Adaptive Control Of Nonlinear Systems Research Articles

A Quasi-ARX Neural Network with Switching Mechanism to Adaptive Control of Nonlinear Systems

This paper introduces an improved quasi-ARX neural network and discusses its application to adaptive control of nonlinear systems. A switching mechanism is employed to improve the performance of th...

Hierarchical anti-disturbance adaptive control for non-linear systems with composite disturbances and applications to missile systems

In this paper, a new anti-disturbance controller is presented for a class of non-linear systems with multiple disturbances. The first part of the disturbance is described by an exogenous model and the second part represents an uncertain variable bounded by a given function. A new non-linear disturbance observer is designed to estimate the composite disturbances. Then, a hierarchical control strategy consisting of disturbance-observer-based control and a robust adaptive controller is presented to achieve the anti-disturbance performance. A stability analysis for both the error estimation systems and the composite closed-loop system is provided. Finally, the approach is applied to a missile control system to show the efficiency of the approach.

Adaptive Control of Non-linear System Using Neural Network

The paper deals with one of possible methods for control of non-linear dynamical system, namely with the adaptive neural PS controller (ANPSC). Its principle is in on-line refinement of the model system and then in the adaptive adjustment of the controller parameters. The model of the plant is realized with a two-layer feedforward neural network. The control part of the ANPSC has the structure of the classical PS controller, and it is also created in the form of the neural network (simple perceptron). The simulation calculations were performed in MATLAB.

Adaptive control of nonlinear systems using fuzzy systems

In this paper we consider the adaptive control problem for a class of systems governed by nonlinear differential equations. Using Takagi-Sugeno approach, we have proposed a fuzzy model, which is linear in nature, the behavior of which is close to that of the unknown (nonlinear) plant. Based on this fuzzy model, we have proposed certain control structure with the help of which the plant output is capable of tracking certain desired trajectory. Using a suitable objective function and variation arguments, we have developed a set of necessary conditions with the help of which the parameters of the proposed fuzzy model and controller can be determined. Based on these necessary conditions, a numerical scheme is presented for computing the unknowns. Further, the question of continuous dependence of the proposed estimator and controller on system parameters (robustness) has been studied. Finally, the proposed adaptive control scheme has been applied to two different examples to illustrate the effectiveness of the proposed adaptive control scheme.

Stability and robustness of fuzzy adaptive control of nonlinear systems

In this paper, we propose a new approach that guarantees the stability and robustness of an adaptive control law of a nonlinear system. The control diagram proposed contains a Takagi–Sugeno–Kang fuzzy controller (TSK-FC) and a training block allowing the online adaptation of the FC parameters. The adaptation algorithm used is based on the gradient with minimization of the quadratic error between the system output and that desired by using the direct method of Lyapunov. However, our approach considers the gradient step of each adaptive FC parameter to be bound. This approach was applied to the control of an inverted pendulum. The results obtained confirm well the validity of such an adaptation especially the guarantee of the pendulum stability and the robustness of its control with respect to the disturbances introduced on the FC parameters and the pendulum itself.

Parameter convergence and minimal internal model with an adaptive output regulation problem

The parameter convergence of nonlinear adaptive control systems is an important yet not well addressed issue. In this paper, using the global robust output regulation problem of output feedback systems with unknown exosystems as a platform, we will show that the well known persistency of excitation (PE) condition still guarantees the convergence of the estimated parameter vector to the true parameter vector. Moreover, the PE condition will be satisfied if the internal model is minimal in certain sense.

A Design Scheme of Nonlinear Adaptive Control System Based on System Immersion and Manifold Invariance

A Design Scheme of Nonlinear Adaptive Control System Based on System Immersion and Manifold Invariance

NONLINEAR MODELLING AND CONTROL OF FULL-PENETRATION DUAL BYPASS GAS METAL ARC WELDING OF ALUMINIUM

Dual bypass gas metal arc welding (DB-GMAW) is a novel welding process which is capable of achieving different full penetration level by adjusting bypass current while keeping the total welding current constant for a constant mass input. In this paper, an experimental system is constructed to implement DB-GMAW and full penetration weld is produced on aluminum. To describe the relationship between bypass current (input) and full penetration level (output), a nonlinear model is proposed, identified, and validated based on process analysis and through experiments. To assure the desired full penetration level be produced under varying welding conditions, the parameters are on-line identified/updated and an adaptive control algorithm is proposed. Experiments verified the effectiveness of the developed adaptive nonlinear control system.

On using least-squares updates without regressor filtering in identification and adaptive control of nonlinear systems

In continuous-time system identification and adaptive control the least-squares parameter estimation algorithm has always been used with regressor filtering, which adds to the dynamic order of the identifier and affects its performance. We present an approach for designing a least-squares estimator that uses an unfiltered regressor. We also consider a problem of adaptive nonlinear control and present the first least-squares-based adaptive nonlinear control design that yields a complete Lyapunov function. The design is presented for linearly parametrized nonlinear control systems in ‘normal form’. A scalar linear example is included which adds insight into the key ideas of our approach and allows showing that, for linear systems, our Lyapunov-LS design with unfiltered regressor, presented in the note for unnormalized least-squares, can also be extended to normalized least-squares.

Nonlinear adaptive control system design and experiment for a 3-DOF model helicopter

This paper deals with model following control of a model helicopter with three degree-of-freedom. Since the decoupling matrix is singular, a nonlinear structure algorithm is used to design the controller. Furthermore, since the model dynamics are described linearly by unknown system parameters, a well-known parameter estimation technique is introduced. The integral type of estimation model is proposed here since the use of the derivative type of model cannot obtain the desired estimation result. The experimental results show the effectiveness of the proposed method.

Adaptive guidance law design based on characteristic model for reentry vehicles

In this paper an adaptive guidance law based on the characteristic model is designed to track a reference drag acceleration for reentry vehicles like the Shuttle. The characteristic modeling method of linear constant systems is extended for single-input and single-output (SISO) linear time-varying systems so that the characteristic model can be established for reentry vehicles. A new nonlinear differential golden-section adaptive control law is presented. When the coefficients belong to a bounded closed convex set and their rate of change meets some constraints, the uniformly asymptotic stability of the nonlinear differential golden-section adaptive control system is proved. The tracking control law, the nonlinear differential golden-section control law, and the revised logical integral control law are integrated to design an adaptive guidance law based on the characteristic model. This guidance law overcomes the disadvantage of the feedback linearization method which needs the precise model. Simulation results show that the proposed method has better performance of tracking the reference drag acceleration than the feedback linearization one.

Neural network-based robust adaptive control of nonlinear systems with unmodeled dynamics

A neural network-based robust adaptive control design scheme is developed for a class of nonlinear systems represented by input–output models with an unknown nonlinear function and unmodeled dynamics. By on-line approximating the unknown nonlinear functions and unmodeled dynamics by radial basis function (RBF) networks, the proposed approach does not require the unknown parameters to satisfy the linear dependence condition. It is proved that with the proposed control law, the closed-loop system is stable and the tracking error converges to zero in the presence of unmodeled dynamics and unknown nonlinearity. A simulation example is presented to demonstrate the method.

Indirect adaptive control of non-linear systems using multiple identification models and switching

Transient performance improvement of adaptive control of a class of single-input single-output (SISO) non-linear systems is considered in this study. The system under study is assumed to be minimum-phase and input-output linearisable. The non-linear dynamics is also assumed to be linearly parameterised in terms of the unknown parameters. The improvement in the transient performance under large parametric uncertainties is obtained with the use of multiple identification models and switching, and the closed loop system is shown to be stable with the switching mechanism. A new methodology is proposed for the quantitative evaluation of the transient performance. The study is verified by simulation of a non-linear physical system.

Robust Adaptive Control of Nonlinear Systems with Time-Varying Parameters and Its Application to Chua's Circuit

The problem of designing a robust adaptive control for nonlinear systems with uncertain time-varying parameters is addressed. The upper bound of uncertain parameters, considered even in control coefficients, are not required to be known. An adaptive tracking controller is presented and, using the Lyapunov theory, the closed-loop stability and tracking error convergence is shown. In order to improve the performance of the method, a robust mechanism is incorporated into the adaptive controller yielding a robust adaptive algorithm. The proposed controller guarantees the boundedness of all closed-loop signals and robust convergence of tracking error in spite of time-varying parameter uncertainties with unknown bounds. The parametric uncertain systems under consideration describes a wide class of nonlinear circuits and systems. As an application, a novel parametric model is derived for nonlinear Chua's circuit and then, the proposed method is used for its control. The effectiveness of the method is demonstrated by some simulation results.

Robust Nonlinear Path-Following Control of an AUV

This paper develops a robust nonlinear controller that asymptotically drives the dynamic model of an autonomous underwater vehicle (AUV) onto a predefined path at a constant forward speed. A kinematic controller is first derived, and extended to cope with vehicle dynamics by resorting to backstepping and Lyapunov-based techniques. Robustness to vehicle parameter uncertainty is addressed by incorporating a hybrid parameter adaptation scheme. The resulting nonlinear adaptive control system is formally shown and it yields asymptotic convergence of the vehicle to the path. Simulations illustrate the performance of the derived controller .

A constructive solution for stabilization via immersion and invariance: The cart and pendulum system

Immersion and Invariance (I&I) is the method to design asymptotically stabilizing control laws for nonlinear systems that was proposed in [Astolfi, A., & Ortega, R. (2003). Immersion and invariance: A new tool for stabilization and adaptive control of nonlinear systems. IEEE Transactions on Automatic Control, 48, 590–606]. The key steps of I&I are (i) the definition of a target dynamics, whose order is strictly smaller than the order of the system to be controlled; (ii) the construction of an invariant manifold such that the restriction of the system dynamics to this manifold coincides with the target dynamics; (iii) the design of a control law that renders the manifold attractive and ensures that all signals are bounded. The second step requires the solution of a partial differential equation (PDE) that may be difficult to obtain. In this short note we use the classical cart and pendulum system to show that by interlacing the first and second steps, and invoking physical considerations, it is possible to obviate the solution of the PDE. To underscore the generality of the proposed variation of I&I, we show that it is also applicable to a class of n -dimensional systems that contain, as a particular case, the cart and pendulum system.

Neural-network adaptive controller for nonlinear systems and its application in pneumatic servo systems

In this paper, a novel control law is presented, which uses neural-network techniques to approximate the affine class nonlinear system having unknown or uncertain dynamics and noise disturbances. It adopts an adaptive control law to adjust the network parameters online and adds another control component according to H-infinity control theory to attenuate the disturbance. This control law is applied to the position tracking control of pneumatic servo systems. Simulation and experimental results show that the tracking precision and convergence speed is obviously superior to the results by using the basic BP-network controller and self-tuning adaptive controller.

A new Neuro-Fuzzy intelligent method for indirect adaptive control of nonlinear systems via a novel approach of parameter hopping

A new Neuro-Fuzzy intelligent method for indirect adaptive control of nonlinear systems via a novel approach of parameter hopping

Adaptive Variable Structure Control of Aircraft withan Unknown High-Frequency Gain Matrix

This paper presents nonlinear adaptive and sliding-mode flight control systems for the roll-coupled maneuvers of aircraft. It is assumed that the parameters of the aircraft, as well as its high-frequency gain matrix, are unknown. Based on a backstepping design approach, nonlinear control laws (an adaptive variable structure control law and an adaptive control law) for the trajectory control of the roll angle, angle of attack, and sideslip angle using the aileron, elevator, and rudder are derived. The decomposition of the high-frequency gain matrix is used for the derivation of singularity-free flight control laws. An additional advantage of the control laws lies in the choice of design parameters of matrix decomposition for shaping the response characteristics. In the closed-loop system, the roll angle, angle of attack, and sideslip angle trajectories asymptotically follow the reference output trajectories. Simulation results are presented that show that in the closed-loop system, simultaneous longitudinal and lateral maneuvers are precisely performed in spite of the uncertainties in the aircraft parameters using each control system.

A study on the Adaptive Controller with Chaotic Dynamic Neural Networks

This paper presents an adaptive controller using chaotic dynamic neural networks(CDNN) for nonlinear dynamic system. A new dynamic backpropagation learning method of the proposed chaotic dynamic neural networks is developed for efficient learning, and this learning method includes the convergence for improving the stability of chaotic neural networks. The proposed CDNN is applied to the system identification of chaotic system and the adaptive controller. The simulation results show good performances in the identification of Lorenz equation and the adaptive control of nonlinear system, since the CDNN has the fast learning characteristics and the robust adaptability to nonlinear dynamic system.