Systems In Semi-strict Feedback Form Research Articles

Robust Output Regulation Via Sliding Mode Control and Disturbance Observer: Application in a Forced Van Der Pol Chaotic Oscillator

This paper considers the problem of robust output regulation of nonlinear systems in semi strict-feedback form in the presence of model uncertainties and nonvanishing disturbances. In the proposed procedure, two exosystems are considered to generate the disturbance and reference signals. In order to reduce both the conservatism of the control law and the chattering phenomena, a disturbance observer is designed for disturbance estimation instead of assuming the known upper bound for the disturbance. Moreover, a novel sliding surface is designed based on the tracking error to guarantee that the output of the system tracks the output of the exosystem. In this regard, some theorems are given and according to the Lyapunov approach, it is proved that the robust output regulation is guaranteed in the presence of model uncertainties and external disturbances. Finally, in order to show the applicability of the proposed controller, it is applied to the Van der Pol chaotic oscillator. Computer simulations verify the theoretical results and also show the effective performance of the proposed controller.

Design of adaptive fuzzy backstepping sliding mode control for MIMO uncertain discrete-time nonlinear systems based on noisy measurements

This paper presents an adaptive fuzzy backstepping sliding mode control for multi-input and multi-output uncertain nonlinear systems in semi-strict feedback form. The systems are described by a discrete-time state equation with uncertainties viewed as the modeling errors and the unknown external disturbances, and the observation of the states is taken with independent measurement noises. Combining the adaptive fuzzy backstepping control with the sliding mode control approach for the comprehensive improvement in the stability and the robustness, the adaptive fuzzy backstepping sliding mode control is approximately designed where the design parameters are selected using an appropriate Lyapunov function. The uncertainities are approximated as fuzzy logic systems using the fuzzy inference approach based on the extended single input rule modules to reduce the number of the fuzzy IF-THEN rules. The estimates for the un-measurable states and the adjustable parameters are taken by the proposed simplified weighted least squares estimator. It is proved that the trajectory of the tracking error and the sliding surface is uniformly ultimately bounded. The effectiveness of the proposed approach is indicated through the simulation experiment of a simple numerical system.

Design of terminal block backstepping controllers for perturbed systems in semi-strict feedback form

Based on finite-time stability approach, a terminal block backstepping control with perturbation estimation scheme is proposed in this paper for a class of multi-input systems with matched and mismatched perturbations to solve regulation problems. The design procedure of the proposed control scheme mainly contains two parts. The first part is the design of pseudo-control inputs, the second part is the design of control input functions. In order to eliminate the problem of ‘explosion of complexity’ and overcome the problem of singularity, a derivative estimation algorithm embedded in the controller is utilised to estimate the perturbations. The control efforts are capable of suppressing the mismatched perturbations in most cases effectively so that the controlled states are able to reach zero within finite time. A numerical example is also given for demonstrating the feasibility of the proposed control scheme.

Distributed adaptive controller for the output-synchronization of networked systems in semi-strict feedback form

In this paper, we investigate the output synchronization of networked SISO nonlinear systems that can be transformed into semi-strict feedback form. Due to parameter uncertainty, the agents have heterogeneous dynamics. Combined backstepping method together with graph theory, we construct an augmented Laplacian potential function for analysis and a distributed controller is designed recursively for each agent such that its output can be synchronized to its neighbors' outputs. The distributed controller of each agent has three parts: state feedback of itself, neighborhood information transmitted through the network and adaptive parameter updaters both for itself and its neighbors. Moreover, distributed tuning function is designed to minimize the order of the parameter updater. It is proved that when the undirected graph is connected, all agents’ outputs in the network can be synchronized, i.e., cooperative output synchronization of the network is realized. Simulation results are presented to verify the effectiveness of the proposed controllers.

Adaptive Dynamic Surface Based Nonsingular Fast Terminal Sliding Mode Control for Semistrict Feedback System

This paper focuses on an adaptive dynamic surface based nonsingular fast terminal sliding mode control (ADS-NFTSMC) for a class of nth-order uncertain nonlinear systems in semistrict feedback form. A simple and effective controller has been obtained by introducing dynamic surface control (DSC) technique on the basis of second-order filters that the “explosion of terms” problem caused by backstepping method can be avoided. The nonsingular fast terminal sliding mode control is adopted in the last step of the controller design, and the error convergence rate is improved. An composite adaptive law is used to gain fast and accurate parameter estimation. Finally, simulation results are presented to illustrate the effectiveness of the proposed method.

Stabilising tracking of uncertain switched non-linear systems in semi-strict feedback form

This study concentrates on the stabilising tracking problem of a class of switched non-linear systems in semi-strict feedback form with parametric and non-linear uncertainties. The switching signal is arbitrary and occurs on the known non-linear functions. To solve the tracking problem, a switched adaptive robust dynamic surface control approach is proposed. The continuous error signals are constructed using the dynamic surface control approach, so the switched error dynamics is obtained. Then, semi-global stability analysis is discussed by using the common Lyapunov function method, which shows that the solutions of the closed-loop system are uniformly ultimate bounded and the tracking error can be prescribed arbitrarily small. A numerical example is provided to illustrate the effectiveness of the proposed control method.

Adaptive robust control of a class of nonlinear systems in semi‐strict feedback form with non‐uniformly detectable unmeasured internal states

AbstractThis paper proposes a novel control method for a special class of nonlinear systems in semi‐strict feedback form. The main characteristic of this class of systems is that the unmeasured internal states are non‐uniformly detectable, which means that no observer for these states can be designed to make the observation error exponentially converge to zero. In view of this, a projection‐based adaptive robust control law is developed in this paper for this kind of system. This method uses a projection‐type adaptation algorithm for the estimation of both the unknown parameters and the internal states. Robust feedback term is synthesized to make the system robust to uncertain nonlinearities and disturbances. Although the estimation error for both the unknown parameters and the internal states may not converge to zero, the tracking error of the closed‐loop system is proved to converge to zero asymptotically if the system has only parametric uncertainties. Furthermore, it is theoretically proved that all the signals are bounded, and the control algorithm is robust to bounded disturbances and uncertain nonlinearities with guaranteed output tracking transient performance and steady‐state accuracy in general. The class of system considered here has wide engineering applications, and a practical example—control of mechanical systems with dynamic friction—is used as a case study. Simulation results are obtained to demonstrate the applicability of the proposed control methodology. Copyright © 2010 John Wiley & Sons, Ltd.

Dynamic surface control approach to adaptive robust control of nonlinear systems in semi-strict feedback form

This article considers the adaptive robust control of a class of single-input-single-output nonlinear systems in semi-strict feedback form using radial basis function (RBF) networks. It is well known that the standard backstepping design may suffer from “explosion of terms”. To overcome this problem, the recently developed dynamic surface control technique which employs a first-order low-pass filter at each step of the backstepping design procedure is generalized to the nonlinear system under study. Our attention is paid to achieve guaranteed transient performance of the adaptive controller. At each step of design, a feedback controller strengthened by nonlinear damping terms to counteract nonlinear uncertainties is designed to guarantee input-to-state practical stability of the corresponding subsystem, and then parameter adaptations are introduced to reduce the ultimate error bound. Furthermore, for the output trajectory tracking problem, it is recommended to adopt the partial adaptation policy to reduce the computational burden due to “curse of dimension” of the RBF networks. Finally, numerical examples are included to verify the results of theoretical analysis.

DYNAMIC SURFACE CONTROL APPROACH TO ADAPTIVE ROBUST CONTROL OF NONLINEAR SYSTEMS IN SEMI-STRICT FEEDBACK FORM

This paper consider the adaptive robust control of a class of single-input-single-output (SISO) nonlinear systems in semi-strict feedback form, where nonlinearities can exist in the input channel of each subsystem. To overcome the problem of “explosion of terms”, the recently developed dynamic surface control technique is generalized to the nonlinear systems under study. At each step of design, a feedback controller strengthened by nonlinear damping terms to counteract modelling errors is designed to guarantee input-to-state practical stability of the corresponding subsystem, and then parameter adaptions are introduced to reduce the ultimate error bound. Finally, simulational examples are included to verify the results of theoretical analysis.

Neural network adaptive robust control of nonlinear systems in semi-strict feedback form

In this paper, the recently proposed neural network adaptive robust control (NNARC) design is generalized to synthesize performance oriented control laws for a class of nonlinear systems transformable to the semi-strict feedback forms through the incorporation of backstepping design techniques. Both repeatable (or state dependent) unknown nonlinearities and nonrepeatable unknown nonlinearities such as external disturbances are considered. In addition, unknown nonlinearities can exist in the virtual control input channel of each intermediate step as well. All unknown but repeatable nonlinear functions are approximated by outputs of multi-layer neural networks to achieve a better model compensation for an improved performance. All NN weights are tuned on-line with no prior training needed. In order to avoid the possible divergence of the on-line tuning of neural networks, discontinuous projections with fictitious bounds are used in the NN weight adjusting law to make sure that all NN weights are tuned within a prescribed range. By doing so, even in the presence of approximation error and nonrepeatable nonlinearities such as disturbances, a controlled learning is achieved and the possible destabilizing effect of on-line tuning of NN weights could be avoided. Certain robust control terms can then be constructed to attenuate various model uncertainties effectively for a guaranteed output tracking transient performance and a guaranteed final tracking accuracy in general. The precision motion control of a linear motor drive system with slow electrical dynamics is used as a case study to illustrate the proposed NNARC methodology. Experimental results with a simulated slow electrical dynamics are presented.