@article{MTMT:36217357,
	title = {Adjoint sensitivity method for parameter estimation: applications to inverted pendulum and human standing balance},
	url = {https://m2.mtmt.hu/api/publication/36217357},
	author = {Chen, Jingtian and Lu, Shaoyi and Zhang, Li and Insperger, Tamás and Stépán, Gábor},
	doi = {10.1098/rsif.2024.0843},
	journal-iso = {J R SOC INTERFACE},
	journal = {JOURNAL OF THE ROYAL SOCIETY INTERFACE},
	volume = {22},
	unique-id = {36217357},
	issn = {1742-5689},
	abstract = {The inverted pendulum, a classical mechanical system, often serves as a platform for studying stability and control algorithms. Modelling human standing balance as an inverted pendulum controlled by the time-delayed proportional-derivative (PD) feedback controller can be used effectively to study the related biomechanical mechanisms. In this study, to investigate the human balance control strategy, an adjoint sensitivity analysis method and a corresponding optimizer are implemented to directly determine system parameters, control gains and the time delay in the human balancing model. This study validates the accuracy of the optimizer through numerical simulations and experimental verification based on the physical model of the inverted pendulum on a cart. The experimental results confirm the performance of the identification algorithm for systems involving non-smooth dynamics and inherent time delays. Moreover, the identification based on human balance data indicates that the time-delayed PD feedback controller effectively represents the human balance control strategy. Additionally, the identification reveals a tendency in the control strategy: the control gains are located in the lower-left region of the stability diagram, indicating that the human body tends to adopt an optimal control strategy that minimizes energy consumption.},
	keywords = {IDENTIFICATION; feedback; SYSTEMS; ADAPTATION; TIME-DELAY; Inverted pendulum; Adjoint sensitivity analysis; EQUATIONS; Human balance control; ankle stiffness; time delay system},
	year = {2025},
	eissn = {1742-5662},
	orcid-numbers = {Insperger, Tamás/0000-0001-7518-9774; Stépán, Gábor/0000-0003-0309-2409}
}

@{MTMT:36328232,
	title = {Why Does a Stick Balanced on the Fingertip Fall?},
	url = {https://m2.mtmt.hu/api/publication/36328232},
	author = {Milton, John and Insperger, Tamás},
	booktitle = {Dynamics of Physiological Control},
	doi = {10.1007/978-3-031-82396-1_8},
	unique-id = {36328232},
	abstract = {An inverted pendulum can be fully stabilized using time-delayed feedback. In contrast, for human stick balancers the stick always falls. It is suggested that stick falls are a consequence transient micro-chaotic dynamics which naturally arises because of the interplay between time-delayed feedback, a sensory dead zone and the frequency-dependent encoding of force.},
	year = {2025},
	pages = {149-161},
	orcid-numbers = {Insperger, Tamás/0000-0001-7518-9774}
}

@article{MTMT:36339102,
	title = {A switched optimal control strategy in human balancing on a harmonically moving platform},
	url = {https://m2.mtmt.hu/api/publication/36339102},
	author = {Lu, Shaoyi and Chen, Jingtian and Li, Huifang and Zhang, Li and Insperger, Tamás and Stépán, Gábor},
	doi = {10.1016/j.jbiomech.2025.112923},
	journal-iso = {J BIOMECH},
	journal = {JOURNAL OF BIOMECHANICS},
	volume = {191},
	unique-id = {36339102},
	issn = {0021-9290},
	abstract = {Postural balance is crucial for human daily activities, and understanding the neural-motor control mechanisms underlying balance performance is essential for improving diagnosis and intervention strategies for balance disorders. This study focuses on the human standing balance task on a harmonically moving platform with anterior-posterior translation, exploring the neural-motor control logic using a switched control strategy. It is hypothesized that humans switch between optimal energy gains and optimal decay gains to maintain balance in a safe and energy-efficient manner with the usage of optimal decay gains being closely related to balancing ability. A two-stage identification process is employed to determine switching time instances, starting with the adjoint method to estimate control gains and followed by the enumeration of gain switching instances. The proposed postural stability assessment indices, Control Strategy Ratio and Control Switch Frequency, offer clear physical interpretations and dynamic insights, demonstrating better consistency and sensitivity compared to some stabilometry parameters. These indices show potential for early diagnosis and intervention in balance disorders.},
	keywords = {Biophysics; human balancing; Switched control; Optimal control gain},
	year = {2025},
	eissn = {1873-2380},
	orcid-numbers = {Insperger, Tamás/0000-0001-7518-9774; Stépán, Gábor/0000-0003-0309-2409}
}

@article{MTMT:34040356,
	title = {Extending the admissible control-loop delays for the inverted pendulum by fractional-order proportional-derivative controller},
	url = {https://m2.mtmt.hu/api/publication/34040356},
	author = {Balogh, Tamás and Insperger, Tamás},
	doi = {10.1177/10775463231181662},
	journal-iso = {J VIB CONTROL},
	journal = {JOURNAL OF VIBRATION AND CONTROL},
	volume = {30},
	unique-id = {34040356},
	issn = {1077-5463},
	abstract = {Stabilization of the inverted pendulum by fractional-order proportional-derivative (PD) feedback with two delays is investigated. This feedback law is obtained as a combination of PD feedback with two delays and fractional-order PD feedback with a single delay. Different types of stabilizability boundaries and the corresponding geometric and multiplicity conditions are determined using the D-subdivision method. The stabilizable region is depicted in the plane of the delay parameters for given fractional derivative orders. Several special cases and the concept of delay detuning are also discussed. It is shown that the admissible delay can be slightly increased compared to the integer-order PD feedback by introducing a fractional-order feedback term.},
	keywords = {Time delay; Feedback systems; Acoustics; Engineering, Mechanical; stabilizability; fractional-order control},
	year = {2024},
	eissn = {1741-2986},
	pages = {2596-2604},
	orcid-numbers = {Insperger, Tamás/0000-0001-7518-9774}
}

@article{MTMT:34767934,
	title = {Pole balancing on the fingertip: model-motivated machine learning forecasting of falls},
	url = {https://m2.mtmt.hu/api/publication/34767934},
	author = {Debnath, Minakshi and Chang, Joshua and Bhandari, Keshav and Nagy, Dalma and Insperger, Tamás and Milton, John G. and Ngu, Anne H. H.},
	doi = {10.3389/fphys.2024.1334396},
	journal-iso = {FRONT PHYSIOL},
	journal = {FRONTIERS IN PHYSIOLOGY},
	volume = {15},
	unique-id = {34767934},
	abstract = {Introduction: There is increasing interest in developing mathematical and computational models to forecast adverse events in physiological systems. Examples include falls, the onset of fatal cardiac arrhythmias, and adverse surgical outcomes. However, the dynamics of physiological systems are known to be exceedingly complex and perhaps even chaotic. Since no model can be perfect, it becomes important to understand how forecasting can be improved, especially when training data is limited. An adverse event that can be readily studied in the laboratory is the occurrence of stick falls when humans attempt to balance a stick on their fingertips. Over the last 20 years, this task has been extensively investigated experimentally, and presently detailed mathematical models are available.},
	year = {2024},
	eissn = {1664-042X},
	orcid-numbers = {Nagy, Dalma/0000-0002-1162-4594; Insperger, Tamás/0000-0001-7518-9774}
}

@article{MTMT:35085873,
	title = {Human performance in virtual stabilization of a fractional-order system with reaction delay},
	url = {https://m2.mtmt.hu/api/publication/35085873},
	author = {Balogh, Tamás and Kovács, Balázs András and Insperger, Tamás},
	doi = {10.1098/rsif.2023.0685},
	journal-iso = {J R SOC INTERFACE},
	journal = {JOURNAL OF THE ROYAL SOCIETY INTERFACE},
	volume = {21},
	unique-id = {35085873},
	issn = {1742-5689},
	abstract = {Virtual balancing tasks facilitate the study of human motion control: human reaction to the change of artificially introduced parameters can be studied in a computer environment. In this article, the dynamics of human stick balancing are generalized using fractional-order derivatives. Reaction delay sets a strong limitation on the length of the shortest stick that human subjects can balance. Human processing of visual input also exhibits a memory effect, which can be modelled by fractional-order derivatives. Therefore, we hypothesize a delayed fractional-order PD control of the unstable fractional-order process. The resulting equation of motion is investigated in a dimensionless framework, and stabilizability limits are determined as a function of the dynamics's order. These theoretical limits are then compared with the results of a systematic series of virtual balancing tests performed by 18 subjects. The comparison shows that the theoretical stabilizability limits for controllers with fixed fractional order correspond to the measured data points. The best fit is obtained if the fractional order of the underlying control law is 0.475.},
	keywords = {DYNAMICS; STABILITY; Inverted pendulum; reaction delay; Fractional-order dynamics; virtual balancing},
	year = {2024},
	eissn = {1742-5662},
	orcid-numbers = {Kovács, Balázs András/0000-0003-2942-730X; Insperger, Tamás/0000-0001-7518-9774}
}

@inproceedings{MTMT:35232911,
	title = {Central Nervous System Action on Rolling Balance Board Robust Stabilization: Computer Algebra and MID-Based Feedback Design},
	url = {https://m2.mtmt.hu/api/publication/35232911},
	author = {Trabelsi, Karim L. and Boussaada, Islam and Benarab, Amina and Molnár, Csenge Andrea and Niculescu, Silviu-Iulian and Insperger, Tamás},
	booktitle = {Advances in Partial Differential Equations and Control},
	doi = {10.1007/978-3-031-62265-6_11},
	volume = {Part F3233},
	unique-id = {35232911},
	abstract = {Using the computer algebra system Maple, we consider the stabilization of a rolling balance board by means of the multiplicity-induced-dominancy (MID) property. The human stance on a rolling balance board is analyzed in the sagittal plane through a 2-degree-of-freedom mechanical model. Namely, the human body is modeled by a double-inverted pendulum which connects to the balance board through the ankle joint. The system is stabilized by the ankle torque managed by the central nervous system (CNS). The action of the CNS is modeled by a delayed full state feedback: A pointwise delay stands for all latencies in the neuromechanical system (reaction time, neuromechanical lag, etc.). The aim of the chapter is to achieve a good occurrence in terms of the decay rate, and it exhibits the links between multiple spectral values satisfying the MID property and the exponential stability property of the solution (Note that a preliminary version of this work was published in Benarab et al. (Rolling balance board robust stabilization: A MID-based design, in TDS 2022 - 17th IFAC Workshop on Time Delay Systems, Montreal, 2022).). © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.},
	keywords = {TIME-DELAY; Asymptotic stability; exponential stability; Control design; Vandermonde matrix; Exponential decay rate; Quasipolynomial factorization},
	year = {2024},
	pages = {215-247},
	orcid-numbers = {Molnár, Csenge Andrea/0000-0002-4124-4242; Insperger, Tamás/0000-0001-7518-9774}
}

@CONFERENCE{MTMT:35584936,
	title = {Nonlinear effects in the act-and-wait control of a linear DC actuator},
	url = {https://m2.mtmt.hu/api/publication/35584936},
	author = {Szalai, Péter and Insperger, Tamás and Antali, Máté},
	booktitle = {Online Book of Abstracts of the 11th European Nonlinear Dynamics Conference (ENOC 2024)},
	unique-id = {35584936},
	year = {2024},
	orcid-numbers = {Insperger, Tamás/0000-0001-7518-9774; Antali, Máté/0000-0001-6750-0710}
}

@{MTMT:33151750,
	title = {Dynamics of Human Balancing},
	url = {https://m2.mtmt.hu/api/publication/33151750},
	author = {Insperger, Tamás and Stépán, Gábor and Milton, J.},
	booktitle = {Controlling Delayed Dynamics},
	doi = {10.1007/978-3-031-01129-0_11},
	volume = {604},
	unique-id = {33151750},
	year = {2023},
	pages = {343-364},
	orcid-numbers = {Insperger, Tamás/0000-0001-7518-9774; Stépán, Gábor/0000-0003-0309-2409}
}

@{MTMT:33151752,
	title = {Regenerative Machine Tool Vibrations},
	url = {https://m2.mtmt.hu/api/publication/33151752},
	author = {Insperger, Tamás and Stépán, Gábor},
	booktitle = {Controlling Delayed Dynamics},
	doi = {10.1007/978-3-031-01129-0_10},
	volume = {604},
	unique-id = {33151752},
	year = {2023},
	pages = {311-341},
	orcid-numbers = {Insperger, Tamás/0000-0001-7518-9774; Stépán, Gábor/0000-0003-0309-2409}
}