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The liquid cooling system (LCS) of the proton exchange membrane (PEM) fuel cell suffers from large time delay, coupling, uncertainties, and various disturbances, making it susceptible to temperature regulation overshoot and control oscillation. This article focuses on a composite control scheme for the LCS that has effectively addressed the aforementioned issues. We first propose a two-layer control approach for the pump to minimize coupling, and an average delay model (ADM) for radiator whose parameter uncertainties are removed by equilibrium optimizer (EO). To overcome disturbances, an adaptive sliding mode control (ASMC) based on extended state observer (ESO) is presented, and its finite-time convergence is demonstrated. Additionally, the indirect regulation for the stack temperature is designed to considerably reduce the time delay in the fan control loop. Co-simulation results indicate that the proposed ASMC significantly suppresses the chattering phenomenon compared with regular sliding mode control (SMC). In contrast to incremental fuzzy control, the proposed scheme possesses superiorities in response speed, tracking accuracy, anti-disturbance, as well as suppression of overshoot and oscillation. • A two-layer control approach is developed for the coolant pump. • An average delay model is presented for the radiator. • An adaptive sliding mode control is proposed for the cooling fan. • An indirect regulation method significantly reduces the time delay in the fan control loop. [ABSTRACT FROM AUTHOR]

We consider a hypersonic vehicle optimal flight control problem. The problem is modeled as an optimal control problem of switched systems (OCPSS), which can become a parameter optimization problem (POP). Following that, to achieve the globally optimal solution of the POP, an improved continuous filled function (CFF) algorithm including one adjusting parameter is proposed based on a penalty function, in which the CFF is differentiable, excludes logarithmic terms or exponential terms, and does not require to minimize the cost function. Numerical results show that the proposed algorithm is effective. [ABSTRACT FROM AUTHOR]

The work has devised a novel fixed-time control scheme for a class of nonlinear systems with output constraints. Two distinctive features are incorporated into the gained results. One is that the upper bound of settling time for the closed-loop system can be estimated without dependence on system initial states, and hence, can be acquired arbitrarily small through tuning control design parameters. The other is that the output constraint can be handled by means of a barrier Lyapunov function (BLF). Via the BLF and the backstepping-like technique, a fixed-time controller, which can cope with a type of nonlinear systems concurrently with and without output constraints, is systematically built. The rigorous analysis on the strength of the Lyapunov theory is given to show that the investigated system under the proposed controller is fixed-time stable, and the violation of a preset output constraint is averted. The case studies of a series elastic actuator system are offered to substantiate the derived theoretical results. [ABSTRACT FROM AUTHOR]

A new super-twisting-like fractional (STLF) controller is proposed in this article to improve the control performance for surface-mounted permanent magnet synchronous motor (SPMSM) system. Compared with the conventional super-twisting sliding mode (STSM) algorithm, the most distinctive characteristic of the proposed strategy is to replace the discontinuous switching function hidden under the integration with a nonsmooth term, which can significantly optimize the performance of SPMSM system. Meanwhile, the introduction of nonsmooth term can provide stronger anti-disturbance capability than the widely used smooth controller. In addition, the desired control performance can be achieved by adjusting the parameters of the proposed STLF controller according to the specific situations. Comparative experiments among the proposed STLF, conventional STSM and proportional integral controllers are carried out to demonstrate the feasibility and effectiveness of the proposed STLF technique. [ABSTRACT FROM AUTHOR]

This paper aims to improve the performance of the permanent magnet synchronous motor (PMSM) speed regulation system by combining a novel disturbance observer (DOB) with the super-twisting sliding mode (STSM) technique. First, a STSM controller is constructed to eliminate the adverse effects of the lumped disturbance in the PMSM speed regulation system. A novel DOB is introduced to estimate and compensate the lumped unknown disturbance, which constitutes a composite controller with a feedforward compensation term and a state-feedback control. As a result, the gain of the composite sliding mode controller can be significantly reduced, which will improve the performance of the closed-loop PMSM speed regulation system. The validity and robustness of the proposed composite control scheme are fully verified by simulation and experimental results. [ABSTRACT FROM AUTHOR]

The second-order sliding mode (SOSM) controller design problem for a class of sliding mode dynamics subject to an upper-triangular structure has been discussed in this paper. The proposed SOSM controller design involves two steps. First, a Lyapunov-based SOSM controller is developed by using the adding a power integrator technique to locally finite-time stabilize the sliding variables. Second, by combining the local SOSM controller with a saturation function, a novel SOSM controller with a saturation level is constructed. The feature of the new SOSM controller lies in that the saturation level can be tuned not only to guarantee the global convergence but also to improve the dynamic performance. Lyapunov analysis has been utilized to test the finite-time stability of the closed-loop sliding mode dynamics. The proposed method is eventually demonstrated by simulation results. [ABSTRACT FROM AUTHOR]

A new approach to the design of nonlinear disturbance observers (DOBs) for a class of nonlinear systems described by input–output differential equations is presented in this paper. In contrast with established forms of nonlinear DOBs, the most important feature of this new type of DOB is that only measurement of the output variable is required, rather than the state variables. An inverse simulation model is first constructed based on knowledge of the structure and parameters of a conventional model of the system. The disturbance can then be estimated by comparing the output of the inverse model and the input of the original nonlinear system. Mathematical analysis demonstrates the convergence of this new form of nonlinear DOB. The approach has been applied to disturbance estimation for a linear system and a new form of linear DOB has been developed. The differences between the proposed linear DOB and the conventional form of frequency-domain DOB are discussed through a numerical example. Finally, the nonlinear DOB design method is illustrated through an application involving a simulation of a jacketed continuous stirred tank reactor system. [ABSTRACT FROM AUTHOR]

Summary: Note that the amplitude of chattering existing in the sliding mode control method is proportional to the magnitude of the control gain. Therefore, the key issue to diminish the chattering is to decrease the value of sliding mode controller's gain to an acceptable minimal level defined by the so‐called reaching condition for the sliding mode's existence. For this reason, the nonsingular terminal sliding mode (NTSM) control method and the adaptive technique have been considered in this paper to develop a novel adaptive NTSM control method, which can be used to search the minimal value of the control gain automatically in the presence of the external disturbances. Meanwhile, the average value of a high‐frequency switching signal in the adaptive law can be provided by Arie Levant's differentiator rather than a low‐pass filter. The rigorous mathematical proof verifies that the system states can converge to the origin within a finite time under the proposed adaptive NTSM controller. Both the academic example and the practical application to an active front steering system are illustrated to show that the presented adaptive NTSM controller has better control performance than the conventional sliding mode controller. [ABSTRACT FROM AUTHOR]

In this paper, a novel discontinuous second-order sliding mode control approach has been developed to handle sliding mode dynamics with a nonvanishing mismatched disturbance by using Lyapunov theory and a finite-time disturbance observer. Firstly, the finite-time disturbance observer is designed to estimate the nonvanishing mismatched disturbance. Secondly, a virtual controller has been constructed based on the estimated value such that the sliding variable can be stabilized to zero in a finite time. Then, the real discontinuous controller is designed to guarantee that the virtual controller can be well tracked in a finite time. Lyapunov analysis also verifies the finite-time stability of the closed-loop sliding mode control system. The developed discontinuous second-order sliding mode control method possesses two appealing features including strong robustness with respect to the matched and mismatched nonvanishing disturbances, and relaxation on the constant upper bound of uncertainties widely used in a conventional second-order sliding mode. Finally, an academic example is illustrated to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Summary: In this paper, the global stabilization problem of a class of cascaded systems with upper‐triangular structures is considered. On the basis of the forwarding technique, a series of virtual controllers are recursively constructed for the driving subsystem. According to the mild assumption imposed on the driven subsystem, a partial‐state feedback controller is obtained for the entire cascaded nonlinear system by developing a delicate design fashion. It is shown that the obtained state feedback controller will render the entire cascaded nonlinear system globally asymptotically stable. Numerical examples are conducted to validate the proposed control scheme. [ABSTRACT FROM AUTHOR]

• In this work, a new general control strategy for the asymptotic tracking problem of high-order uncertain nonlinear systems is proposed so that the convergence of tracking error is not affected by the initial value and the Lyapunov function. • The proposed approach ensures that all signals in the whole closed-loop system are bounded, the adaptive compensation is performed for each step, which avoids overestimating parameters and overcomes the inherent nonlinear obstacles of the system. • The flexibility of the control design is increased by introducing the ingenious coordinate transformations and algebraic transformations. The adaptive technology and the technique of adding a power integrator are successfully verified to update and extended to an universal adaptive asymptotic tracking control, which also provides guidance for constructing general adaptive controllers and verifying asymptotic convergence. This paper investigates the asymptotic tracking control of uncertain high-order nonlinear systems with time-varying desired signals.A new universal adaptive tracking control strategy is introduced, which combines the technique of adding a power integrator, adaptive technology and a series of algebraic transformations to achieve asymptotic tracking performance successfully. Compared to the traditional tracking control strategies, the proposed control scheme guarantees that the output tracking error of the high-order nonlinear system asymptotically converges to zero and is no longer limited to a time-varying compact domain. While ensuring that all signals in the closed-loop system are bounded, the controller also has sufficient ability to compensate for the unknown quantity, virtual control coefficient and parameter uncertainty of the system. Finally, the feasibility and effectiveness of the theoretical results are verified by a simulation example. [ABSTRACT FROM AUTHOR]

The dynamics of the second-order sliding mode (SOSM) can be obtained by directly taking the second derivative on the sliding variable when it has a relative degree of 2 with respect to the control input. However, there will always appear some state-dependent certain or uncertain terms in the first derivative of the sliding variable, and the derivative directly imposed on these terms could enlarge the uncertainties in the control channel. One method to reduce the uncertainties in the control channel is to hold this information in the dynamics of the first derivative of the sliding variable, while the original SOSM dynamics could be transformed to be a SOSM system with a mismatched unbounded perturbation. This paper focuses on the controller design problem for SOSM dynamics subject to mismatched unbounded perturbation. By using Lyapunov analysis, a novel backstepping-like design methodology will be proposed. The rigorous mathematical proof will show that under the derived SOSM controller, the closed-loop sliding mode dynamics is globally finite-time stable. Meanwhile, the frequently used constant upper bound assumptions for the standard SOSM system can also be extended to the state-dependent hypotheses in this paper. An academic example is illustrated to verify the effectiveness of the proposed method. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This study provides a new parameterisation for a special class of nested‐saturation controllers, in which some multiplying coefficients appear before saturation functions. In an existing saturation scheme for the chain of integrators, the saturation levels and the multiplying coefficients are separately assigned in two stages, namely determined in the reduction analysis of saturated terms and the stability analysis of a reduced system. In the new parameterisation, it is in the saturation reduction analysis that the mentioned parameters are already determined. Such a convenient parameterisation is also applied to the uncertain multiple integrators and some mechanical systems. [ABSTRACT FROM AUTHOR]

The direct yaw-moment control system can significantly enhance vehicle stability in critical situations. In this paper, the direct yaw-moment control strategies are proposed for in-wheel electric vehicles by using sliding mode (SM) and nonlinear disturbance observer (NDOB) techniques. The ideal sideslip angle at the center of gravity and the yaw rate are first calculated based on a linear two degree of freedom vehicle model. Then, the actual sideslip angle is identified and estimated by constructing a state observer. On this basis, a traditional discontinuous SM direct yaw-moment controller is designed to guarantee that the sideslip angle and the yaw rate will approach the ideal ones as closely as possible. To tackle the chattering problem existing in the traditional SM controller, a second-order sliding mode (SOSM) controller is further designed by taking the derivative of the controller as the new control, which implies that the actual control can be an integration of the SOSM controller. Finally, to avoid the large gains in the derived controllers, by combining the NDOB with the derived controllers, the composite control schemes are also proposed. In comparison with the discontinuous first-order SM controller, the proposed SOSM controller is shown to be more effective. [ABSTRACT FROM AUTHOR]

This article aims at solving the straight-line tracking control problem of agricultural tractors in the presence of negative influences induced by unknown disturbances. Firstly, the path tracking dynamics model with unknown disturbance is established, and then it is further converted into a third-order sliding mode (TOSM) dynamics that facilitates control design. On this basis, a straight-line tracking control strategy for agricultural tractors is proposed by using TOSM. It is demonstrated by strict Lyapunov analysis that the lateral error and heading deviation are stabilized to the origin in a finite time. Finally, the comparative simulation results show that the proposed path-tracking algorithm can achieve the control objective of straight-line tracking of agricultural tractors. [Display omitted] • The third-order sliding mode controller is proposed to handle the problem of agricultural tractor navigation. • The proposed control scheme can ensure that the tracking errors converge to zero in a finite time. • The closed-loop sliding mode dynamics can be driven to the origin in finite time. [ABSTRACT FROM AUTHOR]

This communique proposes a novel second-order sliding mode (SOSM) control method to handle sliding mode dynamics with mismatched term, so as to reduce the terms in the control channel. Meanwhile, it is shown that the proposed control approach can be used to design SOSM controllers under disturbances bounded by positive functions rather than conventional constant upper bounds. The finite-time stability of the sliding variables has been shown by using finite-time Lyapunov theory. The validity of the proposed approach is verified by controlling a Buck converter. [ABSTRACT FROM AUTHOR]

• This is the first work to design a finite-time controller with a new adaptive mechanism by constructing a novel preset region. The dynamical change of the control gain is dependent on the case whether the state trajectories enter or leave a pre-designed domain or not. • The novel adaptive control strategy is presented to avoid the overestimation of the developed adaptive gain based on the adding a power integrator technique and the Lyapunov method. Meanwhile, the novel practical adaptive finite-time controller could improve the dynamic performance of systems and reduce the potential chattering influence. • In practical applications, the system states are usually finite-time stabilized to a neighborhood of the origin, rather than the origin. From this point of view, the investigation of practical finite-time stability (PFTS) for nonlinear systems is more meaningful. In this paper, the PFTS of second-order nonlinear systems has been verified under the developed adaptive finite-time controller. This paper considers the practical adaptive finite-time stabilization problem for a class of second-order systems. Based on the adding a power integrator technique and the adaptive method, a novel adaptive control strategy is presented to assure the trajectories of the closed-loop systems converge to a small neighborhood of the origin in a finite time. Under the adaptive control strategy, the dynamical change of control gain is dependent on the cases whether the state trajectories enter or leave a pre-designed domain or not. In addition, the practical finite-time stability (PFTS) of systems is testified via utilizing the Lyapunov method and adaptive mechanism. Last of all, the validity of the obtained practical adaptive finite-time algorithm is verified via simulation results. [ABSTRACT FROM AUTHOR]

This paper considers the nonsingular terminal sliding mode (TSM) controller design for a nonlinear second-order system subject to input saturation. A new nonsingular TSM manifold is constructed by integrating the conventional nonsingular TSM manifold with a saturation function. When the bound of the uncertainty is known, based on the designed TSM manifold, a saturated controller can be designed directly for the nonlinear system. When the bound of the uncertainty is unknown, a disturbance observer is first employed to estimate the uncertainty, followed by constructing a composite controller consisting of a bounded feedback controller and a forward compensator. Theoretical analysis shows that under the proposed two control methods, the states of the closed-loop system will both converge to zero in finite time. Simulation results demonstrate the effectiveness of the proposed methods. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

High-order sliding mode (HOSM) control is known to provide for finite-time-exact output regulation of uncertain systems with known relative degrees. Yet the corresponding universal HOSM controllers are typically constructed by special recursive procedures and have complicated form. We propose two new families of homogeneous HOSM controllers of a very simple form. Lyapunov functions are provided for a significant part of the first-family controllers. The second family consists of quasi-continuous controllers, which can be done arbitrarily smooth everywhere outside of the HOSM manifold. A regularization procedure ensures high-accuracy output regulation by means of control with required smoothness level. Output-feedback controllers are constructed. Controllers of the orders 3–5 are demonstrated. [ABSTRACT FROM AUTHOR]

This paper considers the problem of global stabilisation of a class of generalised cascaded systems. By using the extended adding a power integrator technique, a global controller is first constructed for the driving subsystem. Then based on the homogeneous properties and polynomial assumption, it is shown that the stabilisation of the driving subsystem implies the stabilisation of the overall cascaded system. Meanwhile, by properly choosing some control parameters, the global finite-time stability of the closed-loop cascaded system is also established. The proposed control method has several new features. First, the nonlinear cascaded systems considered in the paper are more general than the conventional ones, since the powers in the nominal part of the driving subsystem are not required to be restricted to ratios of positive odd numbers. Second, the proposed method has some flexible parameters which provide the possibility for designing continuously differentiable controllers for cascaded systems, while the existing designed controllers for such kind of cascaded systems are only continuous. Third, the homogenous and polynomial conditions adopted for the driven subsystem are easier to verify when compared with the matching conditions that are widely used previously. Furthermore, the efficiency of the proposed control method is validated by its application to finite-time tracking control of non-holonomic wheeled mobile robot. [ABSTRACT FROM AUTHOR]

This paper considers the second-order sliding (2-sliding) mode control design problem for nonlinear systems with uncertainties bounded by positive functions. Two different 2-sliding mode control algorithms are proposed, including a discontinuous one and a quasi-continuous one. The discontinuous algorithm is built based upon the Lyapunov method, and the global finite-time Lyapunov stability rather than the global finite-time convergence is established for the resulting closed-loop system by using the modified adding a power integrator technique. On this basis, a quasi-continuous 2-sliding mode algorithm is further developed, and the chattering problem can be considerably reduced. Simulation results show that the control strategies proposed in this paper are effective. [ABSTRACT FROM PUBLISHER]

There are a variety of disturbances wide existing in the agricultural devices, including uncertain parameters, input voltage variations and load changes and these perturbations heavily affect the output voltage of the Buck converter. The traditional proportional integral (PI) control methods are difficult to obtain satisfactory performance. To solve this problem, many nonlinear theories have been applied to the Buck converter for obtaining better control performance. However, the implementation of these nonlinear controllers, such as adaptive controller and fuzzy-neural controller, generally requires complex hardware circuit or advanced processor, which increases the cost of the production and reduces the reliability of the control circuit. In this paper, based on the disturbance observation theory, a new control method for disturbance attenuation is proposed. First of all, the conventional PI controller is replaced with the variable-parameter PI (VAPI) controller, which not only possesses the easy-implementation characteristic the conventional PI holds, but also guarantees that the closed loop system will have a better performance in different control stages by online tuning the PI parameters. Then, a linear disturbance observer (DOB) is constructed to estimate the exact value of the disturbance which is caused by input voltage variations and load changes. The disturbance is estimated through the information of output voltage and the structure of control system, and the estimated value is used to compensate the disturbance in forward channel, which will significantly improve the convergence and disturbance rejection property of the closed loop system. With the above improvements, a new composite controller can thus be obtained. The composite controller in the paper is implemented by using a semi-physical experimental platform. The platform is mainly based on a data acquisition card and a buck circuit. When the system of the Buck converter is running, the output voltage can be collected by the data acquisition card. By calculating these voltage data, the control output signal can be obtained directly. Later, the data acquisition card will transmit the obtained control signal to the buck converter circuit. The advantages of this semi-physical experimental platform are making the implementation of the algorithm more flexibly and the modification of controller parameters more conveniently. Based on the experiment platform, the implementation of the composite controller can be summarized as three steps. Firstly, the continuous composite controller is constructed in frequency domain. Secondly, the continuous composite control strategy is discretized so that the data can be processed by computer. Finally, the discrete controller is implemented directly by using the LabVIEW program. Experimental results obtained from the semi-physical experiment platform show that after replacing PI controller with the composite controller, when the load varies, the recovery time of the Buck converter can be shortened by 71.4% and the output voltage error can be reduced by 20.8%. When the input voltage varies, the recovery time can be shortened by 58.3% and the output voltage error can be reduced by 30.0%. According to these comparative results, it is obvious that the proposed new composite controller can effectively improve the convergence and anti-disturbance performance of the Buck converter. Meanwhile, considering the property of easy-implementation, the composite control method has potential applications in engineering area. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of robust stabilisation of multiple integrators systems subject to input saturation and disturbance from the viewpoint of state feedback and output feedback. First of all, without considering the disturbance, a backstepping-like method in conjunction with a series of saturation functions with different saturation levels is employed to design a nested-saturation based state-feedback controller with pre-chosen parameters. On this basis, taking the disturbance into account, a sliding mode disturbance observer (DOB) is adopted to estimate the states and the disturbance. Then, by combining the above state-feedback controller and the estimated states together, a composite controller with disturbance compensation is developed. With the removal of the non-increasing restriction on the saturation levels, the controller design becomes very flexible and the convergence performance of the closed-loop system is much improved. Meanwhile, with the aid of the estimated values by the DOB, we obtain not only the output-feedback control scheme but also the better disturbance rejection property for the closed-loop system. A simulation example of a triple integrators system is presented to substantiate the usefulness of the proposed technique. [ABSTRACT FROM PUBLISHER]

Summary: This study is dedicated to solving the problem of a new adaptive second‐order sliding mode (SOSM) controller design for a type of nonlinear systems with multiple uncertainties by using adding a power integrator (API) and the parameter separation techniques. Supported by the finite‐time Lyapunov theory, the finite‐time stability of the closed‐loop system under the proposed adaptive SOSM controller has been firmly guaranteed. The significant advantages here lie in that the prior knowledge about the bounds of uncertainties is not required in the designed adaptive SOSM control approach, and the switching gain can be tuned dynamically. Finally, a numerical example is presented to indicate the notable feature and effectiveness of the designed adaptive SOSM approach. [ABSTRACT FROM AUTHOR]

In this paper, the problem of global decentralised stabilisation for a class of uncertain large-scale feedforward nonlinear systems is investigated. The system under consideration is allowed to contain unknown non-Lipschitz continuous nonlinear terms. The design of the global decentralised controllers takes a two steps procedure. First of all, based on the adding a power integrator technique and the homogeneous domination approach a local homogeneous decentralised controller is proposed for each subsystem of the large-scale feedforward nonlinear system. Then, we integrate a series of nested saturation functions with the homogeneous decentralised controllers and adjust the saturation levels to ensure globally asymptotic stability of the closed-loop system. Simulation studies are conducted to illustrate the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

A flexible spacecraft is a kind of complex systems consisting of rigid bodies and flexible appendages. The attitude maneuvering or external disturbances will unavoidably lead to a continuous vibration of flexible appendages. It is known that the finite-time control technique offers better convergence and disturbance rejection properties. To achieve the high-accuracy attitude stabilization, a nonsmooth attitude-stabilizing control strategy based on the finite-time control technique is investigated for flexible spacecrafts in this paper. The rigorous mathematical stability analysis of the overall closed-loop system is made by means of cascaded systems theory. The novelty of the paper is that the relation between the convergence region of states and the control parameters can be obtained, which indicates that the steady-state error can be preestimated when the control parameters are determined. Simulation results show that not only can the attitude be stabilized precisely, but the elastic vibration of flexible appendages can be suppressed effectively as well. [ABSTRACT FROM AUTHOR]

The guidance law design for the missile–target interception problem in the presence of system uncertainty is investigated in this paper. To improve the disturbance rejection property, two kinds of non-smooth guidance laws based on a finite-time control technique are developed. The first is a high-gain finite-time guidance law, which can be derived by assuming that the system uncertainty is bounded by a constant. The second one is a composite guidance law including a disturbance observer and a finite-time state feedback, where the disturbance observer is introduced to estimate the system uncertainty and the finite-time state feedback is to stabilize the guidance system. Under both of the proposed guidance laws, it can be proved that the line-of-sight angle rate will converge to the origin or a small region of the origin in a finite time. Simulation comparisons show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The second‐order sliding mode control generates important properties for closed‐loop systems, such as robustness, disturbance rejection and finite‐time convergence. In this study, it is shown that the adding a power technique plus the nested saturation method will bring in a new second‐order sliding mode control scheme for non‐linear systems with relative degree two. Based on this, a second‐order sliding mode controller is constructed by imposing a natural assumption on the sliding mode dynamics, that is, the uncertainty of the sliding mode dynamics can be bounded by a known function instead of a constant. Under the proposed sliding mode controller, it is proved that the closed‐loop system is not only globally convergent, but also locally finite‐time stable, which implies the global finite‐time stability. Finally, the effectiveness of the proposed method is verified by a numerical example. [ABSTRACT FROM AUTHOR]

Abstract: This paper addresses the stabilization problems for nonlinear affine systems. First of all, the explicit feedback controller is developed for a nonlinear multiple-input affine system by assuming that there exists a control Lyapunov function. Next, based upon the homogeneous property, sufficient conditions for the continuity of the derived controller are developed. And then the developed control design methodology is applied to stabilize a class of nonlinear affine cascaded systems. It is shown that under some homogeneous assumptions on control Lyapunov functions and the interconnection term, the cascaded system can be globally stabilized. Finally, some interesting results of finite-time stabilization for nonlinear affine systems are also obtained. [Copyright &y& Elsevier]

• The paper projects a finite-time output feedback control framework subject to asymmetric output constraints. • The proposed control strategy can assure the finite-time stability of the whole system under output constraints. • Via an observer, only partial state knowledge is demanded to be measured in the proposed control method. This work has addressed the output-feedback finite-time stabilization issue for a type of asymmetric output-constrained planar systems. The innovation involved in the results of the work owes to the construction of a barrier Lyapunov function (BLF) to the handling of the asymmetric output constraint. By incorporated the BLF into the backstepping-like technique, a state feedback controller is first developed. An implementable observer is subsequently designed to estimate the unmeasurable system state. Lastly, an observer-based finite-time output feedback controller is explicitly proposed. Theoretically, the Lyapunov stability theory is adopted to show that the system states are finite-time stabilized under the presented control scheme. Meanwhile, the violation of a pre-established asymmetric output constraint is circumvented. To testify the derived theoretical results, the case studies of a permanent magnet linear motor system are offered. [ABSTRACT FROM AUTHOR]

Abstract: A global nonsmooth stabilization scheme is presented for a class of nonlinear cascaded systems with uncontrollable linearization. A stepwise constructive control methodology is proposed for the driving subsystem by using the adding a power integrator technique. Under suitable conditions and based on homogeneous properties, it is proved that the stabilization of the driving subsystem implies the stabilization of the overall cascaded system. Due to the versatility of the adding a power integrator technique and homogeneous properties, the proposed controller not only can be used to stabilize the cascaded system asymptotically, but also is able to lead to an interesting result of finite-time stabilization under appropriate conditions. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the attitude stabilization problem for a rigid spacecraft with external disturbances. To obtain a better disturbance rejection property, we employ finite-time control techniques. In the absence of disturbances, by employing continuous finite-time control method, a continuous finite-time controller is designed such that the attitude of the rigid spacecraft will converge to the origin in finite time. In the presence of disturbances, by employing terminal sliding mode method, a discontinuous finite-time control law is proposed such that the states will eventually converge to a small region of the origin, which can be rendered as small as desired. Numerical simulation results show the effectiveness of the method. [Copyright &y& Elsevier]

This paper investigates the control design problem for the second-order sliding mode (SOSM) dynamics with mismatched uncertainty subject to the output constraint by means of the adding a power integrator technique. An unified method through the barrier Lyapunov function (BLF) technique and adding a power integrator technique has been proposed. The contributions of the paper can be summarized as follows. • This is the first time to investigate the stabilization problem for the SOSM dynamics with mismatched uncertainty subject to output constraint. • The homogeneity of the SOSM control method holds due to the modified BLF. • The proposed method can deal with the symmetric output constraint as well as the asymmetric output constraint. • The developed SOSM controller has the generic property since it is also valid in the absence of the output constraint or the mismatched uncertainty. This paper investigates a control design problem for the second-order sliding mode (SOSM) dynamics with mismatched uncertainty subject to the output constraint by means of the adding a power integrator technique. Firstly, a SOSM dynamics with mismatched uncertainty is constructed by retaining some information in the mismatched channel so as to reduce the uncertainty in the control channel, thereby relaxing the control requirement. Secondly, a barrier Lyapunov function (BLF) is designed in consideration of the output constraint to prevent the considered system from escaping from the output constraint. Moreover, the output constraint can be either symmetric or asymmetric. Thirdly, by embedding the above BLF into the adding a power integrator technique, a SOSM controller can be eventually constructed for the SOSM dynamics with the mismatched uncertainty to solve the output constraint problem. The finite-time stability analysis is proved by Lyapunov theory. The simulation results considering the symmetric constraint as well as the asymmetric constraint are provided to demonstrate the validity of the proposed control method. [ABSTRACT FROM AUTHOR]

The output constraints widely exist in the physical systems and severely affect the performance of the closed-loop system. This paper considers the second-order sliding mode controller design subject to an output constraint. By constructing a new barrier Lyapunov function and applying the technique of adding a power integrator, a novel second-order sliding mode control algorithm, which can be used to deal with the output constraint problem, has been developed. The proposed sliding mode algorithm enables the output variable not to violate the boundary of the constraint region. Meanwhile, it has been shown that under the output constraint the sliding variable can still be stabilized to zero in a finite time. Finally, an academic example is given to verify the feasibility of the proposed second-order sliding mode algorithm. [ABSTRACT FROM AUTHOR]

This article addresses the problem of finite-time stabilization for a class of high-order nonlinear stochastic systems with asymmetric output constraints. A novel barrier Lyapunov function (BLF) is first presented to handle such asymmetric constraints. Further, based on the proposed BLF and the adding a power integrator technique, a controller design approach is developed by the backstepping method. It can be rigorously proved that the designed controller can not only make the system states finite-time converge to the origin in probability but also ensure that the constraint on system output is not violated. Another novelty of this approach is that it is a unified tool owing to its simultaneous application to the systems without output constraints. Finally, the validity of the proposed scheme can be verified by a simulation example. [ABSTRACT FROM AUTHOR]

To further improve the response speed and anti-interference capability of permanent magnet synchronous motors (PMSMs), many advanced control algorithms have been developed. Among the various advanced controls, the fixed-time terminal sliding mode control is one of the effective methods. However, there are still some problems, e.g., too many parameters imposed on the control design in the existing results. In this paper, a fixed-time non-singular terminal sliding mode control (FTNTSMC) method is proposed for the speed loop of a PMSM drive system. First, to improve the closed-loop performance of the PMSM drive system, the relationship between the reference q-axis current and the speed of the PMSM is described in a second-order model. Next, a sliding mode surface with variable exponential coefficients is selected, and the expression of the controller is given. Then, the stability of the PMSM drive system is demonstrated by using Lyapunov functions. Using this method, the fixed-time convergence of the PMSM drive system can be realized and the occurrence of singularity phenomena can be avoided in a simpler and easier method. Finally, the effectiveness of the proposed method is verified by simulation and experimental results. [ABSTRACT FROM AUTHOR]

This article is devoted to the design issue of high‐order sliding mode (HOSM) controller subject to asymmetric output constraints. A barrier Lyapunov function (BLF) is first developed to deal with the constraints. Subsequently, by implanting the BLF into the modified adding a power integrator technique, a HOSM control algorithm, which is able to handle the closed‐loop system simultaneously with and without asymmetric output constraints, has been presented. It has been shown on the basis of the rigorous mathematical proof that under the proposed control strategy, the finite‐time stability of the considered system with the asymmetric output constraints is ensured. Meanwhile, the proposed algorithm also satisfies the requirement of the preset asymmetric output constraint. At last, an illustrative example is given to demonstrate the effectiveness of the presented algorithm. [ABSTRACT FROM AUTHOR]

Summary: In this paper, the robust stabilization problem is addressed for a class of high‐order stochastic nonlinear systems with output constraints and disturbances by using finite‐time control technique. One of the features of the considered stochastic systems is that the fractional powers are allowed to be any positive odd rational numbers, rather than grater than or equal to one. By constructing a novel tan‐type barrier Lyapunov function and using the adding a power integrator technique, the explicit steps on how to construct a backstepping‐like finite‐time controller have been developed to handle the robust stabilization and output constraint. Rigorous mathematical proof shows that the system states will finite‐time converge to a small region of the origin and the output constraint can be kept. Finally, a simulation example is given to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper considers the problem of finite-time stabilization in probability for a class of high-order stochastic nonlinear systems with output constraints in which the fractional powers are only required to be positive rather than not less than one. Based on a modified version of adding a power integrator technique and a novel tan-type barrier Lyapunov function, a systematic design approach is developed and a state-feedback controller is constructed. Rigorous mathematical proof shows that the origin of the system is finite-time stable in probability and the constraint requirement on the output is not violated. The effectiveness of the proposed finite-time control scheme is verified by a simulation example. [ABSTRACT FROM AUTHOR]

Efficient path tracking control for autonomous agricultural vehicles (AAVs) is the key technology for realizing agriculture 4.0 and precision agriculture, which makes smart farms more sustainable, profitable, and eco-friendly. It is well recognized that model nonlinearity, unknown disturbances, and wheel slipping are common problems in practical AAV systems in operation. To tackle these issues and improve the path tracking performance, a novel fixed-time generalized super-twisting control scheme is proposed for AAVs in this paper. First, a fixed-time integral sliding mode surface is designed for the considered vehicle by fusing the lateral offset and heading offset together. Then, an innovative auxiliary system dynamics is constructed to collaborate with the foregoing sliding mode surface, compensating for the adverse effects of wheel slipping effectively. Subsequently, based on the kinematic offset model of AAVs, a new type of generalized super-twisting controller is designed to achieve superior path tracking with robustness. Unlike existing super-twisting controllers, the generalized super-twisting continuous controller can fully eliminate chattering by replacing the previous discontinuous terms with a nonsmooth term. Further, rigorous theoretical analysis is conducted by raising a fresh Lyapunov function to verify the closed-loop control system stability. Finally, extensive field experiments have been carried out to show that the proposed control scheme significantly outperforms typical comparative control schemes. • A new generalized super-twisting controller is proposed for vehicle path tracking. • A fixed-time sliding mode surface is designed to overcome the singularity problem. • To handle the issue of wheel slipping, an auxiliary dynamic system is constructed. • Field experiments are conducted to demonstrate the path tracking performances. [ABSTRACT FROM AUTHOR]