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Summary: An output‐feedback super‐twisting algorithm (STA) with variable gains is developed for multiple‐input and multiple‐output plants with arbitrary relative degrees. Global or semi‐global finite‐time exact tracking can be guaranteed for a class of uncertain systems with matched nonlinear time‐varying disturbances, possibly dependent on the unmeasured states. This represents a significant generalization of recently introduced versions of the STAs to a multivariable setup with arbitrary relative degrees, output‐feedback, and variable gains. The construction of such controller is based on a higher‐order sliding‐mode multivariable differentiator with dynamic gains. The gain adaptation for the controller and differentiator employs state‐norm observers to overcome the lack of the full‐state measurement. The stability properties of the proposed control system are demonstrated by means of input‐to‐state stability tools and a Lyapunov function‐based analysis. The theoretical results are verified through numerical and academic examples. [ABSTRACT FROM AUTHOR]

• Adaptive binary controller via output feedback for exact tracking of multivariable uncertain plants with nonuniform arbitrary relative degrees. • Multivariable generalization of the global finite-time differentiators with dynamic gains and higher-order sliding modes. • Global asymptotic stability of the closed-loop system and ultimate exponential convergence to small residual sets are guaranteed. • Fast transient responses, improved tracking precision and chattering-free control signals. • Engineering application to inertially stabilized platforms with numerical results based on data acquired from experiments in real-world conditions. This paper presents an extension of the Binary Model Reference Adaptive Control (BMRAC) for uncertain multivariable (square) systems with non-uniform arbitrary relative degrees using only output feedback and its application to inertially stabilized platforms using a two degree of freedom gimbal as actuator. The BMRAC is a robust adaptive strategy with good transient performance, thus useful for uncertain systems, and the multivariable framework is suitable to deal with mechanical unbalances. Using a newly proposed differentiator with dynamic gains based on higher-order sliding mode, the proposed controller achieves global and exact tracking. To illustrate the effective of the proposed solution, simulations are presented using real-word data obtained from an instrumented vehicle in an irregular ground. [ABSTRACT FROM AUTHOR]

This paper proposes an improved active disturbance rejection control (ADRC) method for output tracking of uncertain plants with unknown control direction. A basic design procedure in the ADRC methodology is to assume the exact knowledge of the system control direction, that is, the sign of its input channel coefficient. Recent works have been proposed to relax such a requirement by performing modifications in its control structure. However, despite considering uncertainties in the input coefficient, many variants of the ADRC method still assume the knowledge of the control direction, which means that the control gain is uncertain in norm, but not in sign. For solving the latter case, and also aiming to generalize the earlier ADRC results for a larger class of systems, the present work incorporates the concept of monitoring functions in the controller design. It is a switching‐based strategy whose main function is to determine the correct sign of the control direction, which is directly related to the sign of the plant input channel coefficient. As a consequence of the resulting new control method, exponential stability with respect to a small residual set is guaranteed for the output tracking problem in closed‐loop. Numerical simulations are performed and discussed initially in an academical example, only for comparing the robustness properties concerning the unknown control direction of the proposed strategy with another ADRC methodology. In the sequence, the proposed ADRC strategy based on monitoring function is applied to the automotive plant system of an Anti‐Lock Braking System for illustrating its performance. [ABSTRACT FROM AUTHOR]

An output-feedback control system for uncertain linear systems with arbitrary delay in the output signal and input disturbances is developed. The state of the system and the disturbances are estimated by observers connected in cascade. Unlike previous works, parametric uncertainties are allowed. Their effects are analysed by using the Small-Gain Theorem. The rejection of the exogenous and matched input disturbances is also considered in the system. The proposed control strategy guarantees global stability of the closed-loop system. A numerical example and an application to underwater vehicle control illustrate the effectiveness of the proposed control strategy to compensate arbitrary delays, disturbances and bounded uncertainties. [ABSTRACT FROM AUTHOR]

Summary: An adaptive sliding‐mode unit vector control approach based on monitoring functions to deal with disturbances of unknown bounds is proposed. An uncertain multivariable linear system is considered with a quite general class of nonsmooth disturbances. Global stabilization/tracking is demonstrated using either state or output feedback. The proposed adaptation method makes the control gain less conservative, becoming large enough when the disturbance grows and becoming smaller when it decreases, leading to reduced chattering effects. In contrast to previous methods, the new switching scheme is able to guarantee a prespecified transient time, maximum overshoot, and steady‐state error for multivariable uncertain plants. The proposed technique is applied to the trajectory tracking control of a surface vessel subjected to ocean currents, wind, and waves. Simulations are presented to show the performance of the new adaptation scheme in this adverse scenario of possibly growing, temporarily large, or vanishing exogenous disturbances. [ABSTRACT FROM AUTHOR]

An algorithm for adaptation of the gains of higher-order sliding mode-based exact differentiators is developed for the case where the upper bound for the ρth derivative of the tracking error signal exists but it is unknown. Unlikely other publications in the literature, the developed adaptive algorithm based on monitoring functions guarantees global and exact tracking when used in closed-loop output feedback. In the closed-loop scenario, a global-exact and finite-time estimate for the variables is applied to construct the sliding surface of the proposed sliding mode controller. The class of uncertain systems of arbitrary relative degree (ρ ≥ 1) takes into account time-varying perturbations with unknown bounds and state-dependent nonlinearities satisfying a linear growth condition with any unknown rate. The norm of the unmeasured state is majorised by using a hybrid state-norm estimator. Numerical examples and an engineering application to wing rock control are presented in order to illustrate the properties and advantages of the novel adaptation approach for sliding mode control design. [ABSTRACT FROM AUTHOR]

This paper presents an output-feedback control strategy based on the variable gain super-twisting algorithm. The proposal achieves robust global/semi-global exact tracking results for plants with arbitrary relative degree. This is ensured in spite of parametric uncertainties and disturbances that may be state-dependent and time-varying. The construction of such controller is based on a (non)homogeneous higher order sliding-mode differentiator with dynamic gains. The gain adaptation schemes for the controller and differentiator are based on norm observers to overcome the lack of state measurement. The continuous nature of the obtained control signal alleviates the chattering phenomenon. The stability properties of the proposed controller are demonstrated by means of a Lyapunov function-based analysis. The theoretical results are verified through a simulation example, and experimentally tested on a seesaw module. [ABSTRACT FROM AUTHOR]

This paper addresses the application of the sliding mode approach to control the arm movements by artificial recruitment of muscles using Neuromuscular Electrical Stimulation (NMES). Such a technique allows the activation of motor nerves using surface electrodes. The goal of the proposed control system is to move the upper limbs of subjects through electrical stimulation to achieve a desired elbow angular displacement. Since the human neuro-motor system has individual characteristics, being time-varying, nonlinear and subject to uncertainties, the use of advanced robust control schemes may represent a better solution than classical Proportional-Integral (PI) controllers and model-based approaches, being simpler than more sophisticated strategies using fuzzy logic or neural networks usually applied in this control problem. The objective is the introduction of a new time-scaling base sliding mode control (SMC) strategy for NMES and its experimental evaluation. The main qualitative advantages of the proposed controller via time-scaling procedure are its independence of the knowledge of the plant relative degree and the design/tuning simplicity. The developed sliding mode strategy allows for chattering alleviation due to the impact of the integrator in smoothing the control signal. In addition, no differentiator is applied to construct the sliding surface. The stability analysis of the closed-loop system is also carried out by using singular perturbation methods. Experimental results are conducted with healthy volunteers as well as stroke patients. Quantitative results show a reduction of 45% in terms of root mean square (RMS) error (from 5.9° to 3 . 3 ∘ ) in comparison with PI control scheme, which is similar to that obtained in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we propose an adaptive output-feedback controller for uncertain linear systems without a priori knowledge of the plant high-frequency-gain sign. To deal with parametric uncertainties and unmodeled dynamics, we consider a robust adaptive strategy named binary model reference adaptive control, which has the good transient properties and robustness of sliding mode control with the important advantage of having a continuous control signal free of chattering. The effective way of tackling unknown high-frequency-gain sign is employing monitoring functions. The developed adaptive control guarantees global exponential stability of the closed-loop error system with respect to a compact residual set. Moreover, in the absence of unmodeled dynamics, exact tracking of a reference signal can be achieved. Numerical simulations illustrate the efficacy of the proposed approach. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper addresses the design of a sliding mode controller for a class of high-order uncertain nonlinear plants with unmatched state-dependent nonlinearities and unknown sign of the high frequency gain, i.e., the control direction is assumed unknown. Differently from most previous studies, the control direction is allowed to switch its sign. We show that it is possible to obtain global exact tracking using only output-feedback by coupling a relay periodic switching function with a norm state observer. One significant advantage of the new scheme is its robustness and improved transient response under arbitrary changes of the control direction which have been theoretically demonstrated for jump variations and successfully tested by simulations. The proposed controller is also evaluated with a DC motor control experiment. [ABSTRACT FROM PUBLISHER]

An output‐feedback sliding‐mode controller is proposed for multivariable uncertain systems with unknown time‐varying state delays and unmatched non‐linear terms. The non‐linearities are allowed to depend not only on the system output, but also on its unmeasurable state, and can be polynomial. This scheme is based on model‐reference unit vector control under a mild Hurwitz condition for the high‐frequency gain matrix. To achieve global stability properties, the amplitude of the control signal is given by a norm observer for the unmeasured state. For the first time, the design of norm observers is applied to a class of time‐delay systems. This approach guarantees finite‐time convergence of the output‐tracking error to zero. Simulation results illustrate the application of the developed control scheme. [ABSTRACT FROM AUTHOR]

Abstract: This paper addresses the design of a sliding mode tracking controller for single-input–single-output (SISO) uncertain plants with relative degree one and unknown control direction, i.e., with unknown sign of the high frequency gain (HFG). We demonstrate that, for a class of linear plants with nonlinear output function, it is possible to achieve global exact tracking using only output-feedback by combining a recently introduced periodic switching function with a well-known control parameterization of Model Reference Control (MRC). Simulation results are presented to illustrate the good tracking performance. One significant advantage of the new scheme is its robustness to time-varying control direction which is here theoretically justified for jump variations of the HFG and successfully tested by simulation in more general conditions. This property makes it adequate for solving extremum-seeking problems. Theoretical justification is presented for a class of systems with nonlinear output function using only output-feedback. An application to the wheel slip control in Antilock Braking Systems (ABSs) illustrates the practical viability of the proposed control scheme. [Copyright &y& Elsevier]