arXiv subjects

Kaikai Zheng

Publications and source records attributed to Kaikai Zheng.

5 recordsLinked to original sources

arXiv2026

Thompson Sampling-Based Learning and Control for Unknown Dynamic Systems

Thompson sampling (TS) is a Bayesian randomized exploration strategy that samples options (e.g., system parameters or control laws) from the current posterior and then applies the selected option that is optimal for a task, thereby balancing exploration and exploitation; this makes TS effective for active learning-based controller design. However, TS relies on finite parametric representations, which limits its applicability to more general spaces, which are more commonly encountered in control system design. To address this issue, this work proposes a parameterization method for control law learning using reproducing kernel Hilbert spaces and designs a data-driven active learning control approach. Specifically, the proposed method treats the control law as an element in a function space, allowing the design of control laws without imposing restrictions on the system structure or the form of the controller. A TS framework is proposed in this work to reduce control costs through online exploration and exploitation, and the convergence guarantees are further provided for the learning process. Theoretical analysis shows that the proposed method learns the relationship between control laws and closed-loop performance metrics at an exponential rate, and the upper bound of control regret is also derived. Furthermore, the closed-loop stability of the proposed learning framework is analyzed. Numerical experiments on controlling unknown nonlinear systems validate the effectiveness of the proposed method.

cs.LG↗

arXiv2025

Open-/Closed-loop Active Learning for Data-driven Predictive Control

An important question in data-driven control is how to obtain an informative dataset. In this work, we consider the problem of effective data acquisition of an unknown linear system with bounded disturbance for both open-loop and closed-loop stages. The learning objective is to minimize the volume of the set of admissible systems. First, a performance measure based on historical data and the input sequence is introduced to characterize the upper bound of the volume of the set of admissible systems. On the basis of this performance measure, an open-loop active learning strategy is proposed to minimize the volume by actively designing inputs during the open-loop stage. For the closed-loop stage, a closed-loop active learning strategy is designed to select and learn from informative closed-loop data. The efficiency of the proposed closed-loop active learning strategy is proved by showing that the unselected data cannot benefit the learning performance. Furthermore, an adaptive predictive controller is designed in accordance with the proposed data acquisition approach. The recursive feasibility and the stability of the controller are proved by analyzing the effect of the closed-loop active learning strategy. Finally, numerical examples and comparisons illustrate the effectiveness of the proposed data acquisition strategy.

eess.SY↗

arXiv2025

Information-triggered Learning with Application to Learning-based Predictive Control

Learning-based control has attracted significant attention in recent years, especially for plants that are difficult to model based on first-principles. A key issue in learning-based control is how to make efficient use of data as the abundance of data becomes overwhelming. To address this issue, this work proposes an information-triggered learning framework and a corresponding learning-based controller design approach with guaranteed stability. Specifically, we consider a linear time-invariant system with unknown dynamics. A set-membership approach is introduced to learn a parametric uncertainty set for the unknown dynamics. Then, a data selection mechanism is proposed by evaluating the incremental information in a data sample, where the incremental information is quantified by its effects on shrinking the parametric uncertainty set. Next, after introducing a stability criterion using the set-membership estimate of the system dynamics, a robust learning-based predictive controller (LPC) is designed by minimizing a worst-case cost function. The closed-loop stability of the LPC equipped with the information-triggered learning protocol is discussed within a high-probability framework. Finally, comparative numerical experiments are performed to verify the validity of the proposed approach.

eess.SY↗

arXiv2022

Event-triggered Observability: A Set-membership Perspective

This work attempts to discuss the observability of linear time-invariant systems with event-triggered measurements. A new notion of observability, namely, $ε$-observability is defined with parameter $ε$, which relates to the worst-case performance of inferring the initial state based on not only the received measurement but also the implicit information in the event-triggering conditions at no-event instants. A criterion is developed to test the proposed $ε$-observability of discrete-time linear systems, based on which an iterative event-triggered set-membership observer is designed to evaluate a set containing all possible values of the state. The proposed set-membership observer is designed as the outer approximation of the ellipsoids predicted based on previous state estimates and the ellipsoids inferred by fusing the received measurement and communication conditions, which is optimal in the sense of trace at each step and is proved to be asymptotically bounded. The efficiency of the proposed event-triggered set-membership state observer is verified by numerical experiments.

eess.SY↗

arXiv2020

Learning Hidden Markov Models for Linear Gaussian Systems with Applications to Event-based State Estimation

This work attempts to approximate a linear Gaussian system with a finite-state hidden Markov model (HMM), which is found useful in solving sophisticated event-based state estimation problems. An indirect modeling approach is developed, wherein a state space model (SSM) is firstly identified for a Gaussian system and the SSM is then used as an emulator for learning an HMM. In the proposed method, the training data for the HMM are obtained from the data generated by the SSM through building a quantization mapping. Parameter learning algorithms are designed to learn the parameters of the HMM, through exploiting the periodical structural characteristics of the HMM. The convergence and asymptotic properties of the proposed algorithms are analyzed. The HMM learned using the proposed algorithms is applied to event-triggered state estimation, and numerical results on model learning and state estimation demonstrate the validity of the proposed algorithms.

eess.SY↗