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. In this paper, tracking controllers are developed 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 uniformly ultimately bounded tracking.

No abstract

No abstract

Abstract-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. The controller yields desired limb trajectory tracking while simultaneously minimizing a cost functional that is positive in the error states and stimulation input. The development of this framework allows tradeoffs to be made between tracking performance and control effort by putting different penalties on error states and control input, depending on the clinical goal or functional task. The controller is examined through a Lyapunov-based analysis. Experiments on able-bodied individuals are provided to demonstrate the performance of the developed controller.Index Terms-Functional electrical stimulation (FES), inverse optimal control, Lyapunov stability, neural network (NN), neuromuscular electrical stimulation, nonlinear system control.

Muscle fatigue during electrical stimulation onsets early and is comparatively more substantial than during volitional contractions, hindering successful application of functional and therapeutic neuromuscular electrical stimulation (NMES). One of the avoidable causes of muscle fatigue can be attributed to the overstimulation during NMES. In this paper, a NMES controller is developed to minimize a quadratic cost functional to balance asymptotic trajectory tracking performance and control effort, potentially reducing overstimulation of the muscle. A Lyapunov-based analysis is used to prove the asymptotic convergence of closed-loop tracking error and asymptotic minimization of the given cost functional.