论文标题
指数稳定的自适应最佳控制不确定的LTI系统
Exponentially Stable Adaptive Optimal Control of Uncertain LTI Systems
论文作者
论文摘要
提出了一种自适应线性二次（LQ）调节的新方法，不确定连续线性时间流动系统。这种方法基于直接的自我调整调节器设计框架和作者早期开发的指数稳定的自适应控制技术。与已知的解决方案不同，提出了一项程序，以从基于LQ的参考跟踪控制系统的初始RE中获得有关未知控制器参数的非横候回归方程（RE）。根据此结果，提出了自适应定律，在轻度回归器有限的激发条件下，LQ-controller参数单调收敛到可调的真实值集，仅由机器精确定义。使用基于Lyapunov的分析，证明上述法律保证了闭环自适应最佳控制系统的指数稳定性。提供了模拟示例以验证理论贡献。
A novel method of an adaptive linear quadratic (LQ) regulation of uncertain continuous linear time-invariant systems is proposed. Such an approach is based on the direct self-tuning regulators design framework and the exponentially stable adaptive control technique developed earlier by the authors. Unlike the known solutions, a procedure is proposed to obtain a non-overparametrized regression equation (RE) with respect to the unknown controller parameters from an initial RE of the LQ-based reference tracking control system. On the basis of such result, an adaptive law is proposed, which under mild regressor finite excitation condition provides monotonous convergence of the LQ-controller parameters to an adjustable set of their true values, which bound is defined only by the machine precision. Using the Lyapunov-based analysis, it is proved that the mentioned law guarantees the exponential stability of the closed-loop adaptive optimal control system. The simulation examples are provided to validate the theoretical contributions.
