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This paper develops a higher-order sliding mode (HOSM) differentiator with adaptive gains to address the exact tracking control problem using only input-output information of a wider class of nonlinear systems with disturbances and parametric uncertainties. The complete state of the plant is assumed unmeasured so that a norm state estimator is constructed to norm bound the state-dependent disturbances and dynamically update the gains of the proposed differentiator. Global/semi-global stability properties and robust exact tracking can be achieved when the proposed adaptive HOSM based differentiator is applied to output-feedback purposes. Numerical simulations are presented for different sliding mode control designs, such as: (a) first-order sliding mode control, (b) non-singular terminal sliding modes, (c) second order sliding mode (SOSM) algorithms (twisting and super-twisting) as well as (d) quasi-continuous HOSM finite-time controllers.

Extremum seeking (ES) methodology is applied to implement adaptive Proportional-Integral-Derivative (PID) closed-loop control for neuromuscular electrical stimulation (NMES). The proposed strategy is designed to control the patient's arm position in order to generate elbow extension/flexion movements. This method obviates the application of initial controller tests directly to patients since the tuning procedure is automatically performed in an online fashion. ES is used to tune the parameters of a PID controller so as to minimize a given cost function which is chosen to reflect the desired performance attributes. The ultimate responses obtained in the experiments with a healthy volunteer complied with the common specifications set in terms of the steady-state error, settling time, and the percentage overshoot.

In addition to the gradient based extremum seeking for delay systems presented in a companion paper, we derive here the control design and analysis for scalar Newtonbased extremum seeking subject to input-output delays. differently from the previous work, a new predictor with a perturbation-based estimate of the Hessian's inverse is incorporated in the closed-loop such that the convergence rate of the real-time controller can be made userassignable, rather than being dependent on the unknown Hessian of the static nonlinear map to be optimized. Exponential stability and convergence to a small neighborhood of the unknown extremum point can be obtained. This result is rigorously achieved by using backstepping transformation and averaging in infinite dimensions. A numerical example is given to illustrate the effectiveness of the proposed predictor based extremum seeking for time-delay compensation.

In this paper, we derive the design and analysis for scalar gradient extremum seeking control (ESC) subject to arbitrarily long input-output delays, by employing a predictor with a perturbation-based estimate of the Hessian. Exponential stability and convergence to a small neighborhood of the unknown extremum point can be guaranteed. This result is carried out using backstepping transformation and averaging in infinite dimensions. Some simulation examples are presented to illustrate the performance of the delay-compensated ESC scheme.

A novel output-feedback tracking sliding mode control strategy is proposed for a class of uncertain multi-input-multi-output (MIMO) systems with strong nonlinearities and unknown high-frequency gain (HAG) matrix, that is, the control direction is assumed unknown. A switching scheme based on a monitoring function is designed to handle the control direction uncertainty. The proposed method provides global stability properties and exact output tracking. Simulation results about a robotics visual servoing system using a fixed but uncalibrated camera illustrate the robustness and practical viability of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, we generalize our previous results of Newton-based extremum seeking of higher derivatives via predictors with averaging-based estimates for uncertain delays. We show necessary conditions for the robustness to small delay uncertainties of the proposed extremum seeking controller with predictor feedback. Local stability and exponential convergence to a small neighborhood of the unknown extremum can still be guaranteed. A numerical simulation example is presented to illustrate the performance of the predictor based control scheme for uncertain time-delay compensation.

In this paper we combine the sliding mode control (SMC) strategy with monitoring functions and time-scaling to solve the problem of trajectory tracking for linear minimum or non-minimum phase systems. Unlike other publications which in general assume full/partial state availability, the complete knowledge of the non-minimum phase plant parameters, or just handle the stabilization/regulation problem, here we deal with the tracking objective by assuming the plant is subject parametric uncertainties and applying only output feedback. When using the time-scaling technique, we may expect that the tracking of the reference model occurs slowly, depending on the time-scaling parameter. This is the price to be paid for considering a more general framework of uncertainty. Global asymptotic stability with respect to compact sets is demonstrated for the closed-loop system, where the output tracking error ultimately achieves arbitrarily small residual sets. Simulation results illustrate the performance of our control algorithm.