解析的核学习自适应单步预测控制算法

Adaptive one-step-ahead predictive control law with analytical form using kernel learning

针对非线性系统,在非线性广义最小方差控制律的基础上,提出了一种基于核学习辨识模型的自适应单步预测控制(KLAOPC)算法.首先辨识出非线性系统的核学习模型,并利用Taylor近似线性化方法获得控制律.采用中值定理证明了控制律的收敛性,并利用自适应校正项来提高其控制性能.核学习辨识模型容易获得,且在小样本情况下具有较好的推广性能.KLAOPC控制律具有简单的解析形式,需要调整的参数少且计算量小,适合非线性系统的实时控制.仿真结果表明,与其他控制算法相比,KLAOPC控制器有很好的控制效果,对过程的噪声和扰动等均具有较强的自适应性和鲁棒性.

By introducing kernel learning （KL） framework to nonlinear generalized minimum variance control, a kernel learning adaptive one-step-ahead predictive control （KLAOPC） algorithm was proposed for general unknown nonlinear systems. The main structure of KLAOPC includes two technical parts. Firstly, a one-step-ahead KL predictive model was obtained; secondly, the analytical control law was derived from Taylor linearization method. The convergence analysis of this new control strategy was presented based on the mean-value theorem, meanwhile a novel concept of adaptive modification index was given to improve the tracking ability of KLAOPC and reject unknown disturbance. The KLAOPC scheme has small computation scale, which makes it very suitable for real-time implementation. Numerical simulations show that compared to other related control algorithms, the new simple KLAOPC algorithm exhibits better tracking performance, and possesses satisfactory robustness both to noise and disturbance.