Optimization and Control of Complex Engineering Systems: Mathematical Approaches

Dear Colleagues,

The rapid evolution of modern science and engineering has necessitated the development of increasingly sophisticated mathematical frameworks to describe, analyze, and regulate the behavior of complex systems. These systems, characterized by high dimensionality, nonlinearity, and intricate interconnectivity, span a vast spectrum of domains ranging from industrial automation and cyber–physical networks to biological dynamics and large-scale energy infrastructures. The primary objective of this Special Issue is to bring together rigorous mathematical contributions that advance the theoretical foundations of modeling, control, and decision-making in such systems. The emphasis is placed on methodological innovation with verifiable analytical guarantees, rather than on domain-specific implementations.

We invite original research articles that develop and analyze mathematical frameworks for system representation, stability, and performance under uncertainty. Potential topics include, but are not limited to:

• Optimization under uncertainty: convex and non-convex programming, stochastic and robust optimization, dynamic programming, and surrogate-assisted evolutionary methods, with an emphasis on convergence analysis and complexity bounds.
• Stochastic and robust control: model predictive control, adaptive and sliding mode control, event-triggered strategies, and distributed consensus, with provable stability and robustness certificates.
• Numerical analysis of differential equation-based models: ordinary, partial, fractional-order, and stochastic differential equations arising in system modeling, with a focus on discretization error estimates, convergence rates, and structure-preserving schemes.
• Data-driven methods and mathematical modeling: physics-informed learning, sparse identification of dynamics, operator-theoretic methods (e.g., Koopman theory), and safe reinforcement learning methods, provided that the contributions are mathematically grounded (e.g., bounds on generalization error, stability under learning, or convergence to optimal policies).

By converging these diverse yet interconnected disciplines, this Special Issue seeks to advance the theoretical boundaries of applied mathematics while addressing tangible challenges in engineering, providing a comprehensive repository of solutions for the next generation of complex dynamical systems. All submitted manuscripts must contain non-trivial mathematical content, including, but not limited to, new algorithms accompanied by theoretical analysis, stability or convergence proofs, error estimates, or rigorous complexity analysis.

Dr. Debiao Meng
Dr. Xiaoyan Su
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• optimization under uncertainty
• stochastic control
• robust control
• model predictive control
• nonlinear dynamical systems
• fractional-order systems
• differential equations
• numerical analysis
• convergence analysis
• stability theory
• data-driven modeling
• Koopman operator theory
• safe reinforcement learning
• multi-agent systems
• cyber–physical systems
• machine learning