谐和与宽带随机激励下拟可积哈密顿系统的最优时滞控制

Optimal time-delay control of quasi integrable Hamiltonian systems under combined harmonic and wide-band random excitations

研究在谐和与宽带随机激励下拟可积哈密顿系统的最优时滞控制。首先,简要叙述谐和与宽带随机激励下的最优时滞控制问题的提法;其次,将时滞的控制力用非时滞的状态变量近似表示,从而将原时滞控制系统转换为非时滞的控制系统;然后,考虑到系统固有频率与谐和激励频率之间可能的共振关系,运用随机平均法,得到部分平均It随机微分方程,再运用随机动态规划原理,建立动态规划方程,即Hamilton-Jacobi-Bellman(HJB)方程,求解得到控制力,通过求解与完全平均的It随机微分方程对应的Fokker-Planck-Kolmogorov(FPK)方程或者Monte Carlo数值模拟得到系统的响应;最后,将上述控制策略应用于潜水艇纵轴振动控制,并通过Monte Carlo数值模拟结果来评估这一控制策略的控制效果和控制效率。

The optimal time-delay control of quasi intergrable Hamiltonian systems under combined harmonic and w/de-band random excitations is studied. First, the optimal control problem of quasi integrable Hamiltonian systems under combined harmonic and wide-band random excitations is formulated. Then, the time-delay control forces are approximately expressed in terms of the system state variables without time delay, and the original system is converted into an ordinary controlled quasi integrahle Hamiltonian system without time delay. Considering the possible resonant relations between the natural frequencies and harmonic excitations frequencies, a set of partly averaged It6 equations are obtained by using the stochastic averaging meth- od. A Hamilton-Jacohi-Bellman（HJB） equation is derived for the optimal control of this partially averaged system by using the stochastic dynamical programming principle. The optimal control forces are obtained from solving the HJB equation and the response of original system is predicted by solving the Fokker-Planck-Kolmogorov （FPK） equation associated with the fully averaged Ito equations or by using Monte Carlo simulation. Finally, the optimal time-delay control of the longitudinal vibration of a submarine propeller system is worked out in detail to illustrate the effectiveness and efficiency of the proposed control strategy.