受扰双线性系统的近似最优扰动抑制方法

研究具有外界持续扰动作用下双线性系统的最优控制问题.关于二次型性能指标给出了一种设计最优扰动抑制控制律的逐次逼近方法.利用该算法可将在扰动作用下双线性系统的最优控制问题转化为求解一组线性非齐次两点边值序列问题.通过迭代序列得到的最优扰动抑制控制律由解析的线性前馈-反馈项和序列极限形式的非线性补偿项组成.通过截取非线性补偿序列的有限项,可以得到近似最优扰动抑制控制律.仿真结果表明,该方法抑制外部持续扰动的鲁棒性优于经典反馈最优控制.

Approximate Optimal Disturbance Rejection for Bilinear Systems with Persistent Disturbances

The optimal control problem is considered for bilinear systems affected by external persistent disturbances.A successive approximation algorithm of designing optimal disturbances rejection controllers is developed with respect to quadratic performance indexes.By using the approach,the original optimal control problem of bilinear systems with disturbances is transformed into a sequence of nonhomogeneous linear two-point boundary value(TPBV) problems.By solving iterative the sequences,the optimal control law is obtained which consists of analytical linear feedforward-feedback terms and a nonlinear compensation term,which is the limit of the adjoint vector sequence.By using the finite-step iteration of nonlinear compensation sequence,an approximate optimal disturbance rejection control law is obtained.The simulations indicate the algorithm is efficient and robust with respect to persistent disturbances.