This paper deals with Hamilton–Jacobi–Bellman (HJB) equation based stabilized optimal control of hybrid dynamical systems (HDS). This paper presents the fuzzy clustering based event wise multiple linearized modeling approaches for HDS to describe the continuous dynamic in each event. In the present work a fuzzy clustering validation approach is presented for the selection of number of linearized models which span entire HDS. The method also describes how to obtain event wise operating point using fuzzy membership function, which is used to find the event wise model bank by linearizing the first principles model. The event wise linearized models are used for the formulation of the optimal control law. The HJB equation is formulated using a suitable quadratic term in the objective function. By use of the direct method of Lyapunov stability, the control law is shown to be optimal with respect to objective functional and stabilized the event wise linearized models. The global Lyapunov function is proposed with discrete variables which stabilized the HDS. The proposed modeling and control algorithm have been applied on two HDSs. Necessary theoretical and simulation experiments are presented to demonstrate the performance and validation of the proposed algorithm. 
Clustering based multiple model control of hybrid dynamical systems using HJB solution