Zhang, HuanJames, Matthew2015-12-080363-0129http://hdl.handle.net/1885/37694Optimal control of a. class of hybrid dynamical systems is studied using the method of dynamic programming. It is proved that the value function is a discontinuous viscosity solution of the corresponding Hamilton-Jacobi-Bellman (HJB) equation which appears as a system of quasi-variational inequalities (SQVI) coupled by a nonlocal operator with a variable boundary condition. The comparison theorems are established for the sub- and super-solutions of the SQVI.Keywords: Dynamic programming; Hamiltonians; Mathematical operators; Nonlinear equations; Nonlinear systems; Theorem proving; Comparison theorem; Hybrid dynamical systems; Optimal control; Quasi-variational inequalities; Viscosity solutions; Optimal control systems Comparison theorem; Dynamic programming; Hybrid dynamical systems; Optimal control; System of quasi-variational inequalities; Viscosity solutionsOptimal control of hybrid systems and a system of quasi-variational inequalities200610.1137/0506301312015-12-08