arXiv subjects

Masaaki Nagahara

Publications and source records attributed to Masaaki Nagahara.

At least 19 recordsLinked to original sources

arXiv2026

Sparsity in control problems: Recent trends and open challenges

As in all fields of engineering, control engineers constantly face a dichotomy between achieving high performance and the limited availability of resources for sensing, actuation, and control. This tension often translates into formalizing design problems with sparsity constraints; that is, the design involves decision variables whose number, spatial reach, temporal spread, or other physical expressions are much smaller than in the ideal scenario of unconstrained optimization of a task-related performance metric. Even though this fundamental limitation underlines a plethora of methodological approaches and application domains, the control literature is fragmented into several lines of work tailored to specific scenarios. This survey fills the gap by bringing together several lines of work on handling sparsity in relevant control problems such as actuator scheduling, minimal-energy controllability, maximum hands-off control, and online convex optimization, and weaving a red thread through theoretical foundations and algorithms. Beyond establishing a coherent, structured narrative of problems and solutions for handling sparsity in control scenarios, we discuss open areas and relevant directions for future research, motivated by the growing complexity of control systems and their relations with key domains such as pervasive computing, distributed learning, cyberphysical security, and ecological footprint.

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arXiv2026

Learning Reduced-Order Dynamics with Singularity via Latent-Augmented Neural Ordinary Differential Equations

This paper addresses the issue of self-intersecting trajectories (in phase space) in industrial reduced-order modeling and proposes the Latent-Augmented Neural Ordinary Differential Equations (LA-NODEs) framework. From the perspective of artificial intelligence, the proposed method augments conventional neural ordinary differential equations to enhance model expressiveness, enabling the representation of conflicting vector fields that may arise in reduced-order systems, thereby improving learning accuracy. Through theoretical analysis, the underlying mechanism of the framework is established, and a condition for determining the minimum required augmentation dimension is derived. From the perspective of engineering applications, the effectiveness of the proposed method is validated on the reduced-order system of two representative industrial models, namely an interior permanent magnet synchronous motor (IPMSM) drive and a distributed energy system (DES). Experimental results demonstrate that the proposed method can recover system features that are difficult to capture using conventional approaches and achieve superior performance in terms of prediction accuracy and modeling fidelity, thereby providing an effective approach for high-precision data-driven modeling of complex industrial systems.

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arXiv2026

Infinite-Horizon Sparse Optimal Control: Solution through a Finite-Horizon Subproblem and Its Receding-Horizon Implementation

Sparse optimal control is considered in the infinite horizon. In the literature, sparse control has been considered mostly in a finite horizon for its formulation into a finite-dimensional optimization problem. It is shown in this paper that an optimal solution of the infinite-horizon sparse control problem can be obtained through a solution of some finite-horizon subproblem. This is due to sparsity of the optimal solution in the sense that the optimal control input is constantly equal to zero at its tail. An estimate is given on the horizon length required by this subproblem and its adaptive choice is also discussed. Implementation with a receding-horizon technique is considered and its optimality and sparsity are guaranteed.

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arXiv2026

Sparse Robust Optimal Control in Continuous-Time: A Computationally Viable Approach

This article presents a novel, numerically viable algorithm for solving sparse robust optimal control problems in continuous time. We consider a constrained linear noisy system governed by an ordinary differential equation (ODE), with an $L^1$-type objective function in line with the sparse optimal control literature. The resulting optimal control problem is shown to admit a semi-infinite programming (SIP) formulation. Building upon this insight, we develop a new framework that enables the computation of exact solutions -- to our knowledge, the first such achievement in the context of sparse optimal control. We demonstrate that a finite and computationally viable convex optimization problem can be solved to recover, in a lossless manner, both the optimal value and the corresponding optimizers of the original SIP, while also guaranteeing satisfaction of uncountably many constraints. We also show that the parameter-dependent noisy systems and the minimum attention problem fall into our framework and can be solved efficiently via our algorithm. The efficacy of our algorithm is illustrated through a benchmark numerical example.

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arXiv2026

First-Order Projected Algorithms With the Same Linear Convergence Rate Bounds as Their Unconstrained Counterparts

In this paper, we propose a systematic approach for extending first-order optimization algorithms, originally designed for unconstrained strongly convex problems, to handle closed convex set constraints. We show that the resulting projected algorithms retain the same linear convergence rate bounds, provided that the underlying unconstrained optimization algorithms admit a quadratic Lyapunov function obtained from integral quadratic constraint (IQC) analysis. The projected algorithms are constructed by applying a projection in the norm induced by the Lyapunov matrix, ensuring both constraint satisfaction and optimality at the fixed point. Furthermore, under a linear transformation associated with this matrix, the projection becomes non-expansive in the Euclidean norm, thereby preserving the convergence rate bounds under the composition of the linearly convergent algorithmic operator and the projection. Our results indicate that, when analyzing worst-case convergence rates or when synthesizing first-order optimization algorithms with potentially higher-order dynamics, it suffices to focus solely on the unconstrained dynamics, since the same parameters or stepsizes can be employed without retuning.

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arXiv2026

Towards Lag Consensus with Noisy Digital Twins Perception in Second-order Multi-agent Cyber-physical Systems

In this paper, we study second-order lag consensus in multi-agent cyber-physical networks subject to random noise and input failures, within a framework modeling the interactions and perceptions between physical twins and digital twins. We propose a lag consensus protocol and establish sufficient conditions for the mean-square (exponential) stability of the resulting stochastic lag error dynamics. The consensus criteria are derived via Lyapunov analysis using the Itô formula, ensuring robustness to random perturbations and intermittent input failures. Numerical examples illustrate the effectiveness of the proposed method.

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arXiv2026

A Common Lyapunov Matrix Approach to the Exponential Stability of Augmented Primal-Dual Gradient Flow as LPV Systems

We show that a common Lyapunov matrix exists for the convex combination of two Hurwitz matrices if and only if the intersection of the set of strict Lyapunov matrices for one matrix and the set of non-strict Lyapunov matrices for the other is nonempty. This simple relaxation is useful for the convergence analysis of the augmented primal-dual gradient flow for constrained optimization problems with affine inequality constraints, which can be viewed as a polytopic linear parameter-varying (LPV) system driven by the active-constraint selector. Under a relaxed strong convexity condition, exponential convergence is proved for the LPV system. The analysis can further be extended to the integral quadratic constraints (IQCs) framework for LPV systems to facilitate numerical search of the convergence rate.

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arXiv2026

Finite-Time Optimization via Scaled Gradient-Momentum Flows

In this paper, we develop a scaled gradient-momentum framework for continuous-time optimization that achieves global finite-time convergence. A state-dependent scaling mechanism is introduced to enable classical dynamics, such as Heavy-Ball-type and proportional-integral (PI)-type flows, to attain finite-time convergence. We establish explicit conditions that bridge the gradient-dominance property of the objective function and finite-time stability of the proposed scaled dynamics. Numerical experiments validate the theoretical results.

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arXiv2026

A Canonical Structure for Constructing Projected First-Order Algorithms With Delayed Feedback

This work introduces a canonical structure for a broad class of unconstrained first-order algorithms that admit a Lur'e representation, including systems with relative degree greater than one, e.g., systems with delayed gradient feedback. The proposed canonical structure is obtained through a simple linear transformation. It enables a direct extension from unconstrained optimization algorithms to set-constrained ones through projection in a Lyapunov-induced norm. The resulting projected algorithms attain the optimal solution while preserving the convergence rates of their unconstrained counterparts.

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arXiv2026

Discrete Homogeneity and Quantizer Design for Nonlinear Homogeneous Control Systems

This paper proposes a framework for analysis of generalized homogeneous control systems under state quantization. In particular, it addresses the challenge of maintaining finite/fixed-time stability of nonlinear systems in the presence of quantized measurements. To analyze the behavior of quantized control system, we introduce a new type of discrete homogeneity, where the dilation is defined by a discrete group. The converse Lyapunov function theorem is established for homogeneous systems with respect to discrete dilations. By extending the notion of sector-boundedness to a homogeneous vector space, we derive a generalized homogeneous sector-boundedness condition that guarantees finite/fixed-time stability of nonlinear control system under quantized measurements. A geometry-aware homogeneous static vector quantizer is then designed using generalized homogeneous coordinates, enabling an efficient quantization scheme. The resulting homogeneous control system with the proposed quantizer is proven to be homogeneous with respect to discrete dilation and globally finite-time, nearly fixed-time, or exponentially stable, depending on the homogeneity degree. Numerical examples validate the effectiveness of the proposed approach.

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arXiv2025

Sparse optimal control for infinite-dimensional linear systems with applications to graphon control

Large-scale networked systems typically operate under resource constraints, and it is also difficult to exactly obtain the network structure between nodes. To address these issues, this paper investigates a sparse optimal control for infinite-dimensional linear systems and its application to networked systems where the network structure is represented by a limit function called a graphon that captures the overall connection pattern. The contributions of this paper are twofold: (i) To reduce computational complexity, we derive a sufficient condition under which the sparse optimal control can be obtained by solving its corresponding L1 optimization problem. Furthermore, we introduce a class of non-convex optimal control problems such that the optimal solution always coincides with a sparse optimal control, provided that the non-convex problems admit optimal solutions. (ii) We show that the sparse optimal control for large-scale finite-dimensional networked systems can be approximated by that of the corresponding limit graphon system, provided that the underlying graph is close to the limit graphon in the cut-norm topology. The effectiveness of the proposed approach is illustrated through numerical examples.

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arXiv2025

Switched Systems Control via Discreteness-Promoting Regularization

This paper proposes a novel method for designing finite-horizon discrete-valued switching signals in linear switched systems based on discreteness-promoting regularization. The inherent combinatorial optimization problem is reformulated as a continuous optimization problem with a non-convex regularization term that promotes discreteness of the control. We prove that any solution obtained from the relaxed problem is also a solution to the original problem. The resulting non-convex optimization problem is efficiently solved through time discretization. Numerical examples demonstrate the effectiveness of the proposed method.

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arXiv2025

Exponential Convergence of Augmented Primal-dual Gradient Algorithms for Partially Strongly Convex Functions

We show that the augmented primal-dual gradient algorithms can achieve global exponential convergence with partially strongly convex functions. In particular, the objective function only needs to be strongly convex in the subspace satisfying the equality constraint and can be generally convex elsewhere, provided the global Lipschitz condition for the gradient is satisfied. This condition implies that states outside the equality subspace will converge towards it exponentially fast. The analysis is then applied to distributed optimization, where the partially strong convexity can be relaxed to the restricted secant inequality condition, which is not necessarily convex. This work unifies global exponential convergence results for some existing centralized and distributed algorithms.

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arXiv2022

Hypertracking and Hyperrejection: Control of Signals beyond the Nyquist Frequency

This paper studies the problem of signal tracking and disturbance rejection for sampled-data control systems, where the pertinent signals can reside beyond the so-called Nyquist frequency. In light of the sampling theorem, it is generally understood that manipulating signals beyond the Nyquist frequency is either impossible or at least very difficult. On the other hand, such control objectives often arise in practice, and control of such signals is much desired. This paper examines the basic underlying assumptions in the sampling theorem and pertinent sampled-data control schemes, and shows that the limitation above can be removed by assuming a suitable analog signal generator model. Detailed analysis of multirate closed-loop systems, zeros and poles are given, which gives rise to tracking or rejection conditions. Robustness of the new scheme is fully characterized; it is shown that there is a close relationship between tracking/rejection frequencies and the delay length introduced for allowing better performance. Examples are discussed to illustrate the effectiveness of the proposed method here.

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arXiv2021

Sparse Packetized Predictive Control of Disturbed Plants Over Channels with Data Loss

This paper investigates closed-loop stability of a linear discrete-time plant subject to bounded disturbances when controlled according to packetized predictive control (PPC) policies. In the considered feedback loop, the controller is connected to the actuator via a digital communication channel imposing bounded dropouts. Two PPC strategies are taken into account. In both cases, the control packets are generated by solving sparsity-promoting optimization problems. One is based upon an l2-constrained l0 optimization problem. Such problem is relaxed by an l1-l2 optimization problem in the other sparse PPC setting. We utilize effective solving methods for the latter optimization problems. Moreover, we show that in the presence of plant disturbances, the l2-constrained l0 sparse PPC and unconstrained l1-l2 sparse PPC guarantee practical stability for the system if certain conditions are met. More precisely, in each case, we can derive an upper bound on system state if the design parameters satisfy certain conditions. The bounds we derive are increasing with respect to the disturbance magnitude. We show via simulation that in both cases of proposed sparse PPC strategies, larger disturbances bring about performance degradation with no effect on system practical stability.

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arXiv2020

Necessary condition for sparse optimal control problem with intermediate constraints

This article treats optimal sparse control problems with multiple constraints defined at intermediate points of the time domain. For such problems with intermediate constraints, we first establish a new Pontryagin maximum principle that provides first order necessary conditions for optimality in such problems. Then we announce and employ a new numerical algorithm to arrive at, in a computationally tractable fashion, optimal state-action trajectories from the necessary conditions given by our maximum principle. Several detailed illustrative examples are included.

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arXiv2020

The turnpike property in the maximum hands-off control

This paper presents analyses for the maximum hands-off control using the geometric methods developed for the theory of turnpike in optimal control. First, a sufficient condition is proved for the existence of the maximum hands-off control for linear time-invariant systems with arbitrarily fixed initial and terminal points using the relation with $L^1$ optimal control. Next, a sufficient condition is derived for the maximum hands-off control to have the turnpike property, which may be useful for approximate design of the control.

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arXiv2017

CLOT Norm Minimization for Continuous Hands-off Control

In this paper, we consider hands-off control via minimization of the CLOT (Combined $L$-One and Two) norm. The maximum hands-off control is the $L^0$-optimal (or the sparsest) control among all feasible controls that are bounded by a specified value and transfer the state from a given initial state to the origin within a fixed time duration. In general, the maximum hands-off control is a bang-off-bang control taking values of $\pm 1$ and $0$. For many real applications, such discontinuity in the control is not desirable. To obtain a continuous but still relatively sparse control, we propose to use the CLOT norm, a convex combination of $L^1$ and $L^2$ norms. We show by numerical simulations that the CLOT control is continuous and much sparser (i.e. has longer time duration on which the control takes 0) than the conventional EN (elastic net) control, which is a convex combination of $L^1$ and squared $L^2$ norms. We also prove that the CLOT control is continuous in the sense that, if $O(h)$ denotes the sampling period, then the difference between successive values of the CLOT-optimal control is $O(\sqrt{h})$, which is a form of continuity. Also, the CLOT formulation is extended to encompass constraints on the state variable.

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