柔性作动器驱动的非线性系统随机振动的最优有界控制

柔性作动器具有低刚度、大变形等特征，这一方面使主结构具备了强的环境适应性，另一方面也使主结构易受外界微扰影响，从而降低其操作精度．本文以介电弹性体作动器驱动的单自由度非线性系统为研究对象，通过即时微调电压，抑制系统在平衡位置附近的随机振动．通过随机平均法降低系统维数，将原系统的控制问题转化为关于慢变过程的控制问题；结合随机动态规划原理及控制约束导出最优有界控制策略．该策略具干摩擦形式，具有能量耗散本质，在抑制系统振动的同时提高了系统的稳定性．数值研究表明：最优有界控制策略具有良好的控制效果、控制效率及较高的鲁棒性．

Optimal Bounded Control for Random Vibration of Nonlinear System with Soft Actuator

Soft actuators possess the low-stiffness and large-deformation properties. By applying the soft actuator, the primary structure obtains strong environmental compatibility. At the same time, the primary structure will be easily influenced by external disturbances which induce low operating accuracy. This paper investigates a single degree-of-freedom nonlinear system with dielectric elastomer actuator as the research object, and aims at seeking an optimal control strategy to suppress the random vibration around the equilibrium position by adjusting the imposed voltage in the real time. The dimension of the original system is reduced by using the stochastic averaging. The control problem of the original system is converted to that of a slow-varying process. The optimal bounded control strategy is derived by combining the stochastic dynamic programming principle and the control bound. This strategy possesses a dry friction property and can dissipate system total energy. It suppresses the random vibration and enhances the stability of the controlled system. Numerical results show that the proposed bounded control strategy has good control effectiveness and efficiency, as well as high robustness with respect to the excitation intensity.