UKF-Based Optimal Tracking Control for Uncertain Dynamic Systems with Asymmetric Input Constraints

To enhance system robustness in the face of uncertainty and achieve adaptive optimization of control strategies, a novel algorithm based on the unscented Kalman filter (UKF) is developed. This algorithm addresses the finite-horizon optimal tracking control problem (FHOTCP) for nonlinear discrete-time (DT) systems with uncertainty and asymmetric input constraints. An augmented system is constructed with asymmetric control constraints being considered. The augmented problem is addressed with a DT Hamilton-Jacobi-Bellman equation (DTHJBE). By analyzing convergence with regard to the cost function and control law, the UKF-based iterative adaptive dynamic programming (ADP) algorithm is proposed. This algorithm approximates the solution of the DTHJBE, ensuring that the cost function converges to its optimal value within a bounded range. To execute the UKF-based iterative ADP algorithm, the actor-estimator-critic framework is built, in which the estimator refers to system state estimation through the application of UKF. Ultimately, simulation examples are presented to show the performance of the proposed method.