arXiv subjects

Wallace Gian Yion Tan

Publications and source records attributed to Wallace Gian Yion Tan.

5 recordsLinked to original sources

arXiv2026

Fixed-time-stable ODE Representation of Lasso

Lasso problems arise in many areas, including signal processing, machine learning, and control, and are closely connected to sparse coding mechanisms observed in neuroscience. A continuous-time ordinary differential equation (ODE) representation of the Lasso problem not only enables its solution on analog computers but also provides a framework for interpreting neurophysiological phenomena. This article proposes a fixed-time-stable ODE representation of the Lasso problem by first transforming it into a smooth nonnegative quadratic program (QP) and then designing a projection-free Newton-based ODE representation of the Lasso problem by first transforming it into a smooth nonnegative quadratic program (QP) and then designing a projection-free Newton-based fixed-time-stable ODE system for solving the corresponding Karush-Kuhn-Tucker (KKT) conditions. Moreover, the settling time of the ODE is independent of the problem data and can be arbitrarily prescribed. Numerical experiments verify that the trajectory reaches the optimal solution within the prescribed time.

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arXiv2026

Polynomial Parametric Koopman Operators for Stochastic MPC

This paper develops a parametric Koopman operator framework for Stochastic Model Predictive Control (SMPC), where the Koopman operator is parametrized by Polynomial Chaos Expansions (PCEs). The model is learned from data using the Extended Dynamic Mode Decomposition -- Dictionary Learning (EDMD-DL) method, which preserves the convex least-squares structure for the PCE coefficients of the EDMD matrix. Unlike conventional stochastic Galerkin projection approaches, we derive a condensed deterministic reformulation of the SMPC problem whose dimension scales only with the control horizon and input dimension, and is independent of both the lifted state dimension and the number of retained PCE terms. Our framework, therefore, enables efficient nonlinear SMPC problems with expectation and second-order moment constraints with standard convex optimization solvers. Numerical examples demonstrate the efficacy of our framework for uncertainty-aware SMPC of nonlinear systems.

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arXiv2026

Koopman-BoxQP: Solving Large-Scale NMPC at kHz Rates

Solving large-scale nonlinear model predictive control (NMPC) problems at kilohertz (kHz) rates on standard processors remains a formidable challenge. This paper proposes a Koopman-BoxQP framework that i) learns a linear Koopman high-dimensional model, ii) eliminates the high-dimensional observables to construct a multi-step prediction model of the states and control inputs, iii) penalizes the multi-step prediction model into the objective, which results in a structured box-constrained quadratic program (BoxQP) whose decision variables include both the system states and control inputs, iv) develops a structure-exploited and warm-starting-supported variant of the feasible Mehrotra's interior-point algorithm for BoxQP. Numerical results demonstrate that Koopman-BoxQP can solve a large-scale NMPC problem with $1040$ variables and $2080$ inequalities at a kHz rate.

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arXiv2026

Least-Squares Multi-Step Koopman Operator Learning for Model Predictive Control

MPC is widely used in real-time applications, but practical implementations are typically restricted to convex QP formulations to ensure fast and certified execution. Koopman-based MPC enables QP-based control of nonlinear systems by lifting the dynamics to a higher-dimensional linear representation. However, existing approaches rely on single-step EDMD. Consequently, prediction errors may accumulate over long horizons when the EDMD operator is applied recursively. Moreover, the multi-step prediction loss is nonconvex with respect to the single-step EDMD operator, making long-horizon model identification particularly challenging. This paper proposes a multi-step EDMD framework that directly learns the condensed multi-step state-control mapping required for Koopman-MPC, thereby bypassing explicit identification of the lifted system matrices and subsequent model condensation. The resulting identification problem admits a convex least-squares formulation. We further show that the problem decomposes across prediction horizons and state coordinates, enabling parallel computation and row-wise $\ell_1$-regularization for automatic dictionary pruning. A non-asymptotic finite-sample analysis demonstrates that, unlike one-step EDMD, the proposed method avoids error compounding and yields error bounds that depend only on the target multi-step mapping. Numerical examples validate improved long-horizon prediction accuracy and closed-loop performance.

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arXiv2026

Improved Approximation Bounds for Moore-Penrose Inverses of Banded Matrices with Applications to Continuous-Time Linear Quadratic Control

We present improved approximation bounds for the Moore-Penrose inverses of banded matrices, where the bandedness is induced by a metric on the index set. We show that the pseudoinverse of a banded matrix can be approximated by another banded matrix, and the error of approximation is exponentially small in the ratio of the bandwidth of the approximation to that of the original matrix. An intuitive corollary can be obtained: the off-diagonal blocks of the pseudoinverse decay exponentially with the distance between the node sets associated with row and column indices, on the given metric space. Our bounds are expressed in terms of the bound of singular values of the system. For saddle point systems, commonly encountered in optimization, we provide the bounds of singular values associated under standard regularity conditions. Remarkably, our bounds improve previously reported ones and allow us to establish a perturbation bound for continuous-domain optimal control problems by analyzing the asymptotic limit of their finite difference discretization, which has been challenging with previously reported bounds.

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