Solution of the Hamilton jacobi bellman uncertainties by the interval version of adomian decomposition method

The main purpose of interval arithmetic is look into the uncertain-ties in the practical models with uncertain-but-bounded parameters, which only requires lower and upper bounds of uncertain parameters and with no in-formation about probability distributions. In this paper, an interval numerical method is proposed for solving the Hamilton Jacobi Bellman (HJB) Equations with uncertainties. An interval version of Adomian Decomposition Method is utilized for solving the interval model parameters in the partial differential equations of the HJB. This study assumes that the uncertainty can be happened in both differential coefficients and initial values. The proposed interval method is applied to solve the linear and nonlinear HJB equations in association with appropriate numerical solvers. A practical discussion problem is also solved to analyze the system robustness and to show that the proposed interval decomposition method is a powerful method for systems in the presence of uncertainties.

interval arithmetic, Hamilton Jacobi bellman, partial differential equation, interval adomian decomposition method, nonlinear differential equation, optimal control