Yitao Yan

Yitao Yan, Yu Tong, Jie Bao et al.

The abundance of process operating data in modern industries, along with the rapid advancement of learning techniques, has led to a paradigm shift towards data-centric analysis and control. However, integrating machine learning with control theory for big data-driven control of nonlinear systems remains a challenging open problem. This is because the state-based, model-centric, and causal framework of classical control theory fundamentally contradicts the trajectory-based, set-theoretic, and causality-absent rationale of big data-based learning approaches. Using the behavioral framework, we show that dynamical systems possess an intrinsic state variable that encodes the system behavior in a bijective and causality-free manner, and control design can be carried out entirely within the state space. This approach not only resolves the aforementioned conflict but also complements machine learning techniques well, leading to a neural network architecture that is capable of learning the behavior representation well-suited for control design.

Yitao Yan, Shuangyu Han, Jie Bao et al.

In process operations, it is desirable to manage the sensitivity of the system output against external disturbance in the form of finite $\mathcal{L}_2$-gain stabilization. This matter is, however, nonsensical for stochastic systems because the stochastic uncertainties in the control input almost always lead to an unbounded $\mathcal{L}_2$ gain from the disturbance to the output. To address this issue, this article develops a novel concept that characterizes the $\mathcal{L}_2$ gain of stochastic systems in a probabilistic way. Combined with a large data set, we formulate a data-driven probabilistic finite $\mathcal{L}_2$-gain stabilization design using noisy trajectory measurements and the disturbance forecast that does not necessarily agree with the actual future disturbance. The design approach consists of a data-driven trajectory estimation algorithm, whose resulting estimation error covariance is nicely integrated into the feasibility conditions for controller synthesis, leading to a convex offline design in the form of linear matrix inequalities. The effectiveness of the proposed design, along with the additional insights provided by the approach, is illustrated via a numerical example.