Time-varying Output Constraints Research Articles

Small-gain technique-based adaptive output constrained control design of switched networked nonlinear systems via event-triggered communications

This paper investigates the problem of event-triggered tracking control for switched networked nonlinear systems with asymmetric time-varying output constraints. To handle the output constraints, an output-dependent generic constraint function is constructed to describe relationship between the output and the performance requirement. Meanwhile, an event-triggering rule is designed to reduce communication frequency between the controller and the actuator, thereby reducing the burden of the network communication. Based on the common Lyapunov function method and event-triggered control strategy, an adaptive control method is designed, which can guarantee that the closed-loop signals are bounded and avoid the Zeno behavior. Different from existing results considering constraints, the proposed scheme not only relaxes the restricted condition of constraint boundaries but also both the cases with and without output constraints can be addressed simultaneously. Furthermore, the stability of the system can be guaranteed by the small-gain technique. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed scheme.

Output feedback control with time-varying asymmetric constraints for nonlinear cascade systems

In this paper, the output feedback problem is studied for a class of nonlinear cascade systems with integral input to state stability (iISS) inverse dynamics and an unknown control direction. The tan-type barrier Lyapunov function (UBLF) is introduced for an asymmetric time-varying output constraint, which can be equal to the standard Lyapunov function of an unconstrained system, thereby solving the requirement for the asymmetric time-varying output constraint. A design strategy based on backstepping is proposed to construct a dynamic output feedback control law, and an output feedback controller is designed using the barrier function. The proposed strategy satisfies the constraint condition while keeping all other closed-loop signals bounded. Finally, the effectiveness of the proposed strategy is proven by the simulation results.

Cooperative Fault-Tolerant Control for a Mobile Dual Flexible Manipulator With Output Constraints

This article discusses cooperative control of a mobile dual flexible manipulator system with asymmetric time-varying output constraints and actuator failures. The shift function and a barrier Lyapunov function (BLF) are used to guarantee output constraints when the initial states of the system violate the prescribed constraints. Moreover, an adaptive fault-tolerant control scheme is developed to deal with actuator failures, while suppressing system’s vibration and achieving cooperative operation. Finally, theoretic analysis proves the uniform bounded stability of the system and numerical simulation verifies the effectiveness of the proposed control method. Note to Practitioners—The purpose of this article is to develop a cooperative dual flexible manipulator system with performance limitations and actuator failures. The system can realize the task of stably grasping and moving a rigid object. The existing research on the grasping task of flexible manipulators only focuses on coordinated operation, which limits the application of the dual flexible manipulator system in practical engineering. To further study the problem, this article considers the output constraints and actuator failures of the dual flexible manipulator system in the actual process and proposes a cooperative fault-tolerant control framework. The control framework uses shift function and BLF to deal with output constraints and adopts adaptive technology to deal with actuator failures. In addition, the cooperative operation task of grasping object with dual flexible manipulators is realized. Simulation shows that this control strategy is feasible.

Predefined-time anti-saturation fault-tolerant attitude control for tailless aircraft with guaranteed output constraints

This work investigates the anti-saturation attitude tracking control for the tailless aircraft with guaranteed output constraints, in the presence of uncertain inertia parameters, bounded external disturbance, and actuator faults/failures. A predefined-time adaptive backstepping attitude control scheme has been proposed, the main features of this scheme lie in (a) designing a predefined-time filter to deal with the ‘explosion of complexity’ and singularity problem; (b) introducing a nonlinear state-dependent function to handle the asymmetric time-varying output constraints; (c) compensating for the impact of the actuator faults/failures and input saturation by a nonlinear function and bounded estimation simultaneously. Moreover, the proposed control scheme can ensure all signals in the closed-loop system converge to a residual set around the origin within a predefined time, and this time constant can be set freely by the designer, independently of initial conditions. Finally, numerical simulations have been conducted to verify the performance of the proposed predefined-time fault-tolerant control scheme.

Boundary control of multiple-sectioned flexible marine riser with time-varying output constraint

This article addresses the problem for vibration suppression of a multiple-sectioned marine riser system subject to time-varying external disturbances and asymmetric output constraint. Under the assumption that continuity constraint, multiple-sectioned marine riser’s dynamics are described by some continuously connected partial differential equations (PDEs) coupled with an ordinary differential equation (ODE). We only employ boundary control mechanism that suppresses system’s vibration displacements and compensate the influence of external disturbances. A novel and improved disturbance observer is proposed to estimate unknown boundary disturbance and two different barrier Lyapunov functions are constructed to prevent the time-varying constraint violation. Based on the backstepping technology and Lyapunov-based control, a boundary controller is presented to accomplish the control objectives. Moreover, the uniform boundedness and stability of the closed-loop system are rigorously guaranteed. Finally, simulation results are provided to illustrate the effectiveness of the designed control scheme.

Prescribed-time tracking control for nonlinear systems with guaranteed performance

This paper studies the problem of the prescribed-time tracking control for a class of strict-feedback nonlinear systems with guaranteed performance. We will design a controller to achieve the following: one is to achieve the prescribed-time tracking, in which the settling time is not only independent of the design parameters, nor does it depend on the initial conditions, and can be set according to per our will; the other is to achieve prescribed performance composed of both the time-varying output constraint (TVOC) and the non-overshooting response. First, sufficient conditions on the prescribed-time tracking control with guaranteed performance are proposed. Then, based on the method of time-varying Barrier Lyapunov function (BLF) and LGV-backstepping, a recursive algorithm is developed to construct a controller to achieve the prescribed-time tracking control with guaranteed performance. Finally, two examples are provided to demonstrate the effectiveness of the proposed results.

Adaptive Fault-Tolerant Fast Finite-Time Consensus Protocols for Multiple Mechanical Systems With Output Constraints

In this article, we discuss fast finite-time consensus (FFTC) problems for uncertain nonlinear multiple mechanical systems with actuator faults and time-varying asymmetric output constraints. In order to guarantee the constraints are satisfied, an appropriate nonlinear mapping (NM) is employed to transform the original system with output constrains into an corresponding unconstrained one. Combining neural networks technology, graph theory, fast finite-time control theory, and backstepping technology, the actuator faults are considered to propose a distributed adaptive finite-time consensus (FTC) protocol, which can guarantee the position errors as well as the velocity errors reaching a region in finite time. Finally, an illustrative example is presented to support the obtained theoretical results.

Nonlinear gain-based event-triggered tracking control of a marine surface vessel with output constraints

This paper investigates the tracking control problem of marine surface vessels (MSVs) subject to time-varying output constraints, model uncertainties and unknown external disturbances. Firstly, a nonlinear gain technique is applied to the control design so that the control gain self-regulates with changes in tracking errors. Then, in the case of introducing nonlinear gain, a nonlinear gain-based barrier Lyapunov function (NGBLF) is proposed to guarantee the output tracking errors within predefined time-varying constraints. Subsequently, by employing adaptive neural networks (NNs) to approximate complex uncertainties, a nonlinear gain-based adaptive NN tracking control scheme is developed through the backstepping design tool. Based on this, in order to reduce the update frequency of controllers and mechanical wear of actuators more effectively, while ensuring the control performance, a novel dynamic event-triggered mechanism is incorporated into the control design to tune the thresholds dynamically. Afterwards, the stability analysis indicates that the presented control scheme can guarantee that all signals in the closed-loop system are semi-globally uniformly ultimately bounded and the prescribed time-varying constraints on the tracking errors will not be violated, while the Zeno behavior can be avoided. Finally, the effectiveness of the scheme is verified by simulation results.

Output feedback control for nonholonomic systems with nonvanishing disturbances and asymmetric time-varying constraints

In this paper, an adaptive output feedback control scheme is introduced for nonholonomic systems with nonliner uncertainties, nonvanishing disturbances, and output constraints. A tan-type barrier Lyapunov function is considered to address asymmetric time-varying output constraints. We define the disturbance as the generalized system state. The extended state observer is proposed for uncertain external disturbance. A new estimator is designed for unknown parameter and states. It is shown that under the backstepping technique the output feedback adaptive controller ensures the stability of the closed loop system, while the asymmetric time-varying output constraints are not violated. The simulation results of mobile robot system are provided to validate the effectiveness of the presented control approach.

Swarm Control for Connectivity-Preserving and Collision-Avoiding Unmanned Surface Vehicles Subject to Multiple Constraints

This paper investigates swarm control for unmanned surface vessels subject to multiple constraints. These constraints can be summarized as model parameter uncertainty, the unavailability of velocity measurements, time-varying environmental disturbances, input saturation and output constraints. Firstly, to recover unmeasured velocity information, to identify unknown vehicle dynamics and to estimate time-varying environmental disturbances, a neural adaptive state observer is designed for each vessel. Secondly, to avoid complex calculations, a second-order linear tracking differentiator is employed to generate a smooth reference signal and to extract the time derivative of the kinematic control law. Thirdly, to solve the input saturation, an auxiliary dynamic system is introduced. Fourthly, the barrier Lyapunov function is used to achieve connectivity preservation, collision avoidance and swarm control. Meanwhile, by using the estimated velocities of vessels, an output feedback controller is designed. The stability of the closed-loop system is proved. The simulation results show the effectiveness of the proposed swarm control strategy.

Partial-state feedback adaptive stabilization for a class of output-constrained nonlinear cascaded systems

This paper presents a robust adaptive stabilizing control scheme via partial-state feedback for a class of nonlinear cascaded systems with a time-varying output constraint. Different from the existing achievements, the nonlinear parameterization and unmeasured zero-dynamics are considered in this paper. The notion of input-to-state stability (ISS) and ISS-Lyapunov function are used to describe the zero-dynamics. The time-varying barrier Lyapunov function (TVBLF) is employed to ensure the output constraint satisfaction and the changing supply rates technique is used to deal with the unknown cascaded zero-dynamic states. It is shown that all the signals in the closed-loop system are bounded, and the asymptotic stabilization is achieved without violation of the output constraint. The performance of the proposed control scheme is illustrated through a simulation example.

Finite-time adaptive optimal consensus control for multi-agent systems subject to time-varying output constraints

In this paper, a finite-time optimal consensus control strategy is presented for unknown multi-agent systems (MASs) with the time-varying asymmetric output constraint. Different from existing results, the output constraint problem investigated here eliminates the requirements that constraint boundary functions must be strictly non-zero and have different signs, which is successfully handled by introducing special barrier functions. Moreover, to deal with disturbances well, a reinforcement learning (RL) with the critic-actor-disturbance structure is introduced. Meanwhile, the weights of neural networks are adjusted online by applying the gradient descent method to positive functions newly constructed, which not only significantly simplifies the algorithm but also eliminates the persistent excitation condition. For obtaining a fast convergence rate, the finite-time control technique is embedded into the RL algorithm, and an effective finite-time optimal control scheme is proposed to achieve the consistency of multi-agent system in a finite time. Finally, the effectiveness of the proposed protocol is demonstrated by two simulation examples.

Predefined-time tracking of nonlinear strict-feedback systems with time-varying output constraints

In this paper, the problem of the predefined-time tracking with time-varying output constraints (TVOC) is investigated for a class of nonlinear strict-feedback systems. First, the sufficient conditions for the studied problem are presented. Then, a recursive design algorithm of the controller is proposed by backstepping technique. A novel stabilizing function is constructed by adding a fractional term, which is capable of decreasing the asymmetric time-varying Barrier Lyapunov Function (BLF) to the origin within any desired settling time. After that, it is shown that under our proposed control, all the closed-loop signals are bounded, and the tracking error converges to zero within any desired settling time and remains zero thereafter without the violation of the output constraint. The settling time in this paper is not only independent of the design parameters, nor does it depend on the initial conditions, and can be set according to per our will. Finally, two examples are given to illustrate the effectiveness of the proposed method.

Adaptive neural networks force/position control of uncertain manipulators subject to input saturation and output constraints

In this work, considering the influence of input saturation and time-varying output constraints, an adaptive neural networks force/position control method is proposed for a class of uncertain robotic manipulators in contact with the external environment. Radial basis function neural networks are introduced to approximate the system uncertainty and only one parameter needs to be updated online. The output constraints are satisfied by converting the constrained system to an unconstrained one. Moreover, an auxiliary dynamic system is applied in the transformed unconstrained system to handle the input saturation nonlinearity and the Moore–Penrose pseudo-inverse term is introduced for controller design. All signals in the closed-loop system are proved to be bounded by using the Lyapunov method. To show the good performance of the given scheme, comparative simulation is conducted on a two-joint manipulator, which is controlled by the proposed adaptive neural networks force/position tracking controller and a conventional force/position controller without considering input saturation and output constraints. Simulation results show that the adaptive neural network force/position controller has better control performance than the traditional method.

Fault-tolerant adaptive fractional controller design for incommensurate fractional-order nonlinear dynamic systems subject to input and output restrictions

In this article, a fault-tolerant adaptive neural network fractional controller has been proposed for a class of uncertain multi-input single-output (MISO) incommensurate fractional-order non-strict nonlinear systems subject to five different types of unknown input nonlinearities, infinite number of actuators failures and arbitrary independent time-varying output constraints. The barrier Lyapunov function (BLF)-based backstepping technique and fractional Lyapunov direct method (FLDM) have been used to design the controller and establish system stability. To tackle the incommensurate derivatives problem, in each step of the backstepping technique, an appropriate Lyapunov function has been selected based on error variables of the considered step and their boundedness has been proved from the last step to the first one. The computational burden is reduced by decreasing the number of adaptive laws. The developed controller satisfies the output constraints and guarantees convergence of the output tracking error to a small neighborhood of the origin and boundedness of all closed-loop signals. Finally, the effectiveness of the designed controller has been demonstrated via simulating three examples.

High-order control barrier functions-based impedance control of a robotic manipulator with time-varying output constraints

This paper focuses on the impedance control for robotic manipulators with time-varying output constraints. High-order control barrier functions (HoCBFs) are firstly proposed for a nonlinear system with high relative-degree time-varying constraints. Then, the HoCBFs are introduced to impedance control for robotic manipulators, where the HoCBFs are employed to avoid the violation of time-varying output constraints in Cartesian space by quadratic program (QP), and the impedance control is designed to achieve compliance for human–robot interaction (HRI). In this way, the desired trajectory within the safety-critical region can be tracked without violating the output constraints due to the controller generated from QP, and the safe HRI can also be achieved because of the usage of impedance control method. Finally, simulation tests are conducted to verify the proposed control design methods.

Composite learning tracking control for underactuated marine surface vessels with output constraints.

In this paper, a composite learning control scheme was proposed for underactuated marine surface vessels (MSVs) subject to unknown dynamics, time-varying external disturbances and output constraints. Based on the line-of-sight (LOS) approach, the underactuation problem of the MSVs was addressed. To deal with the problem of output constraint, the barrier Lyapunov function-based method was utilized to ensure that the output error will never violate the constraint. The composite neural networks (NNs) are employed to approximate unknown dynamics. The prediction errors can be obtained using the serial-parallel estimation model (SPEM). Both the prediction errors and the tracking errors were employed to construct the NN weight updating. Using approximation information, the disturbance observers were designed to estimate unknown time-varying disturbances. The stability analysis via the Lyapunov approach indicates that all signals of unmanned marine surface vessels are uniformly ultimate boundedness. The simulation results verify the effectiveness of the proposed control scheme.

Finite-Time Output Control for Uncertain Robotic Manipulators With Time-Varying Output Constraints

This paper proposes a finite-time output controller to realize the tracking control of n degrees of freedom (n-DOF) manipulator, which can address the time-varying output constraints and uncertainties, such as modeling error, unknown frictions, and external disturbance. A nonlinear mapping is conducted to convert the constrained manipulator dynamics into unconstrained dynamics. Based on the unconstrained dynamics, a finite-time output controller is established based on the output-feedback control scheme and nonlinear extended state observer (NESO). Fractional order terms are exploited to obtain finite-time convergence, and the switching law is developed for the NESO to estimate both the unmeasured states and uncertainties. The superiority of the NESO and the stability of the overall system are theoretically demonstrated by using the Lyapunov approach. The effectiveness of the proposed controller is illustrated by conducting simulations and experiments with robot manipulators and comparing the obtained results with those of the existing techniques.

Robust Nonlinear Control Scheme for Electro-Hydraulic Force Tracking Control with Time-Varying Output Constraint

This paper presents a robust nonlinear control scheme with time-varying output constraint for the electro-hydraulic force control system (EHFCS). Two typical double-rod symmetrical hydraulic cylinders are employed to simulate force environments in the EHFCS. Therefore, in order to improve the performance of the EHFCS, firstly, the model of the EHFCS is established with taking external disturbances, parameter uncertainties as well as structural vibrations into consideration. Secondly, in order to estimate external disturbances, parameter uncertainties and structural vibrations in the EHFCS and compensate them in the following robust controller design, two disturbance observers (DOs) are designed according to the nonlinear system model. Thirdly, with two estimation values from two DOs, a time-varying constraint-based robust controller (TVCRC) is presented in detail. Moreover, the stability of the proposed controller is analyzed by defining a proper Lyapunov functions. Finally, in order to validate the performance of the proposed controller, a series of simulation studies are conducted using the MATLAB/Simulink software. These simulation results give a fine proof of the efficiency of the proposed controller. What’s more, an experimental setup of the EHFCS is established to further validate the performance. Comparative experimental results show that the proposed controller exhibits better performance than the TVCRC without two DOs and a conventional proportional integral (PI) controller.

Distributed control for output-constrained nonlinear multi-agent systems with completely unknown non-identical control directions

This paper studies the consensus problem for a class of nonlinear multi-agent systems with asymmetric time-varying output constraints and completely unknown non-identical control directions. Firstly, in order to deal with the problem of asymmetric time-varying output constraints, the original output-constrained multi-agent systems are transformed into new unconstrained multi-agent systems by constructing the state transformation for each agent. Secondly, the emergence of multiple Nussbaum-type function terms is avoided by introducing novel sliding-mode-esque auxiliary variables and consensus estimate variables, which allows the control directions to be completely unknown non-identical. Thirdly, a novel control strategy is proposed by combining novel variables with state transformation method for the first time, which makes the design of distributed consensus protocol more concise. Through Lyapunov stability analysis, the proposed distributed protocol ensures that the output constraints are never violated and the consensus can be achieved asymptotically. Finally, a practical simulation example is given to demonstrate the effectiveness of the proposed distributed consensus protocol.