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Nonlinear state estimation by the derivative-free Sigma Point Kalman Filters is treated. Particularly, impact of the derivative-free Kalman filters on estimation quality of the Sigma Point Gaussian Sum Filters is discussed. New relations between the Unscented Kalman Filter and the Divided Difference Filters are derived. The main stress is laid on the covariance matrixes which have crucial role for the behaviour explanation of the Sigma Point Gaussian Sum Filters. The theoretical results are illustrated in some numerical examples.

The paper proposes a suboptimal adaptive control for a nonlinear stochastic system subject to functional uncertainty. The problem of a real-time identification of the unknown nonlinear system is tackled by using the Gaussian process based non-parametric model. The covariance function of the Gaussian process is chosen in such a way that allows deriving the control law in a closed form. The control action stems from the bicriterial dual approach that uses two separate criteria to introduce both of the mutually opposing aspects between estimation and control. Properties of the novel dual controller are tested and validated in a numerical example by Monte Carlo analysis.

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The article deals with a challenging problem of adaptive control design for multivariable stochastic systems with a functional uncertainty. Model of the system is based on multi-layered perceptron neural networks where both the unknown parameters and the structure are found in real time without a necessity of any off-line training process. The unknown parameters are estimated by a global estimation method, the Gaussian sum filter, and the structure of the neural network model is optimized by a proposed pruning method. The control law is based on a bicriterial approach to the suboptimal dual control. Two individual criteria are designed and used to introduce conflicting efforts between the estimation and control; probing and caution. A comparison of the proposed dual control and its alternative with an implementation of the pruning algorithm is shown in a numerical example.