Feng, YantaoAnderson, BrianRotkowitz, Michael2015-12-100005-1098http://hdl.handle.net/1885/51266In this paper, an iterative algorithm to solve Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations for a broad class of nonlinear control systems is proposed. By constructing two series of nonnegative functions, we replace the problem of solving an HJBI equation by the problem of solving a sequence of Hamilton-Jacobi-Bellman (HJB) equations whose solutions can be approximated recursively by existing methods. The local convergence of the algorithm and local quadratic rate of convergence of the algorithm are guaranteed and a proof is given. Numerical examples are also provided to demonstrate the effectiveness of the proposed algorithm. A game theoretical interpretation of the algorithm is given.Keywords: Algorithms; Convergence of numerical methods; Game theory; Nonlinear control systems; Existing methods; Exponentially stable; Hamilton-jacobi-bellman; Hamilton-Jacobi-Bellman equations; HJBI; Iterative; Iterative algorithms; Local convergences; Nonlinear Exponentially stable; HJBI; Iterative200910.1016/j.automatica.2008.11.0062016-02-24