Output feedback tracking control for lower‐triangular nonlinear time‐delay systems with asymmetric input saturation

In this paper, the problem of output feedback tracking control is investigated for lower‐triangular nonlinear time‐delay systems in the presence of asymmetric input saturation. A novel design program based on a dynamic high gain design approach is proposed to construct an output feedback tracking controller. The innovation here is that the problem of constructing tracking controller can be transformed into the problem of constructing two dynamic equations, with one being utilized to deal with the nonlinear terms and the other one being applied to analyze the influence of asymmetric input saturation. It is proved by an appropriate Lyapunov‐Krasovskii functional that the proposed tracking controller subject to saturation can ensure that all the signals of the closed‐loop system are globally bounded and the tracking error is prescribed sufficiently small when time is long enough. A practical example is given to illustrate the effectiveness of the proposed method.     

Retrofit fault‐tolerant tracking control design of an unmanned quadrotor helicopter considering actuator dynamics

This paper presents a retrofit fault‐tolerant tracking control (FTTC) design method with application to an unmanned quadrotor helicopter (UQH). The proposed retrofit fault‐tolerant tracking controller is developed to accommodate loss‐of‐effectiveness faults in the actuators of UQH. First, a state feedback tracking controller acting as the normal controller is designed to guarantee the stability and satisfactory performance of UQH in the absence of actuator faults, while actuator dynamics of UQH are also considered in the controller design. Then, a retrofit control mechanism with integration of an adaptive fault estimator and an adaptive fault compensator is devised against the adverse effects of actuator faults. Next, the proposed retrofit FTTC strategy, which is synthesized by the normal controller and an additional reconfigurable fault compensating mechanism, takes over the control of the faulty UQH to asymptotically stabilize the closed‐loop system with an acceptable performance degradation in the presence of actuator faults. Finally, both numerical simulations and practical experiments are conducted in order to demonstrate the effectiveness of the proposed FTTC methodology on the asymptotic convergence of tracking error for several combinations of loss‐of‐effectiveness faults in actuators.     

Fixed‐time attitude tracking control for spacecraft based on adding power integrator technique

In this article, the fixed‐time attitude tracking problem for rigid spacecraft is investigated based on the adding‐a‐power‐integrator control technique. First, a fixed‐time attitude tracking controller is designed to guarantee fixed‐time convergence of tracking errors. Then, by considering the presence of random disturbance and actuator faults, an adaptive fault‐tolerant attitude tracking controller is designed to guarantee tracking errors converge to a residual set of zero in a fixed time. The complete bounds on settling time are derived independently of initial conditions. The simulation results illustrate the highly precise and robust attitude control performance obtained by using the proposed controllers.     

Path‐Tracking Control of a Riderless Bicycle Via Road Preview and Speed Adaptation

In this study, a genetic‐fuzzy control system is used to control a riderless bicycle where control parameters can adapt to the speed change of the bicycle. The equations of motion are developed for a bicycle with constraints of rolling‐without‐slipping contact condition between the wheels and ground. This controller consists of two loops: the inner is a roll‐angle‐tracking controller which generates steering torque to control the roll angle while guaranteeing the stability, and the outer is a path‐tracking controller which generates the reference roll angle for the inner loop. The inner loop is a sliding‐mode controller (SMC) designed on the basis of a linear model obtained from a system identification process. By defining a stable sliding surface of error dynamics and an appropriate Lyapunov function, the bicycle can reach the roll‐angle reference in a finite time and follow that reference without chattering. The outer loop determines the proper reference roll‐angle by using a fuzzy‐logic controller (FLC) in which previewing and tracking errors are taken into consideration. The robustness of the proposed controller against speed change and external disturbances is verified by simulations.     

Fast terminal sliding‐mode finite‐time tracking control with differential evolution optimization algorithm using integral chain differentiator in uncertain nonlinear systems

This paper presents a fast terminal sliding‐mode tracking control for a class of uncertain nonlinear systems with unknown parameters and system states combined with time‐varying disturbances. Fast terminal sliding‐mode finite‐time tracking systems based on differential evolution algorithms incorporate an integral chain differentiator (ICD) to feedback systems for the estimation of the unknown system states. The differential evolution optimization algorithm using ICD is also applied to a tracking controller, which provides unknown parametric estimation in the limitation of unknown system states for trajectory tracking. The ICD in the tracking systems strengthens the tracking controller robustness for the disturbances by filtering noises. As a powerful finite‐time control effort, the fast terminal sliding‐mode tracking control guarantees that all tracking errors rapidly converge to the origin. The effectiveness of the proposed approach is verified via simulations, and the results exhibit high‐precision output tracking performance in uncertain nonlinear systems.     

Observer‐based H ∞ output tracking control for networked control systems

This paper is concerned with observer‐based H _∞ output tracking control for networked control systems. An observer‐based controller is implemented through a communication network to drive the output of a controlled plant to track the output of a reference model. The inputs of the controlled plant and the observer‐based tracking controller are updated in an asynchronous way because of the effects of network‐induced delays and packet dropouts in the controller‐to‐actuator channel. Taking the asynchronous characteristic into consideration, the resulting closed‐loop system is modeled as a system with two interval time‐varying delays. A Lyapunov–Krasovskii functional, which makes use of information about the lower and upper bounds of the interval time‐varying delays, is constructed to derive a delay‐dependent criterion such that the closed‐loop system has a desired H _∞ tracking performance. Notice that a separation principle cannot be used to design an observer gain and a control gain due to the asynchronous inputs of the plant and the controller. Instead, a novel design algorithm is proposed by applying a particle swarm optimization technique with the feasibility of the stability criterion to search for the minimum H _∞ tracking performance and the corresponding gains. The effectiveness of the proposed method is illustrated by an example. Copyright © 2013 John Wiley & Sons, Ltd.     

Dynamic modeling and nonlinear tracking control of a novel modified quadrotor

In this article, a nonlinear tracking controller is designed based on Lyapunov stability for a novel aerial robot. The proposed 6‐rotor configuration improves stability and payload lifting capacity of the robot compared with conventional quadrotors while avoiding further complexities in the robot dynamics and steering principles. The dynamical model of the robot is derived using Newton‐Euler method. The model represents a nonlinear, coupled, and underactuated system. The proposed control strategy includes 2 main parts: an attitude controller and a position controller. Both the attitude and position controls are Lyapunov‐based nonlinear tracking controllers that guarantee the asymptotic convergence of the states' tracking errors to zero. Simulation results are presented to illustrate appropriate performance of the closed‐loop system in terms of position/attitude tracking even in the presence of wind disturbance.     

Perfect position/force tracking of robots with dynamical terminal sliding mode control

According to a given performance criteria, perfect tracking is defined as the performance of zero tracking error in finite time. It is evident that robotic systems, in particular those that carry out compliant task, can benefit from this performance since perfect tracking of contact forces endows one or many constrained robot manipulators to interact dexterously with the environment. In this article, a dynamical terminal sliding mode controller that guarantees tracking in finite‐time of position and force errors is proposed. The controller renders a dynamic sliding mode for all time and since the equilibrium of the dynamic sliding surface is driven by terminal attractors in the position and force controlled subspaces, robust finite‐time convergence for both tracking errors arises. The controller is continuous; thus chattering is not an issue and the sliding mode condition as well the invariance property are explicitly verified. Surprisingly, the structure of the controller is similar with respect to the infinite‐time tracking case, i.e., the asymptotic stability case, and the advantage becomes more evident because terminal stability properties are obtained with the same Lyapunov function of the asymptotic stability case by using more elaborate error manifolds instead of a more complicated control structure. A simulation study shows the expected perfect tracking and a discussion is presented. © 2001 John Wiley & Sons, Inc.     

Multivariable integral linear quadratic Gaussian robust control of islanded microgrid to mitigate voltage oscillation for improving transient response

A novel robust integral linear quadratic Gaussian (ILQG) controller is presented in this paper to control the voltage of islanded microgrid and improves its transient response. Microgrid is a small grid that consists of number of distributed generator units, power‐electronic components with inductor‐capacitor (LC) filters and loads. The loads are parametrically uncertain and unknown that produces the voltage or power oscillation. The ILQG controller is capable to compensate for the voltage oscillation and exhibits the tracking of grid voltage against the different load dynamics. The design of ILQG controller is carried out by augmenting the plant dynamics with an integrator. The robustness of the ILQG controller is studied by considering a number of uncertainties within the plant model. The performance of ILQG controller is compared with linear quadratic regulator (LQR) and linear quadratic Gaussian (LQG) controller in terms of rise time, settling time, bandwidth and tracking error. The comparison results ensure the high bandwidth and tracking performance of ILQG controller as compared to other controllers.     

Output tracking of stochastic nonlinear systems with unstable linearization

This paper studies the output tracking problem for a class of stochastic nonlinear systems whose linearization parts may have unstable modes via output‐feedback control. This is in contrast with most of the existing results where only state‐feedback control is considered. On the basis of the homogeneous domination technique, an output tracking controller is designed. It is shown that the expectation of tracking error can be made arbitrarily small while all the states of the closed‐loop system remain to be bounded in probability. Finally, a simulation example is given to illustrate the effectiveness of the tracking controller.     

Augmented TP model transformation‐based parallel distributed compensation control design

The usual sampled hyper grid points of uniform sampling method are distributed equally in the TP model transformation, thus, the sampling results often omit the local extrema when the sampling step is not fine‐tuned. Then the resultant tensor which is used for controller design can not fully cover the state space, although the gain which is the feasible solution of the linear matrix inequalities. In this paper, we proposed a non‐uniform sampling method for tensor product model transformation, local extrema are considered in the sampling step, while the sampling step can vary dynamically for different function entries. In this paper, TP model transformation‐based parallel distributed compensation (PDC) controller is extended in three folds: (i) The existing TP model transformation‐based PDC controller with uniform sampling method is extended to TP model transformation‐based PDC tracking controller with the uniform sampling method and an extended signal. (ii) A new TP model transformation‐based PDC tracking controller is proposed based on a new sampling method, that is, the Hammersley sampling method. (iii) TP model transformation‐based PDC tracking controller is also proposed based on the non‐uniform sampling method. The proposed adaptive TP model transformation‐based PDC tracking controller is able to enhance the performance of the TP model transformation‐based PDC controller, and the adaptive TP model transformation‐based PDC controller obtains the best results due to the nearly exact sampling of the system.     

Global asymptotic tracking for nonminimum‐phase nonlinear systems in output feedback form

The problem of global asymptotic tracking by output feedback is studied for a class of nonminimum‐phase nonlinear systems in output feedback form. It is proved that the problem is solvable by an n‐dimensional output feedback controller under the two conditions: (a) the nonminimum‐phase nonlinear system can be rendered minimum‐phase by a virtual output; and (b) the internal dynamics of the nonlinear system driven by a desired signal and its derivatives has a bounded solution trajectory. With the help of a new coordinate transformation, a constructive method is presented for the design of a dynamic output tracking controller. An example is given to validate the proposed output feedback tracking control scheme.     

Model‐assisted extended state observer and dynamic surface control–based trajectory tracking for quadrotors via output‐feedback mechanism

In this paper, an output‐feedback trajectory tracking controller for quadrotors is presented by integrating a model‐assisted extended state observer (ESO) with dynamic surface control. The quadrotor dynamics are described by translational and rotational loops with lumped disturbances to promote the hierarchical control design. Then, by exploiting the structural property of the quadrotor, a model information–assisted high‐order ESO that relies only on position measurements is designed to estimate not only the unmeasurable states but also the lumped disturbances in the rotational loop. In addition, to account for the problem of “explosion of complexity” inherent in hierarchical control, the output feedback–based trajectory tracking and attitude stabilization laws are respectively synthesized by utilizing dynamic surface control and the corresponding estimated signals provided by the ESO. The stability analysis is given, showing that the output‐feedback trajectory tracking controller can ensure the ultimate boundedness of all signals in the closed‐loop system and make the tracking errors arbitrarily small. Finally, flight simulations with respect to an 8‐shaped trajectory command are performed to verify the effectiveness of the proposed scheme in obtaining the stable and accurate trajectory tracking using position measurements only.     

A distributed leader‐following tracking controller using delayed control input information from neighbors

In this paper, we propose a simple, continuous, and distributed controller for the second‐order multiagent system to achieve leader‐following trajectory tracking, by exploiting the control input information of neighbors (CIIN) and using proportional‐derivative (PD) control in terms of local neighborhood synchronization error. A constant time delay is introduced in the CIIN as a design parameter to avoid the algebraic loop issue arising from the control input coupling. We develop an easily testable condition on the PD gains to ensure that the resulting neutral‐type error system is input‐to‐state stable for an arbitrary bounded delay, and prove that when the leader's acceleration is a Lipschitz continuous function with respect to time, the ultimate bound of tracking errors is strictly increasing with respect to the introduced time delay. Moreover, we analyze the robustness of the controller with respect to model uncertainties and show its potential advantages over two existing controllers in balancing the steady‐state tracking precision, the communication cost, and the continuity of controller signal. Finally, extensive simulations are conducted to show the effect of the delay on system stability, to verify the condition on PD gains, to confirm the robustness of the controller, and to demonstrate the detailed advantages.     

Immersion and Invariance Based Robust Adaptive Control of High‐Speed Train with Guaranteed Prescribed Performance Bounds

This paper proposes a novel robust adaptive algorithm for train tracking control with guaranteed prescribed transient and steady‐state performance. As speed increases, the inherent time‐varying uncertainties and unmodeled dynamics in the longitudinal dynamics of a high‐speed train seriously impacts the tracking performance of automatic train operation. To improve train operation performance, an estimator based on immersion and invariance technology is developed to recover the unknown and time‐varying plant parameters, and it renders the estimation error converging to a bounded residual set exponentially while providing more freedom for the controller. After certain error transformation, the prescribed tracking performance is introduced into the controller design. Then, an input‐to‐stable stable controller is developed through the backstepping technique, and it is proven that stabilization of the transformed system is sufficient to guarantee the prescribed performance. Rigorous theoretical analysis for the presented algorithm is provided, and a series of simulation studies also are given to verify the effectiveness of it.     

Enhanced direct adaptive fuzzy control of robot manipulators

In this article, an enhanced direct adaptive fuzzy robot controller is developed to overcome problems of high‐frequency oscillations across the boundary of the constraint set and large control signals. The direct adaptive fuzzy robot control algorithm employs tracking errors of the joint motion to drive the parameter adaptation. The predominant concern of the adaptation law is to reduce the tracking errors, and closed‐loop stability is ensured by appending a supervisory controller. This adaptive controller, appended with the supervisory controller, does not require the exact robot dynamics, but only the boundary of the dynamics. Theoretical results and simulation studies on a two‐link robot manipulator show that by modifying the activation function of the supervisory controller, the enhanced direct adaptive fuzzy robot controller is as robust as before and the problems of high‐frequency oscillations across the boundary of the constraint set and large control signals are alleviated. ©1999 John Wiley & Sons, Inc.     

Adaptive prescribed performance tracking control for strict‐feedback nonlinear systems with zero dynamics

This paper focuses on the adaptive tracking control problem for strict‐feedback nonlinear systems with zero dynamics via prescribed performance. Based on polynomial fitting, an adjustable performance function is firstly proposed, whose parameters can be adjusted in real time according to the tracking error. Furthermore, an adaptive prescribed performance tracking controller is constructed via the backstepping method, which guarantees that all the states in the closed‐loop system are bounded. Meanwhile, the output tracking error falls within an adjustable performance boundary and asymptotically converges to zero. Simulation comparison demonstrates the advantages of the developed controller as follows: (1) the parameters of the adjustable performance function are adjusted online according to the tracking errors for a faster convergent performance boundary; (2) the steady‐state performance of the system is further optimized simultaneously.     

AN ALGORITHM FOR DIGITAL IMPLEMENTATION OF TRAJECTORY TRACKING CONTROLLERS

In this work, we study the problem of the digital implementation of continuous‐time solutions to the trajectory tracking control problem for nonlinear systems. We exhibit an example that shows that, in general, no proper behavior of the tracking error can be expected when these solutions are implemented via the Sampling and Zero Order Hold technique. Inspired in some constructions developed in the context of Positional Games, we present a sampled‐data controller that, based on a continuous‐time solution of the tracking problem, assures semiglobal practical stability of the tracking error, with final error arbitrarily small if we choose a suitable sampling period. The controller is robust with respect to small external disturbances and small errors in the measurements.     

Robust approximation‐based adaptive control of multiple state delayed nonlinear systems with unmodeled dynamics

This paper addresses the problem of tracking control for a class of uncertain nonstrict‐feedback nonlinear systems subject to multiple state time‐varying delays and unmodeled dynamics. To overcome the design difficulty in system dynamical uncertainties, radial basis function neural networks are employed to approximate the black‐box functions. Novel continuous functions that deal with whole states uncertainties are introduced in each step of the adaptive backstepping to make the controller design feasible. The robust problem caused by unmodeled dynamics when constructing a stable controller is solved by employing an auxiliary signal to regulate its boundedness. A novel Lyapunov‐Krasovskii functional is developed to compensate for the delayed nonlinearity without requiring the priori knowledge of its upper bound functions. On the basis of the proposed robust adaptive neural controller, all the closed‐loop signals are semiglobal uniformly ultimately bounded with good tracking performance.     

Sliding mode control of boost and buck‐boost power converters using the dynamic sliding manifold

Non‐minimum phase tracking control is studied for boost and buck‐boost power converters. A sliding mode control algorithm is developed to track directly a causal voltage tracking profile given by an exogenous system. The approximate causal output non‐minimum phase asymptotic tracking in non‐linear boost and buck‐boost power converters is addressed via sliding mode control using a dynamic sliding manifold (DSM). Use of DSM allows the stabilization of the internal dynamics when the output tracking error tends asymptotically to zero in the sliding mode. The sliding mode controller with DSM links features of conventional sliding mode control (insensitivity to matched non‐linearities and disturbances) and a conventional dynamic compensator (accommodation to unmatched disturbances). Numerical examples demonstrate the effectiveness of the sliding mode controller even for a known time‐varying load. Copyright © 2003 John Wiley & Sons, Ltd.