基于两级算法的对偶控制

Dual control based on two-level algorithm

考虑具有未知参数的随机系统的最优控制问题.采用包含新息方差指数项的损失函数优化系统的性能.新的损失函数由两部分组成:第一部分反映了对输出的调节作用;第二部分反映了辩识系统中未知参数应尽可能多地收集系统信息的需求.提出了一种两级优化算法.该算法首先把不可分问题转化为可分的两目标优化问题,再从两目标优化的非劣解集中挑出原问题的最优解.该控制律易于实施且具有对偶特点.仿真结果表明本文所得的控制律的有效性.

The control of a stochastic system with unknown parameter was considered. A novel cost function, which includes the exponent term of the variance of innovations, was used to optimize the performance of the system. The cost function consisted of two parts — one reflects the goal of regulating the output, and the other reflects the need to gather as much information as possible about the parameters of this system. A two-level optimization algorithm was proposed. The non-separable problem was first converted into separable two-objective optimization problem, then the optimal control of the original problem is selected from the set of non-inferior solutions of two-objective optimization problem. Such optimal control had an explicit solution that allowed for an easy implementation and dual properties. Finally, simulation results were given to show that the control law obtained in this paper is effectiveness.