of potential functions. The methodology is based on explicit solutions of a modified Duncan–Mortensen–Zakai equation.