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1. Cadence Tracking for Switched FES-Cycling With Unknown Time-Varying Input Delay

   https://doi.org/10.1115/DSCC2019-9078  

   Allen, B. ; Cousin, C. ; Rouse, C. ; Dixon, W. ( October 2019 , ASME 2019 Dynamic Systems and Control Conference)

   Functional electrical stimulation (FES) induced exercise, such as motorized FES-cycling, is commonly used in rehabilitation for lower limb movement disorders. A challenge in closed-loop FES control is the presence of an input delay between the application (and removal) of the electrical stimulus and the production of muscle force. Moreover, switching between motor control and FES control of various muscle groups can be destabilizing. This paper examines the development of a control method and state-dependent trigger condition to account for the time-varying input delayed response. Uniformly ultimately bounded tracking for a switched uncertain nonlinear dynamic system with input delays is achieved. 

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2. Saturated Control of a Switched FES-Cycle with an Unknown Time-Varying Input Delay

   Allen, B. C. ; Stubbs, K. J. ; Dixon, W. E. ( December 2020 , IFAC Conference on Cyber-Physical Human-Systems)

   A common rehabilitation for those with lower limb movement disorders is motorized functional electrical stimulation (FES) induced cycling. Motorized FES-cycling is a switched system with uncertain dynamics, unknown disturbances, and there exists an unknown time-varying input delay between the application/removal of stimulation and the onset/removal of muscle force. This is further complicated by the fact that each participant has varying levels of sensitivity to the FES input, and the stimulation must be bounded to ensure comfort and safety. In this paper, saturated FES and motor controllers are developed for an FES-cycle that ensure safety and comfort of the participant, while likewise being robust to uncertain parameters in the dynamics, unknown disturbances, and an unknown time-varying input delay. A Lyapunov-based stability analysis is performed to ensure uniformly ultimately bounded cadence tracking. 

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3. Learning‐based adaptive‐scenario‐tree model predictive control with improved probabilistic safety using robust Bayesian neural networks

   https://doi.org/10.1002/rnc.6560  

   Bao, Yajie ; Chan, Kimberly J. ; Mesbah, Ali ; Velni, Javad Mohammadpour ( December 2022 , International Journal of Robust and Nonlinear Control)

   Scenario‐based model predictive control (MPC) methods can mitigate the conservativeness inherent to open‐loop robust MPC. Yet, the scenarios are often generated offline based on worst‐case uncertainty descriptions obtaineda priori, which can in turn limit the improvements in the robust control performance. To this end, this paper presents a learning‐based, adaptive‐scenario‐tree model predictive control approach for uncertain nonlinear systems with time‐varying and/or hard‐to‐model dynamics. Bayesian neural networks (BNNs) are used to learn a state‐ and input‐dependent description of model uncertainty, namely the mismatch between a nominal (physics‐based or data‐driven) model of a system and its actual dynamics. We first present a new approach for training robust BNNs (RBNNs) using probabilistic Lipschitz bounds to provide a less conservative uncertainty quantification. Then, we present an approach to evaluate the credible intervals of RBNN predictions and determine the number of samples required for estimating the credible intervals given a credible level. The performance of RBNNs is evaluated with respect to that of standard BNNs and Gaussian process (GP) as a basis of comparison. The RBNN description of plant‐model mismatch with verified accurate credible intervals is employed to generate adaptive scenarios online for scenario‐based MPC (sMPC). The proposed sMPC approach with adaptive scenario tree can improve the robust control performance with respect to sMPC with a fixed, worst‐case scenario tree and with respect to an adaptive‐scenario‐based MPC (asMPC) using GP regression on a cold atmospheric plasma system. Furthermore, closed‐loop simulation results illustrate that robust model uncertainty learning via RBNNs can enhance the probability of constraint satisfaction of asMPC.

    

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4. Vehicle Lateral Motion Dynamics Under Braking/ABS Cyber-Physical Attacks

   https://doi.org/10.1109/TIFS.2023.3293424  

   Mohammadi, Alireza ; Malik, Hafiz ; Abbaszadeh, Masoud ( January 2023 , IEEE Transactions on Information Forensics and Security)

   In face of an increasing number of automotive cyber-physical threat scenarios, the issue of adversarial destabilization of the lateral motion of target vehicles through direct attacks on their steering systems has been extensively studied. A more subtle question is whether a cyberattacker can destabilize the target vehicle lateral motion through improper engagement of the vehicle brakes and/or anti-lock braking systems (ABS). Motivated by such a question, this paper investigates the impact of cyber-physical attacks that exploit the braking/ABS systems to adversely affect the lateral motion stability of the targeted vehicles. Using a hybrid physical/dynamic tire-road friction model, it is shown that if a braking system/ABS attacker manages to continuously vary the longitudinal slips of the wheels, they can violate the necessary conditions for asymptotic stability of the underlying linear time-varying (LTV) dynamics of the lateral motion. Furthermore, the minimal perturbations of the wheel longitudinal slips that result in lateral motion instability under fixed slip values are derived. Finally, a real-time algorithm for monitoring the lateral motion dynamics of vehicles against braking/ABS cyber-physical attacks is devised. This algorithm, which can be efficiently computed using the modest computational resources of automotive embedded processors, can be utilized along with other intrusion detection techniques to infer whether a vehicle braking system/ABS is experiencing a cyber-physical attack. Numerical simulations in the presence of realistic CAN bus delays, destabilizing slip value perturbations obtained from solving quadratic programs on an embedded ARM Cortex-M3 emulator, and side-wind gusts demonstrate the effectiveness of the proposed methodology. 

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5. Integral Quadratic Constraints with Infinite-Dimensional Channels

   https://doi.org/10.23919/ACC55779.2023.10156335  

   Talitckii, Aleksandr ; Seiler, Peter ; Peet, Matthew M. ( May 2023 , Proceedings of the American Control Conference)

   Modern control theory provides us with a spectrum of methods for studying the interconnection of dynamic systems using input-output properties of the interconnected subsystems. Perhaps the most advanced framework for such inputoutput analysis is the use of Integral Quadratic Constraints (IQCs), which considers the interconnection of a nominal linear system with an unmodelled nonlinear or uncertain subsystem with known input-output properties. Although these methods are widely used for Ordinary Differential Equations (ODEs), there have been fewer attempts to extend IQCs to infinitedimensional systems. In this paper, we present an IQC-based framework for Partial Differential Equations (PDEs) and Delay Differential Equations (DDEs). First, we introduce infinitedimensional signal spaces, operators, and feedback interconnections. Next, in the main result, we propose a formulation of hard IQC-based input-output stability conditions, allowing for infinite-dimensional multipliers. We then show how to test hard IQC conditions with infinite-dimensional multipliers on a nominal linear PDE or DDE system via the Partial Integral Equation (PIE) state-space representation using a sufficient version of the Kalman-Yakubovich-Popov lemma (KYP). The results are then illustrated using four example problems with uncertainty and nonlinearity. 

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