arXiv subjects

Shubo Kang

Publications and source records attributed to Shubo Kang.

3 recordsLinked to original sources

arXiv2026

Direct Data-Driven Linear Quadratic Tracking via Policy Optimization

Direct data-driven optimal control provides an elegant end-to-end paradigm, yet its real-time applicability is often hindered by the growing dimensionality of online decision variables. Recent breakthroughs, notably Data-EnablEd Policy Optimization (DeePO), overcome this bottleneck for the Linear Quadratic Regulator (LQR) through sample-covariance parameterization; however, extending this paradigm to Linear Quadratic Tracking (LQT) poses a fundamental challenge. The core difficulty stems from the intricate coupling between time-varying references and the feedback-feedforward policy structure, which prevents a direct application of constant-dimension parameterization. We first introduce a reference-decoupled reformulation of LQT that naturally accommodates the covariance parameterization, guaranteeing a fixed dimension of decision variables independent of data horizon. This formulation is proven to be exactly equivalent to the indirect certainty-equivalence LQT solution. Leveraging this characterization, we develop offline and online DeePO algorithms. Theoretically, we prove global linear convergence for the offline algorithm using local gradient dominance and smoothness, and show that in the online setting the optimality gap decays linearly up to a bias term that scales inversely with the signal-to-noise ratio (SNR). Numerical simulations varify the theoretical results and illustrate the superior tracking performance of the proposed method.

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arXiv2024

Linear Convergence of Data-Enabled Policy Optimization for Linear Quadratic Tracking

Data-enabled policy optimization (DeePO) is a newly proposed method to attack the open problem of direct adaptive LQR. In this work, we extend the DeePO framework to the linear quadratic tracking (LQT) with offline data. By introducing a covariance parameterization of the LQT policy, we derive a direct data-driven formulation of the LQT problem. Then, we use gradient descent method to iteratively update the parameterized policy to find an optimal LQT policy. Moreover, by revealing the connection between DeePO and model-based policy optimization, we prove the linear convergence of the DeePO iteration. Finally, a numerical experiment is given to validate the convergence results. We hope our work paves the way to direct adaptive LQT with online closed-loop data.

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arXiv2022

Minimum Input Design for Direct Data-driven Property Identification of Unknown Linear Systems

In a direct data-driven approach, this paper studies the {\em property identification(ID)} problem to analyze whether an unknown linear system has a property of interest, e.g., stabilizability and structural properties. In sharp contrast to the model-based analysis, we approach it by directly using the input and state feedback data of the unknown system. Via a new concept of sufficient richness of input sectional data, we first establish the necessary and sufficient condition for the minimum input design to excite the system for property ID. Specifically, the input sectional data is sufficiently rich for property ID {\em if and only if} it spans a linear subspace that contains a property dependent minimum linear subspace, any basis of which can also be easily used to form the minimum excitation input. Interestingly, we show that many structural properties can be identified with the minimum input that is however unable to identify the explicit system model. Overall, our results rigorously quantify the advantages of the direct data-driven analysis over the model-based analysis for linear systems in terms of data efficiency.

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