随机系统预测控制稳定性分析及快速预测算法

Stability Analysis and a Fast Algorithm for the Predictive Control of Stochastic Systems

针对随机离散线性系统的预测控制问题,将系统状态的随机预测方程通过基于卡尔曼滤波的预测估计转化为确定性的状态预估方程,从而将随机预测控制问题转化为初始值为当前时刻观测值的确定性在线优化问题;利用构造可行解的方法,推导了随机系统预测控制的稳定性条件;最后利用LQG(linear quadratic Gaussian)虚拟反馈律,提出了一种减少在线计算量并具有稳定性保证的快速预测算法,并通过仿真验证了算法的有效性和稳定性.

For the issue of predictive control of stochastic discrete linear systems, the stochastic predictive equation is transformed into the deterministive predictive-estimate equation based on the predication and estimation of Kalman filter. Accordingly, stochastic predictive control problem is transformed into deterministive online optimization based on the real- time observed value as the initial value. A stability condition for predictive control of stochastic system is deduced by the method of constructing feasible solution. Finally, using virtual LQG （linear quadratic Gaussian） feedback control law, a fast arithmetic with less on-line calculation cost and stability guarantee is presented, and the simulation results show the stability and the validity of the method.