Adaptive dynamic programming for terminally constrained finite-horizon optimal control problems

Adaptive dynamic programming is applied to control-affine nonlinear systems with uncertain drift dynamics to obtain a near-optimal solution to a finite-horizon optimal control problem with hard terminal constraints. A reinforcement learning-based actor-critic framework is used to approximately solve the Hamilton-Jacobi-Bellman equation, wherein critic and actor neural networks (NN) are used for approximate learning of the optimal value function and control policy, while enforcing the optimality condition resulting from the hard terminal constraint. Concurrent learning-based update laws relax the restrictive persistence of excitation requirement. A Lyapunov-based stability analysis guarantees uniformly ultimately bounded convergence of the enacted control policy to the optimal control policy.