一种求解线性控制系统可达集的数值方法

针对线性控制系统,研究应用常微分方程数值方法和优化技术相结合的近似可达集的方法.首先,用常微分方程数值方法对系统进行离散化.然后,提出基于优化技术的外部投影法来近似离散系统的可达集.外部投影法构造有限多个投影问题,每个都对应一个凸优化问题,通过求解这些凸优化问题最终可以得到可达集的近似描述.最后,通过数值仿真结果验证了所提出方法的有效性.与文献中已有的方法相比,在求解相同数量凸优化问题的情况下,外部投影法的近似精度更高.

A numerical method for reachable sets of linear control systems

The approximation of the reachable set of a linear control system is studied.Firstly, the continuous system is discretized into a discrete system by using numerical methods for ordinary differential equations.Then an outer projection method based on optimization techniques is proposed to approximate the reachable set of the discrete system.The outer projection method constructs a finite number of projection problems and each one corresponds to a convex optimization problem.The approximation of the reachable set is achieved by solving finite convex optimization problems.Finally, numerical results show the effectiveness of the proposed method.Compared to the methods in the literatures, when solving the same number of convex optimization problems, the approximation set obtained by using the proposed method is better.