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1. Adaptive Trajectory Tracking During Motorized and FES-Induced Biceps Curls via Integral Concurrent Learning

   https://doi.org/10.1115/DSCC2020-3125  

   Allen, Brendon C.; Stubbs, Kimberly J.; Dixon, Warren E. (October 2020, ASME Dynamic Systems and Control Conference)

   null (Ed.)

   A common rehabilitative technique for those with neuro-muscular disorders is functional electrical stimulation (FES) induced exercise such as FES-induced biceps curls. FES has been shown to have numerous health benefits, such as increased muscle mass and retraining of the nervous system. Closed-loop control of a motorized FES system presents numerous challenges since the system has nonlinear and uncertain dynamics and switching is required between motor and FES control, which is further complicated by the muscle having an uncertain control effectiveness. An additional complication of FES systems is that high gain feedback from traditional robust controllers can be uncomfortable to the participant. In this paper, data-based, opportunistic learning is achieved by implementing an integral concurrent learning (ICL) controller during a motorized and FES-induced biceps curl exercise. The ICL controller uses adaptive feedforward terms to augment the FES controller to reduce the required control input. A Lyapunov-based analysis is performed to ensure exponential trajectory tracking and opportunistic, exponential learning of the uncertain human and machine parameters. In addition to improved tracking performance and robustness, the potential of learning the specific dynamics of a person during a rehabilitative exercise could be clinically significant. Preliminary simulation results are provided and demonstrate an average position error of 0.14 ± 1.17 deg and an average velocity error of 0.004 ± 1.18 deg/s. 

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2. Model reference adaptive control for nonlinear time‐varying hybrid dynamical systems

   https://doi.org/10.1002/acs.3631  

   L'Afflitto, Andrea (August 2023, International Journal of Adaptive Control and Signal Processing)

   M. Grimble (Ed.)

   Summary This paper presents the first model reference adaptive control system for nonlinear, time‐varying, hybrid dynamical plants affected by matched and parametric uncertainties, whose resetting events are unknown functions of time and the plant's state. In addition to a control law and an adaptive law, which resemble those of the classical model reference adaptive control framework for continuous‐time dynamical systems, the proposed framework allows imposing instantaneous variations in the reference model's trajectory to rapidly steer the trajectory tracking error to zero, while retaining the closed‐loop system's ability to follow a user‐defined signal. These results are enabled by the first extension of the classical LaSalle–Yoshizawa theorem to time‐varying hybrid dynamical systems, which is presented in this paper as well. A numerical simulation shows the key features of the proposed adaptive control system and highlights its ability to reduce both the control effort and the trajectory tracking error over a classical model reference adaptive control system applied to the same problem. 

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3. Fast and Guaranteed Safe Controller Synthesis for Nonlinear Vehicle Models

   https://doi.org/10.1007/978-3-030-53288-8\_31  

   Fan, Chuchu; Miller, Kristina; Mitra, Sayan (July 2020, Computer Aided Verification - 32nd International Conference, {CAV} 2020, Los Angeles, CA, USA, July 21-24, 2020, Proceedings, Part {I})

   We address the problem of synthesizing a controller for nonlinear systems with reach-avoid requirements. Our controller consists of a reference controller and a tracking controller which drives the actual trajectory to follow the reference trajectory. We identify a type of reference trajectory such that the tracking error between the actual trajectory of the closed-loop system and the reference trajectory can be bounded. Moreover, such a bound on the tracking error is independent of the reference trajectory. Using such bounds on the tracking error, we propose a method that can find a reference trajectory by solving a satisfiability problem over linear constraints. Our overall algorithm guarantees that the resulting controller can make sure every trajectory from the initial set of the system satisfies the given reach-avoid requirement. We also implement our technique in a tool FACTEST. We show that FACTEST can find controllers for four vehicle models (3–6 dimensional state space and 2–4 dimensional input space) across eight scenarios (with up to 22 obstacles), all with running time at the sub-second range. 

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4. Decoupled Data-Based Approach for Learning to Control Nonlinear Dynamical Systems

   https://doi.org/10.1109/TAC.2021.3108552  

   Wang, Ran; Parunandi, Karthikeya Sharma; Yu, Dan; Kalathil, Dileep; Chakravorty, Suman (August 2021, IEEE Transactions on Automatic Control)

   This paper addresses the problem of learning the optimal control policy for a nonlinear stochastic dynam- ical. This problem is subject to the ‘curse of dimension- ality’ associated with the dynamic programming method. This paper proposes a novel decoupled data-based con- trol (D2C) algorithm that addresses this problem using a decoupled, ‘open-loop - closed-loop’, approach. First, an open-loop deterministic trajectory optimization problem is solved using a black-box simulation model of the dynamical system. Then, closed-loop control is developed around this open-loop trajectory by linearization of the dynamics about this nominal trajectory. By virtue of linearization, a linear quadratic regulator based algorithm can be used for this closed-loop control. We show that the performance of D2C algorithm is approximately optimal. Moreover, simulation performance suggests a significant reduction in training time compared to other state of the art algorithms. 

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5. Adaptive NN-Based Boundary Control for Output Tracking of A Wave Equation with Matched and Unmatched Boundary Uncertainties

   https://doi.org/10.23919/ACC53348.2022.9867897  

   Zhang, Jingting; Stegagno, Paolo; Zeng, Wei; Yuan, Chengzhi (June 2022, Proceedings of the American Control Conference)

   This paper is focused on the output tracking control problem of a wave equation with both matched and unmatched boundary uncertainties. An adaptive boundary feedback control scheme is proposed by utilizing radial basis function neural networks (RBF NNs) to deal with the effect of system uncertainties. Specifically, two RBF NN models are first developed to approximate the matched and unmatched system uncertain dynamics respectively. Based on this, an adaptive NN control scheme is derived, which consists of: (i) an adaptive boundary feedback controller embedded by the NN model approximating the matched uncertainty, for rendering stable and accurate tracking control; and (ii) a reference model embedded by the NN model approximating the unmatched uncertainty, for generating a prescribed reference trajectory. Rigorous analysis is performed using the Lyapunov theory and the C0-semigroup theory to prove that our proposed control scheme can guarantee closed-loop stability and wellposedness. Simulation study has been conducted to demonstrate effectiveness of the proposed approach. 

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