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

Jul 16, 2026

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This article develops a numerically viable method for sparse robust optimal control in continuous time. The study targets constrained linear noisy systems modeled by ordinary differential equations, combining robustness against uncertainty with an L1-type sparse objective commonly used in sparse control. The problem is reformulated as a semi-infinite programming (SIP) model, enabling a finite convex program that recovers the optimal value and optimizers while satisfying uncountably many constraints. Extensions cover parameter-dependent noisy systems and the minimum attention problem, validated on a benchmark numerical example.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages14

Reading Time35 min

Introduction

Problem background: sparsity in control

Motivation: robustness with uncertainties

Contributions and main results

GENERIC COLORIZED JOURNAL, VOL. XX, NO. XX, XXXX 2017 1 Sparse robust optimal control in continuous-time: a computationally viable approach Siddhartha Ganguly, Ashwin Aravind, Souvik Das, Masaaki Nagahara, and Debasish Chatterjee arXiv :2607 . 11827v1 [math .OC] 13 Jul 2026 Abstract—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 L1-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. Index Terms—Optimal control, sparse control, robust control, semi-infinite optimization I. INTRODUCTION Sparsity and the associated study of numerical techniques to promote sparsity have gained significant prominence across various scientific and technological fields interacting with signal processing [1], [2], machine learning [3], and statistics [4] . These tools, often referred to as compressed sensing, compressive sampling, sparse representation, or sparse modeling, provide powerful tools for efficient handling of highdimensional data. Sparsity in control theory has gained significant attention due to its ability to reduce control activity and enhance The current manuscript was submitted on 8th July, 2025 for review. This work was not supported by any funding agency. Siddhartha Ganguly is with the Daniel Guggenheim School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, USA (e-mail: [sganguly41@gatech.edu](sganguly41@gatech.edu)). Ashwin Aravind is with the Fujitsu Research, Kawasaki, Japan (email: [aravind.ashwin@fujitsu.com](aravind.ashwin@fujitsu.com)). Souvik Das is with the Department of Information Physics and Computing, The University of Tokyo, Japan (e-mail: souvikd@g.ecc.u[tokyo.ac.jp](tokyo.ac.jp)). Masaaki Nagahara is with the Graduate School of Advanced Science and Engineering, Hiroshima University, Japan (e-mail: [nagam@hiroshima-u.ac.jp](nagam@hiroshima-u.ac.jp)). Debasish Chatterjee is with the Centre for Systems and Control, Indian Institute of Technology Bombay, India (e-mail: dchat[ter@iitb.ac.in](ter@iitb.ac.in)). Debasish Chatterjee acknowledges support of the ANRF grant ANRF/ARGM/2025/001464/MTR from the Government of India. the ability for multitasking. From an application standpoint, sparsity-driven design has been widely adopted in networked control [5], sensing [6], aerospace [7], and control of partial differential equations [8], [9] . In constrained control systems, inducing sparsity by minimizing certain objective functions helps reduce control activity/attention by keeping actuators inactive for extended periods through constant-valued control inputs—a principle known as sparse optimal control. In the framework of deterministic linear systems, the minimization of the L0-(semi)norm of the control input u(·), which effectively reduces the duration over which u(·) stays nonzero, is referred to as the maximum hands-off control [10],[11] . This approach prioritizes sparsity by inducing prolonged intervals of zero control input, thereby optimizing control

FAQs

What kind of system and optimization objective does the document study?

It studies constrained linear systems in continuous time with process noise and other uncertainties, governed by an ODE. The optimization uses an L1-type objective to induce sparsity in the control trajectory.

How is the robust sparse optimal control problem reformulated?

The resulting optimal control problem is shown to admit a semi-infinite programming (SIP) formulation, which captures a compact but uncountable set of constraints.

What computational method does the document propose to solve the SIP-related problem?

It develops a framework that converts the SIP structure into a finite, computationally viable convex optimization problem. Solving this finite problem recovers the original SIP’s optimal value and optimizers while guaranteeing satisfaction of all uncountably many constraints.

Jul 16, 2026

Upload by Ophelia