Class Of Uncertain Nonlinear Systems Research Articles

Asymptotic tracking control for a class of uncertain nonlinear systems with output constraint

In this paper, we investigate the asymptotic tracking control for a class of strict-feedback nonlinear systems with unknown nonlinear functions and output constraint. The nonlinear transformation function-based system transformation approach is employed to convert the initial constrained system into an unconstrained one. To achieve the objective of asymptotic tracking, the tracking error is scaled by an exponential proportional function. Furthermore, to address the challenge of repetitive derivation of virtual control laws that occurs in the traditional design process of high-order backstepping methods, a first-order filter is applied. The designed control scheme guarantees that the system output will asymptotically track a predefined reference tracking trajectory while ensuring that the output constraint is not violated. Moreover, it is shown that the filter error will converge asymptotically to the origin. The effectiveness of the developed control strategy is verified through simulation results.

A Simple Controller Design for a Class of Uncertain Nonlinear Control Systems Guaranteed to Achieve Arbitrary Exponential Convergence Rates

This paper first proposes the concepts of high-efficiency stabilizable systems and high-efficiency controller. Then, using the time-domain analysis methodology, it is proved that a class of uncertain nonlinear systems can indeed become high-efficiency stabilizable systems under certain conditions; at the same time, we also provide its corresponding high-efficiency controller. Finally, some numerical simulation results are offered to illustrate and demonstrate the correctness of the main theorem and the design process of such a high-efficiency controller

Practical Finite-Time Command-Filtered Adaptive Backstepping With Its Applications to Quadrotor Hovers.

In this article, a practical finite-time command-filtered adaptive backstepping (PFTCFAB) control method is presented for a class of uncertain nonlinear systems with nonparametric unknown nonlinearities and external disturbances. Unlike PFTCFAB control techniques that use neural networks (NNs) or fuzzy-logic systems (FLSs) to deal with system uncertainties, the proposed method is capable of handling such uncertainties without the need for NNs or FLSs, thus reducing complexity and increasing reliability. In the proposed approach, novel function adaptive laws are designed to directly estimate unknown nonparametric nonlinearities and external disturbances by means of command filter techniques, and a type of practical finite-time command filters is proposed to obtain such laws. Moreover, the PFTCFAB controllers and finite-time command filters are designed with practical finite-time Lyapunov stability, which ensures finite-time stability of system tracking and filter estimation errors. Experimental results with a quadrotor hover system are presented and discussed to demonstrate the advantages and effectiveness of the proposed control strategy.

Robust tracking and model following of uncertain nonlinear systems with some uncertainties and dead-zone inputs

The problem of robust tracking and model following is reconsidered for a class of uncertain nonlinear systems with some uncertainties and dead-zone input constraints. In this paper, the system uncertainties are regarded as some nonlinear functions which are not required to must satisfy the matching conditions. That is, being different from traditional robust control theory, the matched structures of uncertainties are sufficient, but not necessary, for being able always to design some types of robust tracking control schemes. In addition, the external disturbances of dynamical systems are assumed to be any bounded functions which is not also required to satisfy the matching condition. By making use of the integral inequality, instead of Lyapunov function, a class of robust tracking control schemes is constructed to guarantee the uniform exponential boundedness of the model tracking errors. Moreover, the upper bounds of nonlinear uncertainties are not required to be known, and it is also unnecessary to know or estimate the characteristic parameters of dead-zone functions. Therefore, the resulting robust tracking control schemes have a simple structure. Actually, the resulting robust tracking control scheme is a linear feedback control one with a self-tuning control gain. Finally, an illustrative numerical example is provided to demonstrate the validity of the presented theoretical results.

Logic-Based Fixed-Time Control for Uncertain Nonlinear Systems With Unknown Control Directions.

The fixed-time control problem is investigated for a class of uncertain nonlinear systems subjected to multiple unknown control directions. The control coefficients of nonlinear systems under consideration are time varying and their signs are not required to be identical. To tackle this challenge, a switching mechanism along with a novel dynamic boundary function is proposed. Utilizing the devised dynamic boundary function, adaptive parameters are introduced into the controller to effectively handle system uncertainties. It is proved that the system output converges to a small neighborhood of the origin in fixed time and the boundedness of all system signals is maintained. Finally, two simulation examples are used to show the validity of the presented switching control strategy.

Adaptive output-feedback global stabilisation for a class of more general nonlinear systems

This article investigates the global stabilisation problem via adaptive output feedback for a class of uncertain nonlinear systems. It is worth emphasising that the system under investigation possesses function control coefficients, input matching uncertainty and the polynomial-of-output growth rate, which is essentially different from the existing related literature, and hence brings some technical difficulties to the control design. To solve this problem, an adaptive output-feedback controller with dynamic high-gain and extended state observer is proposed. Remarkably, only one dynamic gain is introduced to overcome the function control coefficients, the serious uncertainty and the polynomial-of-output in the system growth rate. Moreover, under the designed controller, the states of the original system globally converge to zero. Two simulation examples are given to demonstrate the effectiveness of the proposed approach.

Global Practical Output Tracking for a Class of Uncertain Nonlinear Systems

This paper addresses the problem of global practical output control using output feedback for a class of uncertain nonlinear systems with time-varying delay. First, a homogeneous output feedback controller is designed for a nominally uncertain system by adding power integrator technology. Then, with the help of an appropriate Lyapunov-Krasovsky functional and a reduced-order observer, using the homogeneous dominance approach and adding a power integrator method, an output feedback controller is successfully designed to ensure that all states of the closed-loop system remain constrained while simultaneously making the tracking error arbitrarily small.

Global practical tracking for uncertain nonlinear systems with unknown control coefficients and polynomial growth

This paper studies the problem of global output-feedback tracking control for a class of uncertain nonlinear systems. The system studied in this paper has unknown time-varying control coefficients and unknown reference signal. Notably, the nonlinearities of the system are bounded by the lower triangular linear unmeasured states multiplying the unknown constant, the polynomial-of-output and the polynomial-of-input growth rates, which indicates the presence of serious uncertainties. Motivated by the closely related works, by combining the ideas of universal control and deadzone with backstepping technique, this paper presents a new adaptive tracking control scheme based on two dynamic high-gains in the new forms. The proposed control scheme ensures that the tracking error converges to a specified arbitrarily small interval range after a finite time while the state of the resulting closed-loop system is globally bounded. Finally, the effectiveness of the control scheme is verified by an illustrative example.

Adaptive fast finite‐time control for nonlinear systems subject to output hysteresis by fuzzy approach

SummaryThis article investigates an adaptive fast finite‐time tracking control problem for a class of uncertain nonlinear systems with output hysteresis. The idea of output hysteresis compensation is skillfully extended to adaptive design by employing a hysteresis inverse transformation and barrier Lyapunov function. The backstepping technique is adopted to establish the fast finite‐time control strategy, which can realize finite‐time convergence of the closed‐loop system. A rigorous theoretical analysis is performed to illustrate that the signals in the closed‐loop systems are bounded in finite time, and the tracking error can converge into a compact set with sufficient accuracy. Finally, a numerical simulation is given to confirm the effectiveness of the presented strategy.

A novel adaptive neural predefined time control for a class of nonlinear systems

AbstractIn this article, a novel adaptive neural predefined time control scheme is designed for a class of uncertain nonlinear systems. In the design procedure, the unknown smooth nonlinear functions are approximated by the neural networks (NNs). A neural adaptive predefined time controller is proposed based on NNs, adaptive backstepping technology, and predefined time stability theory. The designed control strategy includes a new adaptive updating law which ensures that the derivative of the Lyapunov function satisfies the predefined time stable form. The proposed control scheme ensures that all the signals in the closed‐loop system are predefined time stability. A practical simulation example validates the effectiveness of the designed controller.

Intermittent monitoring‐based adaptive fault‐tolerant control for uncertain nonlinear systems with actuator switching

AbstractIn this paper, an adaptive fault‐tolerant control (FTC) scheme is proposed for a class of uncertain nonlinear systems with actuator failure, in which a healthy actuator is available as a backup. Instead of monitoring the failure in real‐time, an intermittent monitoring mechanism (IMM) is proposed by designing a set of monitoring functions operating only at discrete time instants, which makes the proposed scheme more applicable for networked control systems for which the actuator status has to be monitored via network. An adaptive backstepping controller is designed with the errors being modified to include shifting functions. Once actuator failure is detected by the monitoring functions, the actuator is switched to its backup and the controller is reconfigured by updating the shifting functions so that the tracking error can be driven into the prescribed performance in a given time.

Finite time fault estimation and fault‐tolerant control for a class of uncertain nonlinear systems based on cascaded observers

AbstractIn this paper, a finite time fault estimation and fault‐tolerant control method is proposed for a class of uncertain nonlinear systems that have both actuator faults and sensor faults. First, the outputs of the original system pass through the low‐pass filters to obtain the augmented states, and then an augmented system is composed of the states of the low‐pass filters and the original system, so as to realize the conversion of the sensor faults of the original system into partial actuator faults of the augmented system. Next, design state observers to reconstruct the unknown states of the augmented system, and develop extended state observers to estimate the actuator faults and disturbance of the augmented system. Again, the fault‐tolerant controllers are completed based on the backstepping control and the finite time control, and the finite time convergences of the designed observers and controllers are proved by theoretical analyses. Finally, based on a permanent magnet synchronous motor (PMSM) speed system, the simulation research and dSPACE simulated experiment research are conducted to verify the effectiveness of the proposed control method and its feasibility in the actual application.

A Multifilters Approach to Adaptive Event-Triggered Control of Uncertain Nonlinear Systems With Global Output Constraint.

This article focuses on the problem of adaptive event-triggered output feedback control for a class of uncertain nonlinear systems under the output constraint. Different from the existing works, the time-varying parameters and the global output constraint are taken into account. First, by means of multifilters, the unmeasurable state variables are reconstructed, under which the unknown time-varying parameters and sensor sensitivity are transformed into the estimation problem of unknown parameters. Second, based on a barrier function, a novel constraint algorithm is established to make the output enter into asymmetric time-varying constraint boundaries, which is independent of the initial value of the output. To avoid continuous sampling of the controller, an event-triggered mechanism is proposed without the Zeno phenomenon. By means of the Lyapunov stability theory, it is strictly proved that the output enters into the pregiven asymmetric constraint boundaries, and never exceeds. Finally, the validity of our proposed control algorithm is illustrated by a numerical simulation.

A fast-response active disturbance rejection control for a class of nonlinear uncertain systems

The nonlinear system control is a classical problem in control engineering. In this paper, rather than try to get accurate nonlinear dynamics, the nonlinear and uncertain dynamics are viewed as a signal. It can be estimated by an extended state observer, and compensated by a control law. Accordingly, the nonlinear uncertain system is linearized. Based on the linearized system and the key point of the U-model control, a controller can be designed to obtain predetermined closed-loop system dynamics. To get a more satisfactory performance, a compensation signal of the total disturbance estimation (CSTDE) is designed. Based on the CSTDE, a compensation of the total disturbance estimation based extended state observer (CTDESO) and a fast-response active disturbance rejection control (FRADRC) are proposed. Convergence of the CTDESO and the closed-loop stability of the FRADRC are analyzed. Four nonlinear systems are considered to testify the proposed approaches. Numerical results show that, no matter disturbances exist or not, the proposed CTDESO can linearize a nonlinear system better, and the predetermined closed-loop responses can also be achieved more satisfactorily by the FRADRC.

Adaptive prescribed‐time tracking control for uncertain nonlinear systems with full state constraints

SummaryThis paper investigates the adaptive tracking control in a prescribed‐time for a class of uncertain nonlinear systems with a full state constraint. Firstly, in order to restrict the state constraints, the barrier Lyapunov function is employed and parameter uncertainty is handled based on linear‐in‐the‐parameters (LIP). A prescribed‐time adaptive controller is then designed by backstepping to ensure that the closed‐loop system can reach zero in a prescribed finite time under any given initial conditions. The prescribed‐time is independent of the design of the parameters. Finally, two simulation examples verify the effectiveness and usability of the proposed method.

Adaptive Anti-Disturbance Control for a Class of Uncertain Nonlinear Systems With Composite Disturbances.

High-precision and safety control in face of disturbances and uncertainties is a challenging issue of both theoretical and practical importance. In this article, new adaptive anti-disturbance control schemes are proposed for a class of uncertain nonlinear systems with composite disturbances, including additive disturbances, multiplicative actuator faults, and implicit disturbances deeply coupled with system states. Both the cases with known and unknown control/fault directions are investigated. By properly fusing the techniques of disturbance observers and adaptive compensation, it is shown that all closed-loop signals are globally uniformly bounded and the tracking error converges to zero asymptotically, no matter the control/fault directions are known or not. In the case of known directions, the proposed control scheme, for the first time, guarantees asymptotic tracking and L ∞ tracking performance simultaneously in face of disturbances and actuator faults. Moreover, novel Nussbaum functions and a contradiction argument are introduced, which allow the system to have multiple unknown nonidentical control directions and unknown time-varying fault direction. Simulation results illustrate the effectiveness of the proposed control schemes.

Observer Design for a Class of Uncertain Nonlinear Systems With Sampled-Delayed Output Using High-Gain Observer and Low-Pass Filter: Application for a Quadrotor UAV

In this paper, a novel structure of a Filtered High-Gain Observer (FHGO) is proposed for a class of nonlinear systems subject to sampled and delayed measurements, bounded disturbances and noise measurements effects. Using an LMI design approach, the novel structure of the continuous-discrete FHGO allows a larger bound of the Maximum Allowable Value of Time Delay (MAVTD). To prove the effectiveness of the proposed observer, a comparison with Kalman-like observer and standard high gain observer is provided and the corresponding experimental results are presented for a quadrotor UAV.

Multiple Filters-based Output Feedback Fault-tolerant Control for a Class of Uncertain Nonlinear Systems With Event-triggered Mechanism

Multiple Filters-based Output Feedback Fault-tolerant Control for a Class of Uncertain Nonlinear Systems With Event-triggered Mechanism

Fault Accommodation of Multiple Faults for A Class of Nonlinear Uncertain Systems: A Dynamic Fault Isolation Information Framework

Fault Accommodation of Multiple Faults for A Class of Nonlinear Uncertain Systems: A Dynamic Fault Isolation Information Framework

Event-Triggered Adaptive Neural Network Tracking Control for Uncertain Systems With Unknown Input Saturation Based on Command Filters.

This brief presents a modified event-triggered command filter backstepping tracking control scheme for a class of uncertain nonlinear systems with unknown input saturation based on the adaptive neural network (NN) technique. First, the virtual control functions are reconstructed to address the uncertainties in subsystems by using command filters. A piecewise continuous function is employed to deal with the unknown input saturation problem. Next, an event-triggered tracking controller is developed by utilizing the adaptive NN technique. Compared with standard NN control schemes based on multiple-function-approximators, our controller only requires a single NN. The closed-loop system stability is analyzed based on the Lyapunov stability theorem, and it is shown that the Zeno behavior is also avoided under the designed event-triggering mechanism. Simulation studies are performed to validate the effectiveness of our controller.