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1. L-GraD: Lyapunov-based Gradient Descent of a DNN-based Hybrid Exoskeleton Controller

   https://doi.org/10.23919/ACC63710.2025.11107845  

   Ting, Jonathan; Basyal, Sujata; Mishra, Kislaya; Allen, Brendon C (July 2025, IEEE)

   Functional electrical stimulation (FES) is widely used for rehabilitating individuals with total or partial limb paralysis, but challenges like muscle fatigue and discomfort limit its effectiveness. Hybrid exoskeletons combine the rehabilitative benefits of exoskeletons and FES, while mitigating the drawbacks of each. However, despite hybrid exoskeletons being highly effective in rehabilitation, the dynamics associated with these systems are complex. Deep neural networks (DNNs) can approximate these complex hybrid exoskeleton dynamics; however, they traditionally lack stability guarantees and robustness, hindering their application in real-world systems. Moreover, traditional training methods (e.g., gradient descent) require an extensive dataset and offline training, further hindering a DNNs practical use. Therefore, this paper presents an innovative Lyapunov-based adaptation law, with a gradient descent-like structure, that is designed to update all layer weights of a DNN in real-time for a DNN-based hybrid exoskeleton control framework. To promote user comfort and safety, a saturation limit was implemented on the DNN-based FES controller and the excess control effort was redirected to the exoskeleton. A Lyapunov-based stability analysis was performed on the DNN-based hybrid exoskeleton control system to prove global asymptotic trajectory tracking. A numerical simulation of the designed controller was performed to validate the results. 

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2. Distributed Feedback Controllers for Stable Cooperative Locomotion of Quadrupedal Robots: A Virtual Constraint Approach*

   https://doi.org/10.23919/ACC45564.2020.9147673  

   Hamed, Kaveh Akbari; Kamidi, Vinay R.; Pandala, Abhishek; Ma, Wen-Loong; Ames, Aaron D. (July 2020, American Control Conference (ACC))

   This paper aims to develop distributed feedback control algorithms that allow cooperative locomotion of quadrupedal robots which are coupled to each other by holonomic constraints. These constraints can arise from collaborative manipulation of objects during locomotion. In addressing this problem, the complex hybrid dynamical models that describe collaborative legged locomotion are studied. The complex periodic orbits (i.e., gaits) of these sophisticated and high-dimensional hybrid systems are investigated. We consider a set of virtual constraints that stabilizes locomotion of a single agent. The paper then generates modified and local virtual constraints for each agent that allow stable collaborative locomotion. Optimal distributed feedback controllers, based on nonlinear control and quadratic programming, are developed to impose the local virtual constraints. To demonstrate the power of the analytical foundation, an extensive numerical simulation for cooperative locomotion of two quadrupedal robots with robotic manipulators is presented. The numerical complex hybrid model has 64 continuous-time domains, 192 discrete-time transitions, 96 state variables, and 36 control inputs. 

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3. Online Cyber‐Physical Neural Network Model for Real‐Time Hybrid Simulation

   https://doi.org/10.1002/eqe.70036  

   Malik, Faisal Nissar; Cao, Liang; Ricles, James; Downey, Austin (October 2025, Earthquake Engineering & Structural Dynamics)

   ABSTRACT Real‐time hybrid simulation (RTHS) is an experimental testing methodology that divides a structural system into an analytical and an experimental substructure. The analytical substructure is modeled numerically, and the experimental substructure is modeled physically in the laboratory. The two substructures are kinematically linked together at their interface degrees of freedom, and the coupled equations of motion are solved in real‐time to obtain the response of the complete system. A key challenge in applying RTHS to large or complex structures is the limited availability of physical devices, which makes it difficult to represent all required experimental components simultaneously. The present study addresses this challenge by introducing Online Cyber‐Physical Neural Network (OCP‐NN) models–neural network‐based models of physical devices that are integrated in real‐time with the experimental substructure during an RTHS. The OCP‐NN framework leverages real‐time data from a single physical device (i.e., the experimental substructure) to replicate its behavior at other locations in the system, thereby significantly reducing the need for multiple physical devices. The proposed method is demonstrated through RTHS of a two‐story reinforced concrete frame subjected to seismic excitation and equipped with Banded Rotary Friction Dampers (BRFDs) in each story. BRFDs are challenging to model numerically due to their complex behavior which includes backlash, stick‐slip phenomena, and inherent device dynamics. Consequently, BRFDs were selected to demonstrate the proposed framework. In the RTHS, one BRFD is modeled physically by the experimental substructure, while the other is represented by the OCP‐NN model. The results indicate that the OCP‐NN model can accurately capture the behavior of the device in real‐time. This approach offers a practical solution for improving RTHS of complex structural systems with limited experimental resources. 

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4. Development of multi-directional real-time hybrid simulation for tall buildings subject to multi-natural hazards

   https://doi.org/10.1016/j.engstruct.2024.118348  

   Al-Subaihawi, Safwan; Ricles, James; Quiel, Spencer; Marullo, Thomas (September 2024, Engineering Structures)

   Real-time hybrid simulation (RTHS) divides a structural system into analytical and experimental substructures that are coupled through their common degrees of freedom. This paper introduces a framework to enable RTHS to be performed on 3D nonlinear models of tall buildings with rate dependent nonlinear response modification devices, where the structure is subjected to multi-directional wind and earthquake natural hazards. A 40-story tall building prototype with damped outriggers is selected as a case study. The analytical substructure for the RTHS consists of a 3-D nonlinear model of the structure, where each member in the building is discretely modeled in conjunction with the use of a super element. The experimental substructure for the RTHS consists of a full-scale rate-dependent nonlinear viscous damper that is physically tested in the lab, with the remaining dampers in the outrigger system modeled analytically. The analytically modeled dampers use a stable explicit non-iterative element with an online model updating algorithm, by which the covariance matrix of the damper model’s state variables does not become ill-conditioned. The damper model parameters can thereby be updated in real-time using measured data from the experimental substructure. The explicit MKR-α method is optimized and used in conjunction with the super element to efficiently integrate the condensed equations of motion of a large complex model having more than 1000 nonlinear elements, thus enabling multi-axis earthquake and wind hybrid nonlinear simulations to be performed in real-time. An adaptive servo-hydraulic actuator control scheme is used to enable precise real-time actuator displacements in the experimental substructure to be achieved that match the target displacements during a RTHS. The IT real-time architecture for integrating the components of the framework is described. To assess the framework, 3D RTHS of the 40-story structure were performed involving multi-axis translational and torsional response to multi-directional earthquake and wind natural hazards. The RTHS technique was applied to perform half-power tests to experimentally determine the amount of supplemental damping provided by the damped outrigger system for translational and torsional modes of vibration of the building. The results from the study presented herein demonstrate that RTHS can be applied to large nonlinear large structural systems involving multi-axis response to multi-directional excitation. 

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5. Improving the Seismic Performance of Structural Steel Systems Through Advanced Testing

   https://doi.org/10.1007/978-3-031-03811-2_6  

   James Ricles (May 2022, Lecture notes in civil engineering)

   Recent earthquakes in many parts of the world have resulted in damage to the civil infrastructure, resulting in fatalities and economic loss. This experience has resulted in stake holders demanding a more resilient infrastructure and the mitigation of earthquake hazards to minimize their impact on society. Researchers have developed concepts for structural steel systems to promote resilient performance. Real-time hybrid simulation (RTHS) provides an experimental technique to meet the need to validate new concepts. RTHS enables a complete structural system, including the soil and foundation to be considered in a simulation, interaction effects and rate dependency in component and system response to be accounted for, and realistic demand imposed onto the system for prescribed hazard levels. This paper presents the concept of RTHS and developments achieved at the Lehigh NHERI Experimental Facility that have advanced RTHS to enable accurate large-scale, multidirectional simulations involving multi-natural hazards to be performed. The role that hybrid simulation has played in these developments and how its use has enabled a deeper understanding of structural system behavior under seismic and wind loading will be discussed. Examples include self-centering steel moment resisting frame systems, braced frame systems with nonlinear viscous, and tall buildings with outriggers that are outfitted with nonlinear viscous. 

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