Model-free Q-learning over Finite Horizon for Uncertain Linear Continuous-time Systems

In this paper, a novel optimal control over finite horizon has been introduced for linear continuous-time systems by using adaptive dynamic programming (ADP). First, a new time-varying Q-function parameterization and its estimator are introduced. Subsequently, Q-function estimator is tuned online by using both Bellman equation in integral form and terminal cost. Eventually, near optimal control gain is obtained by using the Q-function estimator. All the closed-loop signals are shown to be bounded by using Lyapunov stability analysis where bounds are functions of initial conditions and final time while the estimated control signal converges close to the optimal value. The simulation results illustrate the effectiveness of the proposed scheme.