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We propose a mandatory invasive mechanical ventilator prototype for severe COVID-19 patients with volume and pressure control operation modes. This system comprises basic pneumatic elements and sensors. Its performance is similar to commercial equipment, and it presents robustness to external disturbances and parametric uncertainties. To develop a control strategy, we propose a mathematical model with a variable structure that incorporates the dead zone phenomenon of the proportional valve, and considers external disturbances and parametric uncertainties. Based on this model, we propose a global control strategy that is based on pressure and flow regulation controllers, which use the active disturbances rejection control structure (ADRC). In this strategy, we propose robust state observers to estimate disturbances and the signals necessary for implementing the controllers. We illustrate the performance of the prototype and the control strategy through numerical simulations and experiments. We also compare its performance with PID controllers. These results corroborate its effectiveness and the possibility of its application in invasive mechanical ventilators with a simple structure, which can significantly help critical care of COVID-19 inpatients.

This paper proposes a novel Stackelberg game-oriented optimal control approach to address the bounded constraint-following control problem for uncertain mechanical systems. First, the uncertainties (possibly fast time-varying) in the system are assumed to be bounded with an unknown boundary which lies in a specified fuzzy evidence number. In practical engineering, bounded system performance is always demanded, such as the inequality constraint. A diffeomorphism transformation approach is proposed to transform the constrained system into a restructured one satisfying the bounded constraint. Second, we propose an adaptive robust control oriented by the constraint-following control to render the restructured system to follow the specified constraints accurately with deterministic performance (guaranteeing uniform boundedness and uniform ultimate boundedness). The self-adjusting adaptive law (leakage-type) can compensate for the uncertainties and avoid overcompensation. Third, a Stackelberg game-oriented optimization approach is proposed to obtain the optimal control parameters based on the fuzzy evidence theory. In the optimization approach, the two control parameters, are considered as two players with respective cost functions related to system performance and control cost. Furthermore, the optimization problem is solved by obtaining the Stackelberg strategy, which is proved to exist in analytic form. Ultimately, the permanent magnet synchronous linear motor system simulation is presented to show the design process and the excellent performance of the proposed optimal control scheme.

In this paper, a robust control strategy with a cascade structure is designed for the underactuated unmanned aerial manipulator (UAM) to perform favorable trajectory tracking, in the presence of model uncertainties and time-varying external disturbances (e.g. wind drag). In the position loop, a geometric distance is adopted as the criterion for the thrust design. Besides, both the model uncertainties and external disturbances are compensated by employing a robust term. In the attitude loop, the prescribed performance guarantees are enforced in the controller design to standardize transient performance on attitude errors. In particular, just relying on the necessary feedback states, an auxiliary system, the adaptive control technique, and the disturbance observer are respectively designed to estimate the model uncertainties and external disturbances. Through the Lyapunov stability theory analysis, the proposed approach based on a geometric distance can effectively track the desired trajectory. The results of the comparative simulations study demonstrate the effectiveness and advantages of the proposed approach.

Affine nonlinear systems are special kinds of non-linear systems, and they can represent many practical systems. Dealing with affine nonlinear system based on T-S fuzzy model has drawn much attention in literature recently. In this paper, a robust control method is proposed for affine nonlinear system with disturbance based on T-S fuzzy model. First, an optimization T-S fuzzy model is constructed focusing on optimizing the parameters of the weight functions by using differential evolution algorithm (DEA). Second, in order to reconstruct the disturbance, an interval observer is designed for the affine nonlinear system, and then a novelty disturbance reconstruction method based on the interval observer is developed. The disturbance reconstruction value can asymptotically approach the actual disturbance value, and furthermore, it decouples the control input. Third, by taking the optimization T-S fuzzy model as design model and by introducing the reconstruction of disturbance into controller, a feedback robust controller with disturbance compensation is designed to stabilize the affine nonlinear system. Finally, a simulation example of the crane model is given and some comparisons are provided to verify the effectiveness and show the advantages of the proposed method.

Weight-on-Bit is of vital importance to the drilling trajectory orientation in directional drilling. This paper concerns robust control of drilling trajectory with weight-on-bit uncertainty for the directional drilling process. The objective is to develop an equivalent-input-disturbance-based trajectory control scheme such that the drilling trajectory is precisely controlled by suppressing the fluctuations of weight-on-bit. The motion orientation of both the drill bit and a series of stabilizers is used to describe the evolution process of the drilling trajectory. A state-space model with weight-on-bit uncertainty is derived from the evolution equation through a variable transformation. An equivalent-input-disturbance-based trajectory control system is designed, and two control loops are to track and control the trajectory inclination and azimuth, respectively. Two internal models track the trajectory inclination and azimuth respectively to elevate the control accuracy in the trajectory system. Two observer models combined with two low-pass filters estimate the trajectory inclination and azimuth by measuring the bottom hole assembly’s inclination and azimuth. Some sufficient conditions are derived using linear-matrix-inequalities to obtain the control parameters by considering a reasonable fluctuation range of weight-on-bit. Finally, the control effects in the build-up and horizontal section of the drilling trajectory illustrate the proposed approach’s validity.

Uncertainty is a major concern in vehicle path tracking control design. The coefficients of the uncertainty bound are unknown. They are assumed to lie within prescribed fuzzy sets. First, based on the path tracking kinematic model, this paper innovatively formulates the vehicle path tracking task as a constraint-following problem. Second, we put forward a deterministic adaptive robust control law with a tunable parameter to ensure the uniform boundedness and ultimate uniform boundedness of the closed-loop system. Third, an optimal scheme for the tunable parameter is proposed based on the fuzzy uncertainty. The resulting optimal robust control (ORC) minimizes a comprehensive fuzzy performance index that involves the fuzzy system performance and the control cost. The results of the CarSim-Simulink co-simulation and the Hardware-in-loop (HIL) experiment together show that the proposed optimal robust control exhibits a superior path tracking performance.

This paper provides two bounded finite-time control strategies for the stabilization problem of Euler-Lagrange (EL) systems exposed to actuator failures. By the combination of sliding mode technology and adaptive method, two control architectures have been constructed such that the system states will be forced towards the origin within finite time. The first controller is applicable in the case that exact information of the external disturbance and actuator faults are available. However, it still remains challenging for designers to obtain this sort of information in engineering practice. On account for this, adaptive laws are applied in the second controller to obtain estimations about the unknown parameters, thus ensuring desirable fault-tolerance ability and robustness for the EL systems. By resorting to the properties of EL systems and hyperbolic tangent functions, outputs of these two controllers will be proven to be bounded. Simulation examples are presented to manifest the validity of the developed algorithms.

This paper concentrates on a simple and robust control method for the discrete time nonlinear systems to fulfill the requirement of predefined accuracy. A sliding mode control method is designed by introducing equivalent dynamic linearization technique according to the input/output (I/O) information merely. A square-root type error transformation method is presented for the tracking error to be restricted within a preassigned zone. The performance of presented control method is demonstrated through experiments on a nonlinear system. Experiment results show that the presented control method has a superior tracking accuracy compared with PID controller and model-free adaptive control (MFAC).

This paper focuses on modeling a non-fragile state estimator for a class of memristive cellular neural networks (MCNNs) with proportional delay. Due to the state transition characteristics of memristor, the parameters of MCNNs are state-dependent. A discontinuous robust control scheme is applied to address such parameters issue. Using this control scheme, we have derived sufficient conditions to ensure the existence of a non-fragile state estimator for the supposed system. Through the Lyapunov stability analysis and matrix-based inequality techniques, delay-dependent stability criteria are obtained in the form of linear matrix inequalities (LMIs), which shows the asymptotic stableness of the prescribed error system under the consideration of all possible gain variations. Besides, the control gain components are obtained by solving the resulting LMIs using some available MATLAB algorithms. Lastly, to facilitate the efficacy of the proposed estimator design, numerical simulations are examined.

The paper investigates a novel fractional-order Lyapunov-based robust controller based on a fuzzy neural network (FNN) compensator for exoskeleton robotic systems. First, a finite-time fractional-order nonsingular fast terminal sliding mode control (FONFTSMC) method is designed. Second, a FNN algorithm is constructed to approximate the model uncertainty and external disturbances. Then, finite-time stability of the closed-loop control system is proved using Lyapunov stability theorem and adaptive law is derived through it. The proposed fuzzy neural network-based FONFTSMC (FNN-FONFTSMC) guarantees finite-time convergence and robustness against uncertainties for the exoskeleton robots trajectory tracking. Finally, to illustrate the effectiveness of the proposed control strategy, an upper-limb exoskeleton robot is provided as a case study in rehabilitation. The simulation results confirm the superiority of the proposed control method.

To address the difficulty of optimizing turbidity process with large inertia and long time delay, a twice-optimal control and construction pruning (TOCCP) strategy is proposed, which can be used to improve the fast stability and strong robustness of industrial process. The new approach owns the advantages of twice optimal control (TOC) and construction pruning (CP) method. The TOC constructs an infinite-dimensional state observer of the system, which can eliminate the influence of time delay on the system. The CP is adopted to improve the mid-band damping of the open-loop frequency characteristics to improve the robustness of the system. Moreover, an exhaustive algorithm is designed to find the optimal time scale, the most important parameter for adjusting the system response speed. In addition, the influences of different parameter changes on the robustness of the system are analyzed, and a practical parameter tuning formula is provided. Simulation-based comparisons of TOCCP and the other two algorithms were made. The results show that the system optimized by TOCCP has strong robustness, especially in disturbances rejection and set-point tracking. Moreover, TOCCP is practical and easily implemented to set parameters, providing guidelines for industrial application of large inertia and time-delay systems.

This letter quantifies the effect of random model uncertainty on finite horizon linear time-varying (LTV) systems. Mean and standard deviation field are approximated with high accuracy and efficiency by a Hilbert space technique called polynomial chaos expansion (PCE). The deterministic expansion coefficients of the generalized Fourier series are determined via orthogonal projection, also known as Galerkin projection. We propose the projection of uncertain systems in linear fractional representation (LFR), which can have computational benefits. The technique is benchmarked on a two-link robotic manipulator.

This study proposes a new robust control design framework for uncertain mechanical systems, which may be fullyactuated or underactuated. The uncertainty is (possibly fast) time-varying, lies in prescribed fuzzy sets (hence fuzzy mechanical systems), and may be unbounded. The control goal is formulated as servo constraints (hence constraint-following control), which may be holonomic or nonholonomic. We introduce the possibility theory into the Lyapunov stability analysis (LSA), proposing possibilitybased Lyapunov stability analysis (PBLSA), which allows a maximum failure possibility (generally small) prescribed by designers. It can be viewed as a generalization of the conventional LSA, and the resultant performance is interpreted in the context of possibility. By the PBLSA, a class of robust constraint-following controls that is not IF-THEN heuristic rules-based is proposed, which renders approximate constraint-following for the system performance with a prescribed maximal failure possibility. Optimal design of a control parameter considering both system performance and control cost is investigated. The benefits of the proposed design framework are discussed and simulations on two applications are given for demonstrations.

This article investigates the adaptive fuzzy control problem for a class of stochastic nonlinear systems with the risk-sensitive performance index. The desired cost level of the risk-sensitive index, which could be arbitrarily small, is guaranteed by the solution of a specified Hamilton–Jacobi–Bellman (HJB) equation. By considering the unknown uncertainties of the stochastic nonlinear systems, a novel adaptive fuzzy risk-sensitive control method is proposed, which guarantees the input-to-state stability of the system. In addition, the proposed control strategy also reduces the conservatism of the existing adaptive robust control method. Finally, the effectiveness of the proposed approach is verified by a simulation example of one-link manipulator.

This paper presents modeling and designing of robust multi-loop controllers for the terminal voltage and stator frequency regulations of three-phase self-excited induction generator (SEIG) driven by a prime mover. The lack of the internal functionality of the SEIG system often represents a major challenge for most researchers. This is due to the several reasons, such as the absence of perfect mathematical models describing the actual behavior of SEIG, existence of some non-linear modes to be neglected during the linearization step and presence of unavoidable model uncertainties, etc. For this purpose, a small-signal-based method is proposed in order to overcome these drawbacks by designing the frequency and voltage linear models of the SEIG around its operating point. These models are carried out through the preprocessed experimental data recorded previously from actual SEIG system. Each appropriate model is independently computed using the identification toolbox of Matlab® software. The main advantage of the small-signal-based modeling is its simplicity without any knowledge of the equivalent circuit parameters of the SEIG. Accordingly, three robust voltage H ∞ controllers are synthesized from solving a weighted-mixed sensitivity problem using both classical and structured H ∞ synthesis. Each robust voltage controller and a robust frequency controller are operated with together as multi-loop controller. The novelty and contribution of the proposed method involve adjusting the parameters of the robust multi-loop controllers that ensure a good trade-off between performances and robustness using the small-signal model of the voltage and frequency in correspondence with the preselected operating point, recorded and pre-processed input–output data of the SEIG. The advantage of the multi-loop controllers is ensured not only for the nominal plant but also for all neighboring uncertainty models. The real-time implementation of controllers is performed using STM32 microcontroller unit. Simulation and experimental tests show the validity of the proposed linear small-signal models as well as the effectiveness of each proposed robust multi-loop controllers in terms of Nominal Performance (NP) margin, Robust Stability (RS) margin and the trade-off between them. However, when the operating point of the SEIG system changes significantly according to its nominal state, the guarantee of NP-RS trade-off becomes insecure.

For constrained linear parameter varying systems subject to bounded disturbances and noises, this article investigates an off-line output feedback robust model predictive control approach. The sub-observer gains with robust positively invariant sets, and sub-controller gains with robust control invariant sets are simultaneously off-line optimized and stored in a look-up table. According to real-time estimation error bounds and estimated states, the time-varying sub-observer gains and sub-controller gains are on-line searched. The proposed off-line output feedback robust model predictive control approach with the guarantee of nested robust positively invariant sets and robust control invariant sets in theory reduces the on-line computational burden.

This paper addresses the dynamic positioning problem for Liquefied Natural Gas (LNG) carrier with unknown shielding effect via a sea state detector and robust control design. First, to deal with the shielding effect existing between LNG facility and LNG carrier, sea state detector is developed to estimate the variation of wave force on the LNG carrier. In addition, the wind drag coefficients can be obtained adaptively to achieve feedforward control. Then, to guarantee a safe operation, a robust constrained control with prescribed performance is proposed considering actuator dynamic. Further, once a large wave force is identified in the detector, Neural Network compensator will be activated in the controller. Lyapunov analysis is conducted to ensure the boundedness of all the closed-loop states. Finally, the feasibility of the theoretical results is demonstrated by simulation studies.

This paper addresses the robust stability and stabilization problems for fractional-order systems with polytopic uncertainties. By introducing homogeneous polynomial parameter-dependent matrix form...

This paper addresses a novel robust gain-scheduling(GS) state-feedback (SF) H ∞ (induced L 2 ) control method for uncertain continuous-time(CT) systems having actuators with hard rate and magnitude bounds. The proposed method relies on acceleration form representation of the uncertain CT system. The technique enables the user to represent the control signal and its slew rate as auxiliary outputs along with the main controlled output. Two different norms, namely the induced L ∞ and L 2 are used to control the system effectively. While the L ∞ gain from the exogenous disturbance inputs to the control signal related outputs is used to deal with actuator saturation problem, L 2 gain from the disturbance inputs to the performance outputs is utilised in attenuation of the effects of the disturbances. To achieve these goals with minimal conservatism, we develop new forms of dilated Matrix Inequality (MI) conditions for peak-to-peak gain and L 2 gain with no additional conservatism. Then, we propose a novel robust GS control methodology to deal with the problem via dilated MIs and a modified full block S-procedure method (MFBSPM). The utilisation of MFBSPM ensures that the robust control design method of this note applies to any uncertain system having rational parameter dependence. Finally, the efficiency of the presented method is portrayed through extensive simulations of the responses of a marine vessel to wave excitations in which the vessel model is assumed to have magnitude and rate limited active fin stabiliser.

This article addresses the problems of the adaptive robust control design and the parameters optimization for a class of underactuated mechanical systems. We describe the uncertainty by using the fuzzy set theory to form the fuzzy dynamical systems. A novel adaptive robust control with two tunable gain parameters is designed based on the formed system, and the nonholonomic servo constraints are also considered in the control design. By employing the principle of the Nash game theory, we establish an optimization method for the two gain parameters, and the Nash equilibrium orients the optimal values of the two gain parameters. Finally, the effectiveness of the designed optimal control is shown by a numerical simulation.

This article focuses on observer-based state feedback H ∞ control for a jacket structure against DoS attacks and external wave loads. First, a networked model of the structure is formulated as a switched delay system, in which DoS attacks and network-induced delays are considered simultaneously. A matching switched observer is developed for estimating states of the networked jacket structure system. Then, some new sufficient conditions are provided for the observer-based networked H ∞ controller for the resultant switched system. Finally, it is shown from several case studies that the provided mechanism can maintain desired performance of the jacket structure against attacks and wave loads. In addition, the developed control schemes can save the control cost significantly.

Purpose The flexible mode transitions, multiple power sources and system uncertainty lead to challenges for mode transition control of four-wheel-drive hybrid powertrain. Therefore, the purpose of this paper is to improve dynamic performance and fuel economy in mode transition process for four-wheel-drive hybrid electric vehicles (HEVs), overcoming the influence of system uncertainty. Design/methodology/approach First, operation modes and transitions are analyzed and then dynamic models during mode transition process are established. Second, a robust mode transition controller based on radial basis function neural network (RBFNN) is proposed. RBFNN is designed as an uncertainty estimator to approximate lumped model uncertainty due to modeling error. Based on this estimator, a sliding mode controller (SMC) is proposed in clutch slipping phase to achieve clutch speed synchronization, despite disturbance of engine torque error, engine resistant torque and clutch torque. Finally, simulations are carried out on MATLAB/Cruise co-platform. Findings Compared with routine control and SMC, the proposed robust controller can achieve better performance in clutch slipping time, engine torque error, vehicle jerk and slipping work either in nominal system or perturbed system. Originality/value The mode transition control of four-wheel-drive HEVs is investigated, and a robust controller based on RBFNN estimation is proposed. Compared results show that the proposed controller can improve dynamic performance and fuel economy effectively in spite of the existence of uncertainty.

This work investigates the tracking control problem for underactuated mechanical systems. To this end, we develop an extension of the dynamic tube Model Predictive Control (MPC) approach by combining an MPC design, an ancillary energy shaping controller constructed with the Interconnection and Damping Assignment Passivity-Based Control methodology, and an analytical expression of the dynamic tube. In addition, we extend the proposed approach by including the adaptive compensation of a class of unknown disturbances. The stability analysis is presented by employing a Lyapunov approach. The effectiveness of the proposed controller is demonstrated with simulations on two underactuated systems: a two-mass-spring-damper system with uncertain damping and either linear or nonlinear spring; an inertia-wheel-pendulum with unmodeled disturbances.

This paper is devoted to the numerical analysis of non-smooth ensemble optimal control problems governed by the Liouville (continuity) equation that have been originally proposed by R.W. Brockett with the purpose of determining an efficient and robust control strategy for dynamical systems. A numerical methodology for solving these problems is presented that is based on a non-smooth Lagrange optimization framework where the optimal controls are characterized as solutions to the related optimality systems. For this purpose, approximation and solution schemes are developed and analysed. Specifically, for the approximation of the Liouville model and its optimization adjoint, a combination of a Kurganov–Tadmor method, a Runge–Kutta scheme, and a Strang splitting method are discussed. The resulting optimality system is solved by a projected semi-smooth Krylov–Newton method. Results of numerical experiments are presented that successfully validate the proposed framework.

To enhance the lower limbs’ rehabilitation training of stroke patients, in this article, a deterministic adaptive robust control with control gain parameters optimized by a novel cooperative game theory is proposed for the two-degree-of-freedom (DOF) lower limb exoskeleton robot system (LLERs) with uncertainties and external disturbances. On the one hand, the deterministic adaptive robust control put forward will guarantee the uniform boundedness and uniform ultimate boundedness of gait constraint deviation and parameter estimation error. On the other hand, for uncertainties and external disturbance (possibly fast time-varying), which will arise in the two-DOF LLERs inevitably, we suppose that these uncertainties and disturbances are bounded, and their bounds are lying within the fuzzy sets, which can be characterized by membership functions; with such descriptions and control performance analysis, a novel cooperative game with two players participated will be formulated to seek the Pareto optimal solutions for the control gains of deterministic adaptive robust control proposed, and furthermore, the existence of optimal solutions is also shown by invoking a numerical technique. Eventually, the simulation results presented have verified the effectiveness of our proposed methodology on improving rehabilitation training of lower limbs.

In this paper, we consider robust output tracking for an Euler–Bernoulli beam equation under the guidance of the internal model principle, where the disturbances in all possible channels are considered. Three typical cases are investigated in terms of different regulated outputs. The first case is based on boundary displacement output, for which only asymptotic convergence can be achieved due to the compactness of the observation operator. The second case considers two outputs of both boundary displacement and velocity. Since the control is one-dimensional, we can only arbitrarily regulate the boundary displacement and at the same time, the velocity is regulated to track the derivative of the reference. This is not the standard form investigated in the literature for robust error feedback control of abstract infinite-dimensional systems. The last case represents an extreme case that the system is non-well posed. In all the above cases, this paper demonstrates the same technique of an observer-based approach to robust control design. In the latter two cases, we can achieve exponential convergence and the closed loop is also shown to be robust to system uncertainties. Numerical simulations are carried out in all cases to illustrate the effectiveness of the proposed controls.

An adaptive robust control combined with a multi-objective parameter optimization method for a parallel robot under unknown uncertainty is proposed. In the active joint space, the model of the parallel robot can be obtained by combining the closed-chain constraint force and the open-chain system’s dynamic equation. Based on the Udwadia–Kalaba theory, the closed-chain constraint force imposed by the end effector can be calculated if no uncertainty. If there is uncertainty, we propose an adaptive robust control, based on a set of feasible design parameters, which guarantees deterministic performances, including uniform boundedness and uniform ultimate boundedness. To seek the optimal choice of the design parameters, among the feasible pool. We examine the system performance, which includes the transient performance, the steady state performance, and the control cost. By a fuzzy-theoretic D-operation, a performance index is formulated. The problem of choosing the optimal control parameters is equivalent to the problem of finding the minimum value of the performance index. An illustrative example demonstrates the superiority of the adaptive robust control. Mass uncertainty and external disturbance torque are introduced to test the effectiveness of the proposed control strategy.

The introduction of advanced control algorithms may improve considerably the efficiency of wind turbine systems. This work proposes a high order sliding mode (HOSM) control scheme based on the super twisting algorithm for regulating the wind turbine speed in order to obtain the maximum power from the wind. A robust aerodynamic torque observer, also based on the super twisting algorithm, is included in the control scheme in order to avoid the use of wind speed sensors. The presented robust control scheme ensures good performance under system uncertainties avoiding the chattering problem, which may appear in traditional sliding mode control schemes. The stability analysis of the proposed HOSM observer is provided by means of the Lyapunov stability theory. Experimental results show that the proposed control scheme, based on HOSM controller and observer, provides good performance and that this scheme is robust with respect to system uncertainties and external disturbances.

This dissertation focuses on developing tools to study the robust forward invariance of sets for systems with unknown disturbances and hybrid dynamics. In particular, the notions of robust forward invariance properties are proposed for hybrid dynamical systems modeled by differential and difference inclusions with state-depending conditions enabling flows and jumps. A set is said to enjoy robust forward invariance for a system when its solutions start within the set always stay in the set regardless of disturbances. These proposed notions allow for a diverse type of solutions (with and without disturbances), including solutions that have persistent flow and jumps, that are Zeno, and that stop to exist after finite amount of (hybrid) time. Moreover, sufficient conditions for sets to enjoy such properties are presented. The proposed conditions involve the system data and the set to be rendered robust forward invariant.Furthermore, such conditions are exploited to derive conditions guaranteeing that sublevel sets of Lyapunov-like functions are robust forward invariant and, in turn, inspired a constructive way to design invariance-based control algorithms for a class of hybrid systems with control inputs and disturbances. More precisely, when a hybrid system have a Lyapunov-like function V satisfying a set of specific conditions, existence of feedback laws that render sublevel sets of V robustly forward invariant for the closed-loop hybrid systems are presented. In addition, two selection theorems are proposed to design invariance-based controllers for the class of hybrid systems considered.Applications and academic examples are given to illustrate the results. In particular, the presented forward invariance analysis and design tools are applied to the design and validate of hybrid controllers for power conversion systems, specifically, a single-phase DC/AC inverter and a DC/DC boost converter. Moreover, results are applied to the estimation of weakly forward invariant sets, which is an invariance property of interest when employing invariance principles to study convergence properties of solutions. Finally, the developed algorithms are tested on the control of a constrained bouncing ball system.

We formulate control goals of nonlinear underactuated active suspension systems (ASSs) with uncertainties as a class of constraints, which may be holonomic or nonholonomic. The uncertainties in the sprung mass, the external disturbance, the control input, the spring force and damping force are (possibly fast) time-varying, unknown but bounded. However, the bounds are unknown. The task is to design control which drives systems to approximately obey the constraints (hence constraint-following control) under the uncertainties effect. Since these uncertainties do not all fall within the range space of the input matrix, we creatively decompose uncertainties into matched portion and mismatched portion that may be large. Consequently, this decomposition is able to ensure the mismatched portions of uncertainties to “disappear,” which indicates that the control design can be based on only matched portions. To emulate a constant design parameter vector that may be relevant to bounds of the uncertainties, we construct a continuous adaptive law, which call it smooth-zone adaptive law. This sets a base for an adaptive robust control design. We prove the uniform boundedness and the uniform ultimate boundedness of ASSs under the proposed control by the Lyapunov approach. Furthermore, experimental and numerical simulation results on a 2-DOF nonlinear ASS with uncertainties are presented for demonstrations of the proposed control.