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.

中文翻译：

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基于 UKF 的不对称输入约束不确定动态系统最优跟踪控制


为了增强系统在面对不确定性时的鲁棒性并实现控制策略的自适应优化，开发了一种基于无迹卡尔曼滤波 （UKF） 的新算法。该算法解决了具有不确定性和非对称输入约束的非线性离散时间 （DT） 系统的有限视界最优跟踪控制问题 （FHOTCP）。在考虑不对称控制约束的情况下构建了一个增强系统。增广问题通过 DT Hamilton-Jacobi-Bellman 方程 （DTHJBE） 解决。通过分析成本函数和控制律的收敛性，提出了基于 UKF 的迭代自适应动态规划 （ADP） 算法。该算法近似于 DTHJBE 的解，确保成本函数收敛到有界范围内的最佳值。为了执行基于 UKF 的迭代 ADP 算法，构建了 actor-estimator-critic 框架，其中估计器指的是通过应用 UKF 进行系统状态估计。最后，提出了仿真实例来展示所提出的方法的性能。