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为研究具有高斯白噪声的持续外界随机扰动线性离散系统的最优控制问题。提出了对于随机干扰的处理算法,并给出基于卡尔曼滤波方法的推导过程。利用求解Riccati方程和Stein方程推导出前馈-反馈最优控制律,根据分离原理推导出随机干扰的线性离散系统前馈-反馈最优控制律。通过仿真试验表明,噪声系统得到有效的改善,并在抑制外部扰动和鲁棒性方优于经典的状态反馈最优控制。
To study the optimal control problem of continuous discrete stochastic perturbed linear discrete systems with Gaussian white noise. The algorithm for processing random disturbance is proposed and the derivation process based on Kalman filter is given. The feedforward-feedback optimal control law is derived by solving the Riccati equation and the Stein equation. According to the principle of separation, a feedforward-feedback optimal control law of linear discrete-time system with random disturbance is derived. The simulation results show that the noise system is effectively improved, and the optimal disturbance rejection and robustness are better than the classical state feedback optimal control.