Approximate closed-form solutions to finite-horizon optimal control of nonlinear systems

The Hamilton-Jacobi-Bellman partial differential equation, which is needed to be solved for finite-horizon optimal control of nonlinear systems, is reduced to a state-dependent differential Riccati equation subject to a final condition through some approximations. Afterward, a method, called Finite-SDRE, is developed for finite-horizon near-optimal control synthesis. This technique allows for easier online implementation and its global stability is proved. Finally an approximate solution to the differential equation is given. Performance of the proposed controller in representative numerical examples demonstrates its excellent potential for use in nonlinear finite-horizon problems.