Ankit K. Shah and Dipak M. Adhyaru
Multiple linearized modelling, hybrid dynamical systems, HJB equation, optimal control, Lyapunov function
The multiple linearized modelling (MLM) approach for the hybrid dynamical systems (HDS) is most popular due to its simplicity and equivalence to other classes of the HDS. However, how to estimate the optimal tracking control law for each model is an open problem due to the interaction of discrete event in the HDS. This paper focuses on the Hamilton–Jacobi–Bellman (HJB) equation-based stabilized optimal control law design for the HDS. A new computational framework for the HDS is proposed which can
provide asymptotic stability along with the optimal tracking control law. The necessary conditions for the optimal tracking control for the HDS are solved using suitable quadratic Lyapunov functions. Experimental results on the temperature control heating system
are given to show the validity and eﬀectiveness of the proposed approach.