Accelerated Gradient Approach For Deep Neural Network-Based Adaptive Control of Unknown Nonlinear Systems.

Recent connections in the adaptive control literature to continuous-time analogs of Nesterov's accelerated gradient method have led to the development of new real-time adaptation laws based on accelerated gradient methods. However, previous results assume that the system's uncertainties are linear-in-the-parameters (LIP). To compensate for non-LIP uncertainties, our preliminary results developed a neural network (NN)-based accelerated gradient adaptive controller to achieve trajectory tracking for nonlinear systems; however, the development and analysis only considered single-hidden-layer NNs.

Data-Based and Opportunistic Integral Concurrent Learning for Adaptive Trajectory Tracking During Switched FES-Induced Biceps Curls.

Hybrid exoskeletons, which combine functional electrical stimulation (FES) with a motorized testbed, can potentially improve the rehabilitation of people with movement disorders. However, hybrid exoskeletons have inherently nonlinear and uncertain dynamics, including combinations of discrete modes that switch between different continuous dynamic subsystems, which complicate closed-loop control. A particular complication is the uncertain muscle control effectiveness associated with FES.

Encouraging Volitional Pedaling in Functional Electrical Stimulation-Assisted Cycling Using Barrier Functions.

Stationary motorized cycling assisted by functional electrical stimulation (FES) is a popular therapy for people with movement impairments. Maximizing volitional contributions from the rider of the cycle can lead to long-term benefits like increased muscular strength and cardiovascular endurance. This paper develops a combined motor and FES control system that tasks the rider with maintaining their cadence near a target point using their own volition, while assistance or resistance is applied gradually as their cadence approaches the lower or upper boundary, respectively, of a user-defined safe range.

Electromechanical delay during functional electrical stimulation induced cycling is a function of lower limb position.

Introduction: Functional electrical stimulation (FES) induced cycling has been shown to be an effective rehabilitation for those with lower limb movement disorders. However, a consequence of FES is an electromechanical delay (EMD) existing between the stimulation input and the onset of muscle force. The objective of this study is to determine if the cycle crank angle has an effect on the EMD.

Characterization of the Time-Varying Nature of Electromechanical Delay During FES-Cycling.

Functional electrical stimulation (FES) induced cycling is a common rehabilitative technique for people with neuromuscular disorders. A challenge for closed-loop FES control is that there exists a potentially destabilizing time-varying input delay, termed electromechanical delay (EMD), between the application of the electric field and the corresponding muscle contraction. In this article, the FES-induced torque production and EMD are quantified on an FES-cycle for the quadriceps femoris and gluteal muscle groups.

FES Cycling in Stroke: Novel Closed-Loop Algorithm Accommodates Differences in Functional Impairments.

Objective: The objective of this paper was to develop and test a novel control algorithm that enables stroke survivors to pedal a cycle in a desired cadence range despite varying levels of functional abilities after stroke.

Methods: A novel algorithm was developed which automatically adjusts 1) the intensity of functional electrical stimulation (FES) delivered to the leg muscles, and 2) the current delivered to an electric motor. The algorithm automatically switches between assistive, uncontrolled, and resistive modes to accommodate for differences in functional impairment, based on the mismatch between the desired and actual cadence.

Controlling the Cadence and Admittance of a Functional Electrical Stimulation Cycle.

For an individual suffering from a neurological condition, such as spinal cord injury, traumatic brain injury, or stroke, motorized functional electrical stimulation (FES) cycling is a rehabilitation strategy, which offers numerous health benefits. Motorized FES cycling is an example of physical human-robot interaction in which both systems must be controlled; the human is actuated by applying neuromuscular electrical stimulation to the large leg muscle groups, and the cycle is actuated through its onboard electric motor. While the rider is stimulated using a robust sliding-mode controller, the cycle utilizes an admittance controller to preserve rider safety.

Distributed Repetitive Learning Control for Cooperative Cadence Tracking in Functional Electrical Stimulation Cycling.

Closed-loop control of functional electrical stimulation coupled with motorized assistance to induce cycling is a rehabilitative strategy that can improve the mobility of people with neurological conditions (NCs). However, robust control methods, which are currently pervasive in the cycling literature, have limited effectiveness due to the use of high stimulation intensity leading to accelerated fatigue during cycling protocols. This paper examines the design of a distributed repetitive learning controller (RLC) that commands an independent learning feedforward term to each of the six stimulated lower-limb muscle groups and an electric motor during the tracking of a periodic cadence trajectory.

The State Following Approximation Method.

A function approximation method is developed which aims to approximate a function in a small neighborhood of a state that travels within a compact set. The method provides a novel approximation strategy for the efficient approximation of nonlinear functions for real-time simulations and experiments. The development is based on the theory of universal reproducing kernel Hilbert spaces over the n -dimensional Euclidean space.

Approximate Dynamic Programming: Combining Regional and Local State Following Approximations.

An infinite-horizon optimal regulation problem for a control-affine deterministic system is solved online using a local state following (StaF) kernel and a regional model-based reinforcement learning (R-MBRL) method to approximate the value function. Unlike traditional methods such as R-MBRL that aim to approximate the value function over a large compact set, the StaF kernel approach aims to approximate the value function in a local neighborhood of the state that travels within a compact set. In this paper, the value function is approximated using a state-dependent convex combination of the StaF-based and the R-MBRL-based approximations.

Influence of Elbow Flexion and Stimulation Site on Neuromuscular Electrical Stimulation of the Biceps Brachii.

Functional electrical stimulation (FES) can help individuals with physical disabilities by assisting limb movement; however, the change in muscle geometry associated with limb movement may affect the response to stimulation. The aim of this paper was to quantify the effects of elbow flexion and stimulation site on muscle torque production. Contraction torque about the elbow was measured in 12 healthy individuals using a custom elbow flexion testbed and a transcutaneous electrode array.

Position and torque control via rehabilitation robot and functional electrical stimulation.

Two common rehabilitation therapies for individuals possessing neurological conditions are functional electrical stimulation (FES) and robotic assistance. This paper focuses on combining the two rehabilitation strategies for use on the biceps brachii muscle group. FES is used to elicit muscle contractions to actuate the forearm and a rehabilitation robot is used to challenge the muscle group in its efforts.

Synchronization of Uncertain Euler-Lagrange Systems With Uncertain Time-Varying Communication Delays.

A decentralized controller is designed for leader-based synchronization of communication-delayed networked agents. The agents have heterogeneous dynamics modeled by uncertain, nonlinear Euler-Lagrange equations of motion affected by heterogeneous, unknown, exogenous disturbances. The developed controller requires only one-hop (delayed) communication from network neighbors and the communication delays are assumed to be heterogeneous, uncertain, and time-varying.

The Time-Varying Nature of Electromechanical Delay and Muscle Control Effectiveness in Response to Stimulation-Induced Fatigue.

Neuromuscular electrical stimulation (NMES) and Functional Electrical Stimulation (FES) are commonly prescribed rehabilitative therapies. Closed-loop NMES holds the promise to yield more accurate limb control, which could enable new rehabilitative procedures. However, NMES/FES can rapidly fatigue muscle, which limits potential treatments and presents several control challenges.

Switched Tracking Control of the Lower Limb During Asynchronous Neuromuscular Electrical Stimulation: Theory and Experiments.

Neuromuscular electrical stimulation (NMES) induces muscle contractions via electrical stimuli. NMES can be used for rehabilitation and to enable functional movements; however, a fundamental limitation is the early onset of fatigue. Asynchronous stimulation is a method that can reduce fatigue by utilizing multiple stimulation channels to segregate and switch between different sets of recruited motor units.

Model-Based Reinforcement Learning for Infinite-Horizon Approximate Optimal Tracking.

This brief paper provides an approximate online adaptive solution to the infinite-horizon optimal tracking problem for control-affine continuous-time nonlinear systems with unknown drift dynamics. To relax the persistence of excitation condition, model-based reinforcement learning is implemented using a concurrent-learning-based system identifier to simulate experience by evaluating the Bellman error over unexplored areas of the state space. Tracking of the desired trajectory and convergence of the developed policy to a neighborhood of the optimal policy are established via Lyapunov-based stability analysis.

Switched Control of Cadence During Stationary Cycling Induced by Functional Electrical Stimulation.

Functional electrical stimulation (FES) can be used to activate the dysfunctional lower limb muscles of individuals with neurological disorders to produce cycling as a means of rehabilitation. However, previous literature suggests that poor muscle control and nonphysiological muscle fiber recruitment during FES-cycling causes lower efficiency and power output at the cycle crank than able-bodied cycling, thus motivating the investigation of improved control methods for FES-cycling. In this paper, a stimulation pattern is designed based on the kinematic effectiveness of the rider's hip and knee joints to produce a forward torque about the cycle crank.

Identification-Based Closed-Loop NMES Limb Tracking With Amplitude-Modulated Control Input.

An upper motor neuron lesion (UMNL) can be caused by various neurological disorders or trauma and leads to disabilities. Neuromuscular electrical stimulation (NMES) is a technique that is widely used for rehabilitation and restoration of motor function for people suffering from UMNL. Typically, stability analysis for closed-loop NMES ignores the modulated implementation of NMES.

Closed-Loop Asynchronous Neuromuscular Electrical Stimulation Prolongs Functional Movements in the Lower Body.

Neuromuscular electrical stimulation (NMES) is commonly used in rehabilitative settings and is also used for assistive purposes to create functional movements, where it is termed functional electrical stimulation (FES). One limitation of NMES/FES is early onset of muscle fatigue. NMES-induced fatigue can be reduced by switching between multiple stimulation channels that target different motor units or synergistic muscles (i.

Comparing the Induced Muscle Fatigue Between Asynchronous and Synchronous Electrical Stimulation in Able-Bodied and Spinal Cord Injured Populations.

Neuromuscular electrical stimulation (NMES) has been shown to impart a number of health benefits and can be used to produce functional outcomes. However, one limitation of NMES is the onset of NMES-induced fatigue. Multi-channel asynchronous stimulation has been shown to reduce NMES-induced fatigue compared to conventional single-channel stimulation.

Approximate N-Player Nonzero-Sum Game Solution for an Uncertain Continuous Nonlinear System.

An approximate online equilibrium solution is developed for an N -player nonzero-sum game subject to continuous-time nonlinear unknown dynamics and an infinite horizon quadratic cost. A novel actor-critic-identifier structure is used, wherein a robust dynamic neural network is used to asymptotically identify the uncertain system with additive disturbances, and a set of critic and actor NNs are used to approximate the value functions and equilibrium policies, respectively. The weight update laws for the actor neural networks (NNs) are generated using a gradient-descent method, and the critic NNs are generated by least square regression, which are both based on the modified Bellman error that is independent of the system dynamics.

Comparing the force ripple during asynchronous and conventional stimulation.

Introduction: Asynchronous stimulation has been shown to reduce fatigue during electrical stimulation; however, it may also exhibit a force ripple. We quantified the ripple during asynchronous and conventional single-channel transcutaneous stimulation across a range of stimulation frequencies.

Methods: The ripple was measured during 5 asynchronous stimulation protocols, 2 conventional stimulation protocols, and 3 volitional contractions in 12 healthy individuals.

Adaptive Inverse optimal neuromuscular electrical stimulation.

Neuromuscular electrical stimulation (NMES) is a prescribed treatment for various neuromuscular disorders, where an electrical stimulus is provided to elicit a muscle contraction. Barriers to the development of NMES controllers exist because the muscle response to an electrical stimulation is nonlinear and the muscle model is uncertain. Efforts in this paper focus on the development of an adaptive inverse optimal NMES controller.

A novel modulation strategy to increase stimulation duration in neuromuscular electrical stimulation.

Introduction: Neuromuscular electrical stimulation (NMES) has been shown to be an effective treatment for muscular dysfunction. Yet, a fundamental barrier to NMES treatments is the rapid onset of muscle fatigue. The purpose of this study is to examine the effect of feedback-based frequency modulation on the closed-loop performance of the quadriceps during repeated dynamic contractions.

Predictor-based compensation for electromechanical delay during neuromuscular electrical stimulation.

Electromechanical delay (EMD) is a biological artifact that arises due to a time lag between electrical excitation and tension development in a muscle. EMD is known to cause degraded performance and instability during neuromuscular electrical stimulation (NMES). Compensating for such input delay is complicated by the unknown nonlinear muscle force-length and muscle force-velocity relationships.