Advances in Robust Control Theory and Its Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: 30 June 2026 | Viewed by 992

Special Issue Editors


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Guest Editor
Department of Systems and Control, Technical University of Sofia, 1000 Sofia, Bulgaria
Interests: robust control; applied mathematics

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Guest Editor
Department of Systems and Control, Faculty of Automatics, Technical University of Sofia, Sofia, Bulgaria
Interests: system modelling and identification; robust control; embedded control systems; process control
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Special Issue Information

Dear Colleagues,

A Special Issue on "Advances in Robust Control Theory and Its Applications" presents recent advances in the analysis, design, and practical implementation of control systems capable of providing robust stability and robust performance in the presence of structured or unstructured uncertainties. The uncertainties can affect both system parameters and reflect the action of external signal disturbances. Robust control frameworks known for their ability to address challenges posed by nonlinear or time-varying plants include H-infinity theory, MU design, sliding mode control, and LQR control. The Special Issue encourages both pure theoretical works with solid mathematical background as well as practical implementations of robust control in areas such as unmanned vehicles, power systems, industrial, and economic systems, etc.

Dr. Jordan Kralev
Dr. Tsonyo Slavov
Guest Editors

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Keywords

  • nonlinear control
  • robust control
  • control applications
  • control systems
  • dynamic systems
  • control methodologies
  • sliding mode control
  • LQR-control
  • nonlinear control techniques

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Published Papers (2 papers)

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Research

25 pages, 1052 KB  
Article
Regime-Adaptive Conformal Calibration of Entropic Soft-Min Relaxations for Heterogeneous Optimization Problems
by J. Ernesto Solanes and Aitana Francés-Falip
Mathematics 2026, 14(7), 1188; https://doi.org/10.3390/math14071188 - 2 Apr 2026
Viewed by 292
Abstract
Entropic soft-min relaxations are widely used to obtain smooth approximations of minimum operators in optimization, machine learning, and control. The accuracy of this approximation is governed by an inverse temperature (or sharpness) parameter that controls the trade-off between smoothness and fidelity, yet its [...] Read more.
Entropic soft-min relaxations are widely used to obtain smooth approximations of minimum operators in optimization, machine learning, and control. The accuracy of this approximation is governed by an inverse temperature (or sharpness) parameter that controls the trade-off between smoothness and fidelity, yet its principled selection is typically heuristic. This work studies the data-driven calibration of the inverse temperature parameter governing the entropic soft-min relaxation, with explicit guarantees on the relaxation error between the soft-min operator and the infimum of the cost function. After establishing monotonicity properties and approximation bounds for the relaxation error, we introduce a conformal calibration rule that selects the smallest inverse temperature ensuring that the approximation error satisfies a prescribed tolerance with distribution-free finite-sample validity. The resulting selector adapts to the distribution of candidate cost-vector geometries represented in the calibration sample, enabling regime-specific inverse temperature selection in heterogeneous settings. Numerical experiments, including an adaptive cruise control application with safety filtering, show that the proposed method accurately tracks oracle calibration inverse temperatures and achieves near-target coverage in the exchangeable setting covered by the theory, while an additional shifted evaluation illustrates the role of this assumption. Full article
(This article belongs to the Special Issue Advances in Robust Control Theory and Its Applications)
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24 pages, 4461 KB  
Article
Approximated Adaptive Dynamic Programming Control of Axial-Piston Pump
by Jordan Kralev, Alexander Mitov and Tsonyo Slavov
Mathematics 2026, 14(7), 1127; https://doi.org/10.3390/math14071127 - 27 Mar 2026
Viewed by 358
Abstract
This article presents the synthesis, real-time implementation, and experimental validation of an approximated adaptive dynamic programming (AADP) actor–critic controller for precise flow rate regulation of a variable-displacement axial-piston pump designed for open-circuit hydraulic systems. Replacing the conventional hydro-mechanical regulator with an electrohydraulic proportional [...] Read more.
This article presents the synthesis, real-time implementation, and experimental validation of an approximated adaptive dynamic programming (AADP) actor–critic controller for precise flow rate regulation of a variable-displacement axial-piston pump designed for open-circuit hydraulic systems. Replacing the conventional hydro-mechanical regulator with an electrohydraulic proportional spool valve, the model-free controller employs two compact two-layer neural networks: the actor generates valve PWM signals from the flow tracking error, its integral, and measured discharge pressure, while the critic approximates the infinite-horizon quadratic cost-to-go via the online solution of the Bellman equation through gradient descent on Bellman residuals. Lyapunov analysis establishes closed-loop stability under bounded learning rates, with initial weights tuned via nominal plant simulation to ensure convergence from feasible starting policies. After extensive laboratory testing across four fixed loading conditions and dynamic load variations, the adaptive controller demonstrated superior performance compared with a proportional-integral (PI) controller, a Lyapunov model-reference adaptive controller (LMRAC), and an H controller (Hinf). Real-time metrics confirm bounded critic signals and near-zero Bellman errors, validating optimal policy convergence amid unmodeled hydraulic nonlinearities. Full article
(This article belongs to the Special Issue Advances in Robust Control Theory and Its Applications)
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