一类双线性系统的最优跟踪控制问题

针对一类具有二次型性能指标的双线性系统的最优跟踪控制问题,提出了一种通过逐次逼近法设计最优控制律的近似方法。首先将状态向量含有时滞的双线性系统的最优跟踪问题转化为最优调节问题;然后利用逐次逼近算法,将既含有时滞项又含有超前项的两点边值问题转化为不含时滞项和超前项的线性两点边值问题族,得到调节系统的最优控制律,并可以通过截取最优控制序列的有限项得到调节系统的前馈-反馈次优控制律。最后,将最优控制问题转化为最优跟踪问题。仿真结果表明,此方法达到了较好的跟踪效果。

Optimal Tracking Control for Time-delay Systems with Persistent Disturbances

The optimal tracking control problem for a class of bilinear systems with a quadratic performance index is considered.First,we transform the optimal tracking control problem of linear systems with state time-delay into the optimal control problem.Second,the linear two-point boundary value(IPBV) problem with both time-delay terms and time-advance terms is transformed to a sequence of nonhomogeneous linear TPBV problems without time-delay terms and time-advance terms with the successive approximation algorithm.We obtain a optimal control law.And then,by taking the finite-times iteration of the compensating sequence,we obtain a suboptimal control law.Lastly we transform the optimal control law into the optimal tracking control law.The simulations show that the approach is efficient to realize the tracking control.