Optimal feedback control of nonlinear systems with a finite horizon based on HJ equations

An optimal control problem for nonlinear systems with a finite horizon are considered. In the design process, we meet the Hamilton Jacobi (HJ) equations which are extremely difficult to solve. Even so, there are a lot of effective techniques to numerically solve HJ equations when we restrict ourselves to the infinite horizon case. This paper proposes a new approach to tackle with the finite horizon case, based on the fruitful results obtained in the infinite horizon case. Some simulations are given to illustrate the effectiveness of the approach.