带有持续扰动非线性系统的前馈-反馈最优控制

研究具有外界持续扰动作用下非线性系统的最优控制问题，提出了一种设计前馈一反馈最优控制器的逐次逼近算法．利用该算法可将在扰动作用下的非线性系统的最优控制问题转化为求解线性非齐次两点边值序列的问题．得到的最优控制律由解析的线性前馈-反馈项和伴随向量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，可得到前馈-反馈次优控制律．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．

Feedforward and feedback optimal control for nonlinear systems with persistent disturbances

The optimal control problem is considered for nonlinear systems affected by external persistent (disturbances.) A successive (approximation) algorithm of designing feedforward and feedback optimal controllers is (developed.) By using the successive approximation approach, the original optimal control problem is transformed into a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems. The obtained optimal control law consists of analytical linear feedforward and 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, a feedforward and feedback suboptimal control law is obtained. Simulations show the result is more robust with respect to external persistent disturbances than the classical feedback optimal control.