一类混合不确定系统的对偶自适应控制

Dual Adaptive Control for a Class of Mixed Uncertainty Systems

在具有未知常数且状态能够精确测量的线性二次型高斯(linear quadratic Gaussian, LQG)问题中,因为参数估计和控制增益存在耦合,所以分离定理不再成立,导致控制律无法获得解析解.为此,提出了一种对偶自适应控制方法,首先建立参数估计的状态空间模型,利用滚动动态规划获得控制增益,用Kalman滤波对未知参数进行估计,解决了估计增益与控制增益相互耦合的问题,进而设计了具有次优性质的控制器.该控制器既能优化控制目标,又能对未知参数进行有效学习.仿真结果表明了所提控制算法的有效性.

For the linear quadratic Gaussian （LQG） problems with unknown constant parameters and accurately measurable state, the separation theorem is no longer valid due to the coupling between parameters estimation and control gain, which lead to the failure to the analytical solution of the control law. The dual adaptive control method is proposed in this paper, where a state space model of parameters estimation is established, control gain is obtained by rolling dynamic programming, Kalman filter is used to estimate unknown parameters, the present difficulties about the mutual coupling between estimated gain and control gain are overcome, and the controller with suboptimal characteristics is designed. On the one hand, the controller can optimize the control target, on the other hand, it can also learn unknown parameters effectively. The simulation results show the effectiveness of the proposed control algorithm.