Lyapunov-based control methods for neuromuscular electrical stimulation

Neuromuscular electrical stimulation (NMES) is the application of a potential field across a muscle in order to produce a desired muscle contraction. NMES is a promising treatment that has the potential to restore functional tasks in persons with movement disorders. Towards this goal, the research objective in the dissertation is to develop NMES controllers that will enable a person's lower shank to track a continuous desired trajectory (or constant setpoint).;A nonlinear musculoskeletal model is developed in Chapter 2 which describes muscle activation and contraction dynamics and body segmental dynamics during NMES. The definitions of various components in the musculoskeletal dynamics are provided but are not required for control implementation. Instead, the structure of the relationships is used to define properties and make assumptions for control development.;A nonlinear control method is developed in Chapter 3 to control the human quadriceps femoris muscle undergoing non-isometric contractions. The developed controller does not require a muscle model and can be proven to yield asymptotic stability for a nonlinear muscle model in the presence of bounded nonlinear disturbances. The performance of the controller is demonstrated through a series of closed-loop experiments on healthy normal volunteers. The experiments illustrate the ability of the controller to enable the shank to follow trajectories with different periods and ranges of motion, and also track desired step changes with changing loads.;The most promising and popular control methods for NMES are neural network (NN)-based methods since these methods can be used to learn nonlinear muscle force to length and velocity relationship, and the inherent unstructured and time-varying uncertainties in available models. Further efforts in Chapter 3 focus on the use of a NN feedforward controller that is augmented with a continuous robust feedback term to yield an asymptotic result (in lieu of typical uniformly ultimately bounded (UUB) stability). Specifically, a NN-based controller and Lyapunov-based stability analysis are provided to enable semi-global asymptotic tracking of a desired time-varying limb trajectory (i.e., non-isometric contractions). The added value of incorporating a NN feedforward term is illustrated through experiments on healthy normal volunteers that compare the developed controller with the pure RISE-based feedback controller.;A pervasive problem with current NMES technology is the rapid onset of the unavoidable muscle fatigue during NMES. In closed-loop NMES control, disturbances such as muscle fatigue are often tackled through high-gain feedback which can overstimulate the muscle which further intensifies the fatigue onset. In Chapter 4, a NMES controller is developed that incorporates the effects of muscle fatigue through an uncertain function of the calcium dynamics. A NN-based estimate of the fatigue model mismatch is incorporated in a nonlinear controller through a backstepping method to control the human quadriceps femoris muscle undergoing non-isometric contractions. The developed controller is proven to yield UUB stability for an uncertain nonlinear muscle model in the presence of bounded nonlinear disturbances (e.g., spasticity, delays, changing load dynamics). Simulations are provided to illustrate the performance of the proposed controller. Continued efforts will focus on achieving asymptotic tracking versus the UUB result, and on validating the controller through experiments.;Another impediment in NMES control is the presence of input or actuator delay. Control of nonlinear systems with actuator delay is a challenging problem because of the need to develop some form of prediction of the nonlinear dynamics. The problem becomes more difficult for systems with uncertain dynamics. Motivated to address the input delay problem in NMES control and the absence of non-model based controllers for a nonlinear system with input delay in the literature, tracking controllers are developed in Chapter 5 for an Euler-Lagrange system with time-delayed actuation, parametric uncertainty, and additive bounded disturbances. One controller is developed under the assumption that the inertia is known, and a second controller is developed when the inertia is unknown. For each case a predictor-like method is developed to address the time delay in the control input. Lyapunov-Krasovskii functionals are used within a Lyapunov-based stability analysis to prove semi-global UUB tracking. Extensive experiments show better performance compared to traditional PD/PID controller as well as robustness to uncertainty in the inertia matrix and time delay value. Experiments are performed on healthy normal individuals to show the feasibility, performance, and robustness of the developed controller.;In addition to efforts focussed on input delayed nonlinear systems, a parallel motivation exists to address another class of time delayed systems which consist of nonlinear systems with unknown state delays. A continuous robust adaptive control method is designed in Chapter 6 for a class of uncertain nonlinear systems with unknown constant time-delays in the states. Specifically, the robust adaptive control method, a gradient-based desired compensation adaptation law (DCAL), and a Lyapunov-Kravoskii (LK) functional-based delay control term are utilized to compensate for unknown time-delays, linearly parameterizable uncertainties, and additive bounded disturbances for a general nonlinear system. Despite these disturbances, a Lyapunov-based analysis is used to conclude that the system output asymptotically tracks a desired time varying bounded trajectory.;Chapter 7 concludes the dissertation with a discussion of the developed contributions and future efforts.