线性系统近似生存域的计算

研究了构造控制系统近似生存域的方法和线性系统的近似生存性条件. 基于集合的逼近法锥, 给出了凸紧集的过剩近似生存域表达式．在凸紧集边界上采样足够多个点的情况下, 此近似生存域可以逼近真实的生存域. 并研究了连续线性控制系统和离散线性控制系统在此近似生存域上的生存性, 将求生存控制器的问题转化为线性不等式组问题. 最后, 以悬挂点可以移动的钟摆模型和两类细菌数量变化模型为例说明了算法的有效性.

Computation of approximate viable sets for linear systems

We investigate the approximate viability conditions for linear control systems and the method of constructing approximate viable sets for control systems. Based on the proximal normal cone, a surplus viable set for a convex compact set is given, which can approximate the real viable set if the number of sample points on the boundary of the convex compact set is large enough. For continuous-time linear systems and discrete-time linear systems, the method to verify the viability of approximate viable set is given. Furthermore, the problem of viable controller design is formulated as a linear inequalities problem. Finally, we illustrate the effectiveness of the main results of this paper with a pendulum model with a movable suspension point and the other model of two types of bacteria.