Adaptive robust output‐feedback motion control of hydraulic actuators

Most previous advanced motion control of hydraulic actuators used full‐state feedback control techniques. However, in many cases, only position feedback is available, and thus, there are imperious demands for output‐feedback control for hydraulic systems. This paper firstly transforms a hydraulic model into an output feedback–dependent form. Thus, the K‐filter can be employed, which provides exponentially convergent estimates of the unmeasured states. Furthermore, this observer has an extended filter structure so that online parameter adaptation can be utilized. In addition, it is a well‐known fact that any realistic model of a hydraulic system suffers from significant extent of uncertain nonlinearities and parametric uncertainties. This paper constructs an adaptive robust controller with backstepping techniques, which is able to take into account not only the effect of parameter variations coming from various hydraulic parameters but also the effect of hard‐to‐model nonlinearities such as uncompensated friction forces, modeling errors, and external disturbances. Moreover, estimation errors that come from initial state estimates and uncompensated disturbances are dealt with via certain robust feedback at each step of the adaptive robust backstepping design. After that, a detailed stability analysis for the output‐feedback closed‐loop system is scrupulously checked, which shows that all states are bounded and that the controller achieves a guaranteed transient performance and final tracking accuracy in general and asymptotic output tracking in the presence of parametric uncertainties only. Extensive experimental results are obtained for a hydraulic actuator system and verify the high‐performance nature of the proposed output‐feedback control strategy.     

Adaptive backstepping repetitive learning control design for nonlinear discrete‐time systems with periodic uncertainties

This paper addresses a tracking problem for uncertain nonlinear discrete‐time systems in which the uncertainties, including parametric uncertainty and external disturbance, are periodic with known periodicity. Repetitive learning control (RLC) is an effective tool to deal with periodic unknown components. By using the backstepping procedures, an adaptive RLC law with periodic parameter estimation is designed. The overparameterization problem is overcome by postponing the parameter estimation to the last backstepping step, which could not be easily solved in robust adaptive control. It is shown that the proposed adaptive RLC law without overparameterization can guarantee the perfect tracking and boundedness of the states of the whole closed‐loop systems in presence of periodic uncertainties. In addition, the effectiveness of the developed controller is demonstrated by an implementation example on a single‐link flexible‐joint robot. Copyright © 2014 John Wiley & Sons, Ltd.     

Adaptive finite‐time formation tracking control for multiple nonholonomic UAV system with uncertainties and quantized input

An adaptive finite‐time formation tracking control approach is proposed for multiple unmanned aerial vehicle (UAV) system with quantized input signals in this paper. The UAVs are described by nonholonomic kinematic model and autopilot model with uncertainties. An enhanced hysteretic quantizer is introduced to avoid chattering, and some restrictions are released by using a new quantization decomposition method. Based on backstepping technique and finite‐time Lyapunov stability theory, the adaptive finite‐time controller is designed for the trajectory tracking of the multi‐UAV formation. The nonholonomic constraints are solved by a transverse function. A transformation is introduced to the control input signals to eliminate the quantization effect. Stability analysis proves that the tracking errors can converge to a small neighborhood of the origin within finite time and all the closed‐loop signals are semiglobally finite‐time bounded. The effectiveness of the proposed control approach is validated by simulation and experiment.     

A switching periodic adaptive control approach for time‐varying parameters with unknown periodicity

Periodic variations are encountered in many real systems, which can exist in the system parameters, as a disturbance or as the tracking objective. However, there exist a great number of situations where the periodicity is not known in advance. Hence, how to compensate for the effects of time‐varying parameters with unknown periodicity remains a challenge for the controller design. In this paper, we proposed a switching periodic adaptive control approach for continuous‐time nonlinear parametric systems with periodic uncertainties in which the period and bound are not known in advance. We utilized a fully saturated periodic adaptation law to identify the unknown periodic parameters in a pointwise manner. In addition, we provided a logic‐based switching scheme to estimate the unknown period and bound online simultaneously. By virtue of Lyapunov stability analysis, we show that the asymptotic convergence can be guaranteed irrespective of the initial conditions. Finally, we carried out numerical simulations to demonstrate the efficacy of the switching periodic adaptive control algorithm. The proposed approach can be applied to parametric nonlinear systems with time‐varying parameters of unknown periodicity irrespective of the types of periodic uncertainties. Copyright © 2015 John Wiley & Sons, Ltd.     

Composite learning fuzzy synchronization for incommensurate fractional‐order chaotic systems with time‐varying delays

This paper presents a composite learning fuzzy control to synchronize two different uncertain incommensurate fractional‐order time‐varying delayed chaotic systems with unknown external disturbances and mismatched parametric uncertainties via the Takagi‐Sugeno fuzzy method. An adaptive controller together with fractional‐order composite learning laws is designed based on both a parallel distributed compensation technology and a fractional Lyapunov criterion. The boundedness of all variables in the closed‐loop system and the Mittag‐Leffler stability of tracking error can be guaranteed. T‐S fuzzy systems are provided to tackle unknown nonlinear functions. The distinctive features of the proposed approach consist in the following: (1) a supervisory control law is designed to compensate the lumped disturbances; (2) both the prediction error and the tracking error are used to estimate the unknown fuzzy system parameters; (3) parameter convergence can be ensured by an interval excitation condition. Finally, the feasibility of the proposed control strategy is demonstrated throughout an illustrative example.     

Precision motion control of a small launching platform with disturbance compensation using neural networks

A kind of launching platform driven by two permanent magnet synchronous motors which is used to launch kinetic load to hit the target always faces strong parameter uncertainties and strong external disturbance such as the air current impulsion which would degrade their tracking accuracy greatly. In this paper, a practical method which combines adaptive robust control with neural network‐based disturbance observer is proposed for high‐accuracy motion control of the launching platform. The proposed controller not only accounts for the parametric uncertainties but also takes the external disturbances into account. Adaptive control is designed to compensate the former, while neural network‐based disturbance observer is designed to compensate the latter respectively and both of them are integrated together via a feedforward cancellation technique. A new kind of parametric adaptation and weight adaptation strategy is designed by using the linear combination of the system's tracking error and the weight estimation error as a driving signal for parametric adaptation and disturbance approximation. The stability of the novel control scheme is analyzed via a Lyapunov method and this method presents a prescribed output tracking performance in the presence of both parameter uncertainties and unmodeled nonlinearities. Extensive comparative simulation and experimental results are obtained to verify the high‐performance of the proposed control strategy. Copyright © 2016 John Wiley & Sons, Ltd.     

Cooperative adaptive neural partial tracking errors constrained control for nonlinear multi‐agent systems

This paper considers the problem of partial tracking errors constrained for high‐order nonlinear multi‐agent systems in strict‐feedback form. In the control design, radial‐based function neural networks are utilized to identify uncertain nonlinear functions, and a cooperative adaptive dynamic surface control is proposed to avoid the explosion of complexity in the backstepping technique. Based on the minimal learning parameter technique and the predefined performance approach, a novel cooperative adaptive neural network control method is developed. The proposed controller is able to guarantee that all the closed‐loop network signals are cooperative semi‐globally uniformly ultimately bounded, and partial tracking errors confine all times within the predefined bounds. Finally, simulation example and comparative example with previous methods are given to verify and clarify the effectiveness of the new design procedure. Copyright © 2016 John Wiley & Sons, Ltd.     

Set theoretic performance verification of low‐frequency learning adaptive controllers

Although adaptive control has been used in numerous applications, the ability to obtain a predictable transient and steady‐state closed‐loop performance is still a challenging problem from the verification and validation standpoint. To that end, we considered a recently developed robust adaptive control methodology called low‐frequency learning adaptive control and utilized a set of theoretic analysis to show that the transitory performance of this approach can be expressed, analyzed, and optimized via a convex optimization problem based on linear matrix inequalities. This key feature of this design and analysis framework allows one to tune the adaptive control parameters rigorously so that the tracking error components of the closed‐loop nonlinear system evolve in a priori specified region of the state space whose size can be minimized by selecting a suitable cost function. Simulation examples are provided to demonstrate the efficacy of the proposed verification and validation architecture showing the possibility of performing parametric studies to analyze the interplay between the size of the tracking error residual set and important design parameters such as the adaptation rate and the low‐pass filters time constant of the weights adaptation algorithm. Copyright © 2014 John Wiley & Sons, Ltd.     

Adaptive nonsingular terminal sliding mode control of MEMS gyroscope based on backstepping design

An adaptive nonsingular terminal sliding mode (NTSM) tracking control scheme based on backstepping design is presented for micro‐electro‐mechanical systems (MEMS) vibratory gyroscopes in this paper. The NTSM controller is designed based on backstepping strategy to eliminate the singularity, while ensuring the control system to reach the sliding surface and converge to equilibrium point in a finite period of time from any initial state. In addition, the proposed approach develops an online identifier scheme, which can real‐time estimate the angular velocity and the damping and stiffness coefficients. All adaptive laws in the control system are derived in the same Lyapunov framework, which can guarantee the globally asymptotical stability of the closed‐loop system. Numerical simulations for a MEMS gyroscope are investigated to demonstrate the validity of the proposed control approaches. Copyright © 2014 John Wiley & Sons, Ltd.     

Predictor‐based iterative neural dynamic surface control for three‐phase voltage source PWM rectifier

This paper addresses the control problem of a three‐phase voltage source pulse width modulation rectifier in the presence of parametric uncertainties and external time‐varying disturbances. An adaptive controller is designed by combining a modified dynamic surface control method and a predictor‐based iterative neural network control algorithm. Especially, neural networks with iterative update laws based on prediction errors are employed to identify the lumped uncertainties. Besides, a finite‐time‐convergent differentiator, instead of a first‐order filter, is used to obtain the time derivative of the virtual control law. Using a Lyapunov–Krasovskii functional, it is proved that all signals in the closed‐loop system are ultimately uniformly bounded. Both simulation and experimental studies are provided to show the effectiveness of the proposed approach. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Composite learning adaptive backstepping control using neural networks with compact supports

The ability to learn is crucial for neural network (NN) control as it is able to enhance the overall stability and robustness of control systems. In this study, a composite learning control strategy is proposed for a class of strict‐feedback nonlinear systems with mismatched uncertainties, where raised‐cosine radial basis function NNs with compact supports are applied to approximate system uncertainties. Both online historical data and instantaneous data are utilized to update NN weights. Practical exponential stability of the closed‐loop system is established under a weak excitation condition termed interval excitation. The proposed approach ensures fast parameter convergence, implying an exact estimation of plant uncertainties, without the trajectory of NN inputs being recurrent and the time derivation of plant states. The raised‐cosine radial basis function NNs applied not only reduces computational cost but also facilitates the exact determination of a subregressor activated along any trajectory of NN inputs so that the interval excitation condition is verifiable. Numerical results have verified validity and superiority of the proposed approach.     

Decentralized adaptive multi‐dimensional Taylor network tracking control for a class of large‐scale stochastic nonlinear systems

This paper investigates the problem of adaptive multi‐dimensional Taylor network (MTN) decentralized tracking control for large‐scale stochastic nonlinear systems. Minimizing the influence of randomness and complex nonlinearity, which increases computational complexity, and improving the controller's real‐time performance for the stochastic nonlinear system are of great significance. With combining adaptive backstepping with dynamic surface control, a decentralized adaptive MTN tracking control approach is developed. In the controller design, MTNs are used to approximate nonlinearities, the backstepping technique is employed to construct the decentralized adaptive MTN controller, and the dynamic surface control technique is adopted to avoid the “explosion of computational complexity” in the backstepping design. It is proven that all the signals in the closed‐loop system remain bounded in probability, and the tracking errors converge to a small residual set around the origin in the sense of a mean quartic value. As the MTN contains only addition and multiplication, the proposed control method is more simplified and of good real‐time performance, compared with the existing control methods for large‐scale stochastic nonlinear systems. Finally, a numerical example is presented to illustrate the effectiveness of the proposed design approach, and simulation results demonstrate that the method presented in this paper has good real‐time performance and control quality, and the dynamic performance of the closed‐loop system is satisfactory.     

Command-filtered-based neuroadaptive control for multi-input multi-output saturated nonstrict-feedback nonlinear systems with prescribed tracking performance

In this article, the prescribed performance control strategy is extended to multi-input multi-output nonstrict-feedback nonlinear systems with asymmetric input saturation, and not only each element in tracking error vector converges to a prescribed small region within preassigned finite time, but also the converging mode during the preset time is prespecifiable and controllable explicitly. By blending the barrier function with novel speed function, a prescribed performance controller using command-filtered-based vector-backstepping design framework is proposed to steer the tracking error vector for the first time, where the boundedness of filter errors is guaranteed by sufficiently small time constant and an error compensator is constructed to handle the effects of filter errors. To attenuate the adverse effects resulted from nondifferentiable input saturation, hyperbolic tangent function is utilized to estimate asymmetric saturation function such that the control input is designed as a new state variable with initial value of zero in augmented system. Nussbaum function is employed to overcome singularity problem caused by the differentiation of hyperbolic tangent function. At each step of backstepping design, the universal approximation property of neural network and the command filter system are utilized to approximate uncertain dynamics and to solve algebraic loop obstacle due to nonstrict-feedback structure, respectively. Moreover, only one parameter needs to be updated online to cope with the lumped uncertain dynamics by virtual parameter technology, rendering a control strategy with low complexity computation. The validity of the presented controller is verified by theoretical analysis and two-link robotic system.     

Decentralized prescribed performance adaptive tracking control for Markovian jump uncertain nonlinear systems with input saturation

A decentralized prescribed performance adaptive tracking control problem is investigated for Markovian jump uncertain nonlinear interconnected large‐scale systems. The considered interconnected large‐scale systems contain unknown nonlinear uncertainties, unknown control gains, actuator saturation, and Markovian jump signals, and the Markovian jump subsystems are in the form of triangular structure. First, by defining a novel state transformation with the performance function, the prescribed performance control problem is transformed to stabilization problem. Then, introducing an intermediate control signal into the control design, employing neural network to approximate the unknown composite nonlinear function, and based on the framework of the backstepping control design and adaptive estimation method, a corresponding decentralized prescribed performance adaptive tracking controller is designed. It is proved that all the signals in the closed‐loop system are bounded, and the prescribed tracking performances are guaranteed. A numerical example is provided to illustrate the effectiveness of the proposed control strategy. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive finite-time tracking control for robotic manipulators with funnel boundary

The finite-time tracking control problem with the output-constraint property of robotic manipulators subjected to system uncertainties is addressed. Specifically, the radial basis function neural network is employed to compensate for system uncertainties. The finite-time stability theorem is used for the backstepping design process, by which the limit of the settling time is set. A funnel boundary is used to limit the output overshoot. The proposed controller guarantees that all the signals are semi-globally practically finite-time bounded, while the tracking errors are enveloped by the funnel boundary. The performance of the proposed control method is illustrated by a numerical simulation of a 3-DOF manipulator. It is shown that the tracking errors are bounded by prescribed funnel boundaries. In the meantime, the manipulator is stabilized within a finite period of time.     

Adaptive tracking control for dynamic nonholonomic mobile robots with uncalibrated visual parameters

The trajectory tracking control problem of uncertain dynamic nonholonomic mobile robots is addressed in this paper. A novel uncertain camera‐object visual servoing kinematic tracking error model is proposed firstly. And then, on the basis of this model, a new adaptive torque tracking controller is presented in the presence of parametric uncertainties associated with the camera system and mechanical dynamic system. The controller synthesis is based on Lyapunov's direct method and backstepping technique. Simulation results are provided to illustrate the performance of the control law. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive tracking control for electrically‐driven robots without overparametrization

This paper addresses the motion tracking control of robot systems actuated by brushed direct current motors in the presence of parametric uncertainties and external disturbances. By using the integrator backstepping technique, two kinds of adaptive control schemes are developed: one requires the measurements of link position, link velocity and armature current for feedback and the other requires only the measurements of link position and armature current for feedback. The developed adaptive controllers guarantee that the resulting closed‐loop system is locally stable, all the states and signals are bounded, and the tracking error can be made as small as possible. The attraction region can be not only arbitrarily preassigned but also explicitly constructed. The main novelty of the developed adaptive control laws is that the number of parameter estimates is exactly equal to the number of unknown parameters throughout the entire electromechanical system. Consequently, the phenomenon of overparametrization, a significant drawback of employing the integrator backstepping technique to treat the control of electrically driven robots in the previous literature, is eliminated in this study. Finally, simulation examples are given to illustrate the tracking performance of electrically driven robot manipulators with the developed adaptive control schemes. Copyright © 2002 John Wiley & Sons, Ltd.     

Adaptive prescribed performance control for hydraulic system with disturbance compensation

In this article, an adaptive prescribed performance controller is developed for hydraulic system with uncertainties. An extraordinary feature is that better prescribed performance control can be achieved by compensating the uncertainties including parameter uncertainties and disturbances. For this reason, the transformation of system output error is realized by a prescribed performance function, which is employed to constrain the boundary of tracking error and convergence rate, then the tracking error of the original system with a priori prescribed performance can be realized by stabilizing the transformed system. Adaptive control is employed to solve the system parametric uncertainties; extended state observers are built to estimate the multiple disturbances. Based on the backstepping method, they are integrated into the design of the novel controller to guarantee prescribed tracking error performance. The stability analysis of the proposed controller is carried out via the Lyapunov theory. Finally, experimental results indicate good performance of the proposed algorithm.     

Robust adaptive iterative learning control for discrete‐time nonlinear systems with both parametric and nonparametric uncertainties

A new robust adaptive iterative learning control approach is proposed for discrete‐time nonlinear systems with both parametric and nonparametric uncertainties. By virtue of a well‐designed dead‐zone function, the learning of the parametric and nonparametric uncertainties can be performed concurrently. Rigorous Lyapunov function‐based analysis ensures that the effect of system uncertainties can be fully compensated, and the tracking error will converge to zero asymptotically in the iteration domain, even under random initial conditions and iteration‐varying reference trajectories. The efficacy of the proposed controller is demonstrated by simulating a single‐link robot manipulator with unknown frictions. Copyright © 2015 John Wiley & Sons, Ltd.     

Adaptive output feedback actuator failure compensation for a class of non‐linear systems

An adaptive compensation control scheme using output feedback is designed and analysed for a class of non‐linear systems with state‐dependent non‐linearities in the presence of unknown actuator failures. For a linearly parameterized model of actuator failures with unknown failure values, time instants and pattern, a robust backstepping‐based adaptive non‐linear controller is employed to handle the system failure, parameter and dynamics uncertainties. Robust adaptive parameter update laws are derived to ensure closed‐loop signal boundedness and small tracking errors, in general, and asymptotic regulation, in particular. An application to controlling the angle of attack of a non‐linear hypersonic aircraft dynamic model in the presence of elevator segment failures is studied and simulation results show that the developed adaptive control scheme has desired actuator failure compensation performance. Copyright © 2004 John Wiley & Sons, Ltd.