In this work, a novel approach based on incremental state models is proposed for the modeling and control of multivariable delayed systems with colored noise. One of the key features of the new approach is that the proposed incremental state model compared with the non-incremental one, solves the problem of computing the target state in a natural way, since for a desired output, a zero incremental state can be taken as an objective. Moreover, the control action in an incremental form is equivalent to introduce an integral action, thereby cancelling the steady state errors, even in presence of disturbances. An optimal Linear Quadratic Regulator (LQR) control, based on the incremental model, is proposed and a Kalman filter is used to obtain the estimated state. Thus, another advantage of the proposed method is minimizing the output variance. Illustrative examples are chosen to evaluate the effectiveness of the proposed method.

在这项工作中，提出了一种基于增量状态模型的新颖方法，用于对有色噪声的多变量延迟系统进行建模和控制。新方法的关键特征之一是，与非增量模型相比，所提出的增量状态模型解决了自然计算目标状态的问题，因为对于所需的输出，可以采用零增量状态作为目标。而且，以增量形式的控制动作等效于引入积分动作，从而即使在存在干扰的情况下也消除了稳态误差。提出了基于增量模型的最优线性二次调节器（LQR）控制，并使用卡尔曼滤波器获得估计状态。因此，所提出的方法的另一个优点是使输出方差最小。