arXiv subjects

Kangyu Lin

Publications and source records attributed to Kangyu Lin.

5 recordsLinked to original sources

arXiv2026

Time-Certified and Efficient NMPC via Koopman Operator

Certifying and accelerating execution times of nonlinear model predictive control (NMPC) implementations are two core requirements. Execution-time certificate guarantees that the NMPC controller returns a solution before the next sampling time, and achieving faster worst-case and average execution times further enables its use in a wider set of applications. However, NMPC produces a nonlinear program (NLP) for which it is challenging to derive its execution time certificates. Our previous works, \citep{wu2025direct,wu2025time} provide data-independent execution time certificates (certified number of iterations) for box-constrained quadratic programs (BoxQP). To apply the time-certified BoxQP algorithm \citep{wu2025time} for state-input constrained NMPC, this paper i) learns a linear model via Koopman operator; ii) proposes a dynamic-relaxation construction approach yields a structured BoxQP rather than a general QP; iii) exploits the structure of BoxQP, where the dimension of the linear system solved in each iteration is reduced from $5N(n_u+n_x)$ to $Nn_u$ (where $n_u, n_x, N$ denote the number of inputs, states, and length of prediction horizon), yielding substantial speedups (when $n_x \gg n_u$, as in PDE control).

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arXiv2025

A Gap Penalty Reformulation for Mathematical Programming with Complementarity Constraints: Convergence Analysis

Our recent study (Lin and Ohtsuka, 2024) proposed a new penalty method for solving mathematical programming with complementarity constraints (MPCC). This method first reformulates MPCC as a parameterized nonlinear programming called gap penalty reformulation and then solves a sequence of gap penalty reformulations with an increasing penalty parameter. This study examines the convergence behavior of the new penalty method. We prove that it converges to a strongly stationary point of MPCC, provided that: (i) The MPCC linear independence constraint qualification holds. (ii) The upper-level strict complementarity condition holds. (iii) The gap penalty reformulation satisfies the second-order necessary conditions in terms of the second-order directional derivative. Because strong stationarity is used to identify the MPCC local minimum, our analysis indicates that the new penalty method can find an MPCC solution.

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arXiv2024

Dynamical System Approach for Optimal Control Problems with Equilibrium Constraints Using Gap-Constraint-Based Reformulation

This study focuses on using direct methods (first-discretize-then-optimize) to solve optimal control problems for a class of nonsmooth dynamical systems governed by differential variational inequalities (DVI), called optimal control problems with equilibrium constraints (OCPEC). In the discretization step, we propose a class of novel approaches to smooth the DVI. The generated smoothing approximations of DVI, referred to as gap-constraint-based reformulations, have computational advantages owing to their concise and semismoothly differentiable constraint system. In the optimization step, we propose an efficient dynamical system approach to solve the discretized OCPEC, where a sequence of its smoothing approximations is solved approximately. This system approach involves a semismooth Newton flow, thereby achieving fast local exponential convergence. We confirm the effectiveness of our method using a numerical example.

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arXiv2024

A Successive Gap Constraint Linearization Method for Optimal Control Problems with Equilibrium Constraints

In this study, we propose a novel gap-constraint-based reformulation for optimal control problems with equilibrium constraints (OCPECs). We show that the proposed reformulation generates a new constraint system equivalent to the original one but more concise and with favorable differentiability. Moreover, constraint regularity can be recovered by a relaxation strategy. We show that the gap constraint and its gradient can be evaluated efficiently. We then propose a successive gap constraint linearization method to solve the discretized OCPEC. We also provide an intuitive geometric interpretation of the gap constraint. Numerical experiments validate the effectiveness of the proposed reformulation and solution method.

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arXiv2022

A Non-Interior-Point Continuation Method for the Optimal Control Problem with Equilibrium Constraints

In this study, we focus on the numerical solution method for the optimal control problem with equilibrium constraints (OCPEC).It is extremely challenging to solve OCPEC owing to the absence of constraint regularity and strictly feasible interior points. To solve OCPEC efficiently, we first relax the discretized OCPEC to recover the constraint regularity and then map its Karush--Kuhn--Tucker (KKT) conditions into a perturbed system of equations. Subsequently, we propose a novel two-stage solution method, called the non-interior-point continuation method, to solve the perturbed system. In the first stage, a non-interior-point method, which solves the perturbed system using the Newton method and globalizes convergence using a dedicated merit function, is employed. In the second stage, a predictor-corrector continuation method is utilized to track the solution trajectory as a function of the perturbed parameter, starting at the solution obtained in the first stage. The proposed method regularizes the KKT matrix and does not enforce iterates to remain in the feasible interior, which mitigates the numerical difficulties of solving OCPEC. Convergence properties are analyzed under certain assumptions. Numerical experiments demonstrate that the proposed method can accurately track the solution trajectory while demanding significantly less computation time compared to the interior-point method.

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