arXiv subjects

Yitao Yan

Publications and source records attributed to Yitao Yan.

5 recordsLinked to original sources

arXiv2026

Behavioral Systems Theory Meets Machine Learning: Control-Aware Learning of the Intrinsic Behavior from Big Data

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.

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arXiv2026

Data-Driven Probabilistic Finite $\mathcal{L}_2$-Gain Stabilization of Stochastic Linear Systems

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.

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arXiv2025

The Intrinsic State Variable in Fundamental Lemma and Its Use in Stability Design for Data-based Control

In the data-based setting, analysis and control design of dynamical systems using measured data are typically based on overlapping trajectory segments of the input and output variables. This could lead to complex designs because the system internal dynamics, which is typically reflected by the system state variable, is unavailable. In this paper, we will show that the coefficient vector in a modified version of Willems' fundamental lemma is an intrinsic and observable state variable for the system behavior. This argument evolves from the behavioral framework without the requirement of prior knowledge on the causality among system variables or any predefined representation structure (e.g., a state space representation). Such a view allows for the construction of a state map based on the fundamental lemma, bridging the trajectory space and the state space. The state property of the coefficient vector allows for a simple stability design approach using memoryless quadratic functions of it as Lyapunov functions, from which the control action for each step can be explicitly constructed. Using the coefficient vector as a state variable could see wide applications in the analysis and control design of dynamical systems including directions beyond the discussions in this paper.

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arXiv2023

Distributed Data-driven Predictive Control via Dissipative Behavior Synthesis

This paper presents a distributed data-driven predictive control (DDPC) approach using the behavioral framework. It aims to design a network of controllers for an interconnected system with linear time-invariant (LTI) subsystems such that a given global (network-wide) cost function is minimized while desired control performance (e.g., network stability and disturbance rejection) is achieved using dissipativity in the quadratic difference form (QdF). By viewing dissipativity as a behavior and integrating it into the control design as a virtual dynamical system, the proposed approach carries out the entire design process in a unified framework with a set-theoretic viewpoint. This leads to an effective data-driven distributed control design, where the global design goal can be achieved by distributed optimization based on the local QdF conditions. The approach is illustrated by an example throughout the paper.

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arXiv2021

Behavioural Approach to Distributed Control of Interconnected Systems

This paper formulates a framework for the analysis and distributed control of interconnected systems from the behavioural perspective. The discussions are carried out from the viewpoint of set theory and the results are completely representation-free. The core of a dynamical system can be represented as the set of all trajectories admissible through the system and interconnections are interpreted as constraints on the choice of trajectories. We develop a structure in which the interconnected behaviour can be directly built from the behaviours of the subsystems in an explicit way without any presumed forms of representations. We show that the interconnected behaviour can also be fully obtained from local observations of the subsystem. Furthermore, we develop the necessary and sufficient conditions for the existence of distributed controller behaviours and their explicit construction. Due to the entirely representation-free nature of this framework, it unites various representations and descriptions of features of dynamical systems (e.g. models, dissipativity, data, etc.) as behaviours, allowing for the formation of a unified platform for the analysis and distributed control for interconnected systems.

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