Optimal control of affine nonlinear continuous-time systems
Optimal control of affine nonlinear continuous-time systems
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DOI：
10.1109/cdc.2010.5717676
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发表时间：
2010-12
期刊：
影响因子：
--
通讯作者：
T. Dierks;S. Jagannathan
中科院分区：
文献类型：
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作者：
T. Dierks;S. Jagannathan
在本文中，最优调节和跟踪控制的仿射非线性连续时间系统与已知的动态进行使用一种新的单在线逼近器（SOL）为基础的计划。基于SOLA的自适应方法被设计用于学习无限时域连续时间Hamilton-Jacobi-Bellman（HJB）方程及其相应的最优控制输入。提出了一种新的参数整定算法，该算法不仅保证了系统的最优性能和控制输入，而且保证了在线学习过程中系统状态的有界性。李雅普诺夫方法证明了所有信号都是一致最终有界的，且逼近的控制信号以较小的有界误差逼近最优控制输入。在没有奥拉重建误差的情况下，渐近收敛到最优控制。仿真结果验证了该方法的有效性。
In this paper, the optimal regulation and tracking control of affine nonlinear continuous-time systems with known dynamics is undertaken using a novel single online approximator (SOL)-based scheme. The SOLA-based adaptive approach is designed to learn the infinite horizon continuous-time Hamilton-Jacobi-Bellman (HJB) equation and its corresponding optimal control input. A novel parameter tuning algorithm is derived which not only ensures the optimal cost (HJB) function and control input are achieved, but also ensures the system states remain bounded during the online learning process. Lyapunov techniques show that all signals are uniformly ultimately bounded (UUB) and the approximated control signal approaches the optimal control input with small bounded error. In the absence of OLA reconstruction errors, asymptotic convergence to the optimal control is shown. Simulation results illustrate the effectiveness of the approach.