本文提出一針對非線性系統的最佳化控制法。透過最佳化線性法則，我們可以利用核回歸模型來建構出非線性隨機狀態最佳化控制系統。此外，我們利用進化演算法取代傳統的方法來挑選適當的特徵值向量，以建構出更理想的核回歸模型。本文提出的方法使得非線性數位系統的進階數位控制演算法更具發展性。

An optimal controller for nonlinear system identified by generalized kernel model is proposed in this thesis. EP algorithm is used to tune the elements of the diagonal covariance matrix for the kernel regressors. By applying EP algorithm on the kernel model, the error between regressors and the actual nonlinear system could be minimized and the terms of the regrssors could be reduced as well. By applying the optimal linearization approach, a generalized kernel model with estimated states for nonlinear continuous–time stochastic systems can be constructed for the optimal control. The proposed method enables development of digitally implement advanced control algorithm for nonlinear stochastic hybrid systems.

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