具有小时滞的线性系统次优控制的无滞后转换法

Non-Delay Transformation Approach of Suboptimal Control for Linear Systems with Small Time-Delay

该文研究线性时滞定常系统的次优控制问题。根据无滞后转换法的思想 ,先引入状态向量的增量 ,将其视为附加扰动输入 ,再利用微分方程的逐次逼近法 ,将既含有时滞项又含有超前项的两点边值问题化为既不含时滞项又不含超前项的两点边值问题族。然后 ,把第 N次逼近得到的控制律近似为系统的最优控制律 ,得到次优控制律。并用实例仿真验证了该算法的有效性。该方法可使小时滞系统的迭代次数大大减少 ,因此尤其适合于小时滞系统的次优控制。

In this paper the suboptimal control of linear systems with time-delay is studied. We introduce an increment of state terms as an additional disturbance, and use the asymptotic approximation method in differential equation theory to solve the problem. We transform the two-point boundary value problem with time-delay terms and time-advance terms to a group of problems without time-delay terms and time-advance terms according to the concept of non-delay transformation approach. By taking the N th iterative value of the optimal solutions, we obtain a suboptimal control law. A simulation example is given to test the validity of the algorithm. When the system of the time-delay is small, the number of iterative times may be decreased greatly. Therefore the method is more suitable for the suboptimal control of small time-delay systems.