arXiv subjects

Zuxun Xiong

Publications and source records attributed to Zuxun Xiong.

7 recordsLinked to original sources

arXiv2026

A Koopman Set-Membership Approach for Nonlinear Data-Driven Control with Stability Guarantees

This paper proposes a data-driven controller design method for unknown nonlinear systems based on a Koopman bilinear realization. Using Koopman operator theory, the nonlinear system can be represented as a bilinear discrete-time system with a residual error term. The residual error is proportionally bounded by the norm of the lifted state and input, while the system matrices of the bilinear model are unknown. Assuming that bounds on the residual error are available, the unknown system matrices are characterized via a set-membership representation using the collected input-state data pairs of the nonlinear system. A data-driven controller design method is proposed to ensure stability for all bilinear systems within this set-membership description and for all admissible residual errors. More specifically, we design a rational state-feedback controller that stabilizes the bilinear model with residual error and, consequently, the original nonlinear system, by solving a sum-of-squares (SOS) program. The effectiveness of the proposed approach is demonstrated through numerical examples.

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arXiv2025

On the Design of Rational Polynomial State Feedback Controllers

One of the desirable objectives in feedback control design is to formulate and solve the design problem as an optimisation problem that is convex, so that an optimal solution can be found efficiently. Unfortunately many control design problems are non-convex: approximations, relaxations, or iterative schemes are usually employed to solve them. Several such approaches have been developed in the literature, for example Sum-of-Squares (SOSs) methods have been used for systems described by polynomial dynamics. Alternatively, and relevant to this paper, one can choose a (non-unique) linear-like representation of the system and solve the resulting state-dependent Linear Matrix Inequalities (LMIs) or use SOSs optimisation techniques to derive a control law. This SOS method has been shown to effectively design polynomial and rational controllers for nonlinear polynomial systems, offering a broader class of controllers and the potential for improved performance and robustness guarantees. In this paper, we start off by considering rational functions as controllers for nonlinear systems and propose a procedure for designing such controllers by iteratively solving convex SOS optimisation problems. Our approach decouples the controller structure from the system dynamics and incorporates it as a constraint within the optimisation problem, which results in an optimisation that co-designs aspects of the controller and the Lyapunov function at the same iterative step. We theoretically establish the properties of this procedure by showing that several existing rational controller design methods can be recovered as special cases of this procedure. The proposed method is evaluated on various nonlinear benchmark system examples, demonstrating improved performance and robustness over both polynomial controllers and rational controllers obtained by existing approaches.

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arXiv2025

Data-Enabled Predictive Control for Nonlinear Systems Based on a Koopman Bilinear Realization

This paper extends the Willems' Fundamental Lemma to nonlinear control-affine systems using the Koopman bilinear realization. This enables us to bypass the Extended Dynamic Mode Decomposition (EDMD)-based system identification step in conventional Koopman-based methods and design controllers for nonlinear systems directly from data. Leveraging this result, we develop a Data-Enabled Predictive Control (DeePC) framework for nonlinear systems with unknown dynamics. A case study demonstrates that our direct data-driven control method achieves improved optimality compared to conventional Koopman-based methods. Furthermore, in examples where an exact Koopman realization with a finite-dimensional lifting function set of the controlled nonlinear system does not exist, our method exhibits advanced robustness to finite Koopman approximation errors compared to existing methods.

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arXiv2024

Two-Stage Robust Planning Model for Park-Level Integrated Energy System Considering Uncertain Equipment Contingency

To enhance the reliability of Integrated Energy Systems (IESs) and address the research gap in reliability-based planning methods, this paper proposes a two-stage robust planning model specifically for park-level IESs. The proposed planning model considers uncertainties like load demand fluctuations and equipment contingencies, and provides a reliable scheme of equipment selection and sizing for IES investors. Inspired by the unit commitment problem, we formulate an equipment contingency uncertainty set to accurately describe the potential equipment contingencies which happen and can be repaired within a day. Then, a modified nested column-and-constraint generation algorithm is applied to solve this two-stage robust planning model with integer recourse efficiently. In the case study, the role of energy storage system for IES reliability enhancement is analyzed in detail. Computational results demonstrate the advantage of the proposed model over other planning models in terms of improving reliability.

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arXiv2024

Data-Driven Stable Neural Feedback Loop Design

This paper proposes a data-driven approach to design a feedforward Neural Network (NN) controller with a stability guarantee for plants with unknown dynamics. We first introduce data-driven representations of stability conditions for Neural Feedback Loops (NFLs) with linear plants, which can be formulated into a semidefinite program (SDP). Subsequently, this SDP constraint is integrated into the NN training process to ensure stability of the feedback loop. The whole NN controller design problem can be solved by an iterative algorithm. Finally, we illustrate the effectiveness of the proposed method compared to model-based methods via numerical examples.

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arXiv2024

Model-Free Verification for Neural Network Controlled Systems

Neural network controllers have shown potential in achieving superior performance in feedback control systems. Although a neural network can be trained efficiently using deep and reinforcement learning methods, providing formal guarantees for the closed-loop properties is challenging. The main difficulty comes from the nonlinear activation functions. One popular method is to use sector bounds on the activation functions resulting in a robust analysis. These methods work well under the assumption that the system dynamics are perfectly known, which is, however, impossible in practice. In this paper, we propose data-driven semi-definite programs to formally verify stability and safety for a neural network controlled linear system with unknown dynamics. The proposed method performs verification directly from end-to-end without identifying the dynamics. Through a numerical example, we validate the efficacy of our method on linear systems with controller trained by imitation learning.

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arXiv2022

A Stochastic Planning Method for Low-carbon Building-level Integrated Energy System Considering Electric-Heat-V2G Coupling

The concept of low-carbon building is proposed to ameliorate the climate change caused by environmental problems and realize carbon neutrality at the building level in urban areas. In addition, renewable energy curtailment in the power distribution system, as well as low efficiency due to independent operation of traditional energy systems, has been addressed by the application of integrated energy system (IES) to some extent. In this paper, we propose a planning method for low-carbon building-level IES, in which electric vehicles (EV) and the mode of Vehicle to Grid (V2G) are considered and further increase the flexibility of low-carbon buildings. The proposed planning model optimize the investment, operation costs and CO2 emission for building-level IES, so as to achieve the maximum benefit of the construction of the low-carbon building and help the realization of carbon neutrality. Moreover, we consider the uncertainty of distributed renewable energy, multi-energy load fluctuation and the random behavior of EV users, then formulating a two-stage stochastic programming model with chance constraints, in which heuristic moment matching scenario generation (HMMSG) and sample average approximation (SAA) method are applied. In case study, a real IES commercial building in Shanghai, where photovoltaic (PV), energy storage system (ESS), fuel cell (FC), EV, etc. are included as planning options, is used as numerical example to verify the effectiveness of the proposed planning method, with functions of ESS and EV in IES are analyzed in detail in different operation scenarios.

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