Output Feedback Dynamic Surface Control Research Articles

Fuzzy adaptive output feedback DSC design for SISO nonlinear stochastic systems with unknown control directions and dead-zones

In this paper, the adaptive fuzzy output feedback control problem is investigated for a class of single-input and single-output (SISO) stochastic nonlinear systems unknown dead-zones and unknown control direction. In the design, by using a linear state transformation, the unknown control coefficient and the unknown slope characteristic of the dead-zone are lumped together, and the original system is transformed to a new system. Fuzzy logic systems are employed to identified the uncertain nonlinear systems, a nonlinear fuzzy state observer is constructed to solve the problem of unmeasured states, and a special Nussbaum function is introduced into the control design to solve the unknown control direction problem, respectively. To address the problem of “explosion of complexity”, the dynamic surface control (DSC) technique is employed, a stable adaptive fuzzy output-feedback tracking control scheme is developed. The stability is proven based on Lyapnov theory, and it can guarantee that all the variables of closed-loop system are bounded in probability, and tracking error converges to a small neighborhood of zero. A numerical example is provided to verify the effectiveness of the proposed method.

Modified neural dynamic surface approach to output feedback of MIMO nonlinear systems.

We report an adaptive output feedback dynamic surface control (DSC), maintaining the prescribed performance, for a class of uncertain nonlinear systems with multiinput and multioutput. Designing neural network observers and modifying the DSC method achieves several control objectives. First, to achieve output feedback control, the finite-time echo state networks (ESN) observer with fast convergence is designed to obtain the online system states. Thus, the immeasurable states in traditional state feedback control are estimated and the unknown functions are approximated by ESN. Then, a modified DSC approach is developed by introducing a high-order sliding mode differentiator to replace the first-order filter in each step. Thus, the effect of filter performance on closed-loop stability is reduced. Furthermore, the input to state stability guarantees that all signals of the whole closed-loop system are semiglobally uniformly ultimately bounded. Specifically, the performance functions make the tracking errors converge to a compact set around equilibrium. Two numerical examples illustrated the proposed control scheme with satisfactory results.

Decentralized adaptive output feedback dynamic surface control of interconnected nonlinear systems with unmodeled dynamics

This paper is concerned with the centralized and decentralized adaptive output feedback control problem for a class of uncertain interconnected nonlinear systems with unmodeled dynamics and unmeasured states. The known requirement of the upper bounds of dynamic disturbances and coupling terms in the considered system is avoided. Decentralized observers are constructed based on the K-filters to estimate the unmeasured states of each subsystem. In the design of adaptive output feedback dynamic surface control, the unknown nonlinear functions are directly approximated by neural networks, while the coupling terms being lumped together with those unknown continuous functions produced in deduction are approximated as a whole. Using the defined compact set in the stability analysis, some unknown nonlinear continuous functions are dealt with effectively. It is proved that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. Simulation results are provided to illustrate the effectiveness of the proposed approach.

Prescribed performance adaptive fuzzy output-feedback dynamic surface control for nonlinear large-scale systems with time delays

The adaptive fuzzy decentralized output-feedback control method is proposed for a class of nonlinear large-scale systems. The considered nonlinear systems contain unstructured uncertainties, unknown time-varying delays, and immeasurable states. Fuzzy logic systems are used to approximate the unstructured uncertainties, and a fuzzy state observer is designed to estimate the unmeasured states. Based on the backstepping recursive design technique and the prescribed performance technique, a new adaptive fuzzy output-feedback control method is developed. In order to overcome the problem of “explosion of complexity” inherent in the backstepping control design, the dynamic surface control (DSC) technique is introduced into the control scheme. Based on Lyapunov–Krasovskii functional, it is proved that all the signals in the closed-loop system are bounded and the tracking errors remain an adjustable neighborhood of the origin with the prescribed performance bounds. The simulation examples and comparison with the previous control methods are provided to show the effectiveness of the proposed control approach.

Dynamic surface error constrained adaptive fuzzy output-feedback control of uncertain nonlinear systems with unmodeled dynamics

In this paper, an adaptive fuzzy output-feedback dynamic surface control (DSC) design with prescribed performance is investigated for a class of uncertain nonlinear systems in strict-feedback form. The considered nonlinear systems contain unknown nonlinear functions, unmodeled dynamics and immeasurable states. The fuzzy logic systems are used to model the unknown nonlinear system, and a fuzzy state observer is designed to estimate the immeasurable states. By transforming the errors into new virtual error variables, and based on DSC backstepping design technique and changing supply function, a new robust adaptive fuzzy output feedback control scheme is developed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed–loop system are bounded, and the dynamic surface errors are confined within the prescribed bounds for all times. Two simulation examples are provided to show the effectiveness of the proposed control approach.

Adaptive output feedback dynamic surface control of nonlinear systems with unmodeled dynamics and unknown high-frequency gain sign

In this paper, two adaptive output feedback control schemes are proposed for a class of nonlinear systems with unmodeled dynamics and unmeasured states as well as unknown high-frequency gain. Radial basis function (RBF) neural networks (NNs) are used to approximate the unknown nonlinear functions. K-filters are designed to estimate the unmeasured states. An available dynamic signal is introduced to dominate the unmodeled dynamics. By introducing the dynamic surface control (DSC) method, the bounded condition of the approximation error is removed, and the tracking control is achieved. Moreover, the number of adjustable parameters and the complexity of the design are both reduced. By theoretical analysis, the closed-loop system is shown to be semi-globally uniformly ultimately bounded (SGUUB). Simulation results are provided to illustrate the effectiveness of the proposed approach.

Adaptive nonlinear output-feedback dynamic surface control with unknown high-frequency gain sign

In this paper, an adaptive dynamic surface control (DSC) for a class of nonlinear systems with unknown high-frequency gain (HFG) sign is proposed. The novelty of our scheme is that we separate the first virtual control signal from the HFG, which enables us to estimate the HFG directly. As a result, the traditional Nussbaum function (NF) approach is abandoned. By using the proposed DSC, the adaptive laws are needed only at the first design step and the explosion of terms in backstepping control can be eliminated, which greatly reduces the computational burden. In particular, based on an initialisation technique, we prove that the performance of the system tracking error can be guaranteed even when the HFG sign is unknown. It is shown that all signals of the closed-loop system are semi-globally uniformly bounded. Simulation results illustrate that the proposed scheme is more applicable than that of the NF-based backstepping control.

A robust output-feedback adaptive dynamic surface control for linear systems with input disturbance

In this paper, a robust output-feedback adaptive control is proposed for linear time-invariant (LTI) singleinput single-output (SISO) plants with unmeasurable input disturbance. Using dynamic surface control (DSC) technique, it is shown that the explosion of complexity problem in backstepping control can be eliminated. Furthermore, the proposed adaptive DSC scheme has the following merits: 1) by introducing an initialization technique, the L ∞ performance of system tracking error can be guaranteed even if the plant high-frequency gain is unknown and the input disturbance exists, and 2) the adaptive law is necessary only at the first design step, which significantly reduces the design procedure. It is proved that with the proposed scheme, all the closed-loop signals are semiglobally uniformly ultimately bounded. Simulation results are presented to demonstrate the effectiveness of the proposed scheme.

Multivariable adaptive dynamic surface control based on norm estimation of unknown parameter matrices

In this article, a novel output-feedback adaptive dynamic surface control scheme is proposed for linear time-invariant multivariable plants based on the norm estimation of unknown parameter matrices. Besides avoiding the explosion of complexity problem in traditional multivariable backstepping design, the proposed scheme has the following features: (1) only one parameter needs to be updated on-line regardless of the plant order and input–output dimension, (2) only the Hurwitz condition is required for the high-frequency gain matrix and (3) the ℒ∞ performance of the tracking error can be guaranteed. It is shown that all signals of the closed-loop system are semi-globally uniformly bounded. Simulation results are given to illustrate the effectiveness of the proposed scheme.

A robust adaptive dynamic surface control for linear systems

In this article, a robust output-feedback adaptive dynamic surface control (DSC) is proposed for linear time-invariant single-input single-output plants with unmodelled dynamics and unmeasurable output disturbance. With the proposed adaptive DSC scheme, the ‘explosion of terms’ problem inherent in backstepping control is eliminated and the adaptive law is necessary only at the first design step, which significantly reduces the design procedure. More importantly, it is proved that with an initialisation technique, the ℒ∞ performance of the tracking error can be guaranteed even with unmodelled dynamics, bounded output disturbance exists and the plant high-frequency gain is unknown.

Observer-based adaptive fuzzy backstepping dynamic surface control design and stability analysis for MIMO stochastic nonlinear systems

In this paper, an adaptive fuzzy backstepping output feedback dynamic surface control (DSC) approach is developed for a class of multiinput and multioutput (MIMO) stochastic nonlinear systems with immeasurable states. Fuzzy logic systems are firstly utilized to approximate the unknown nonlinear functions, and then a fuzzy state observer is designed to estimate the immeasurable states. By combining adaptive backstepping technique and dynamic surface control (DSC) technique, an adaptive fuzzy output feedback backstepping DSC approach is developed. The proposed control method not only overcomes the problem of “explosion of complexity” inherent in the backstepping design methods, but also the problem of the immeasurable states. It is proved that all the signals of the closed-loop adaptive control stochastic system are semiglobally uniformly ultimately bounded (SUUB) in probability, and the observer errors and the output of the system converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approach.

An adaptive output feedback dynamic surface control for a class of nonlinear systems with unknown backlash-like hysteresis

This paper is devoted to the output feedback control for a class of nonlinear systems with unknown backlash-like hysteresis at the input. Based on a high-gain observer, an adaptive dynamic surface control scheme is proposed which is able to mitigate the effect of the hysteresis, to eliminate the explosion of terms inherent in backstepping control, and in particular, by introducing an initialization technique, to guarantee the ∞ performance of the system's tracking error. Another advantage of the proposed scheme is that the adaptive law is needed only at the first design step, which greatly simplifies the design procedure and makes our control easy to implement. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Adaptive dynamic surface control for a class of output-feedback nonlinear systems with guaranteed ℒ∞ tracking performance

In this article, an output-feedback adaptive dynamic surface control (DSC) is proposed for a class of nonlinear systems. It is proved that, by using the new scheme, the explosion of the complexity problem in a traditional backstepping design can be eliminated, the semi-global stability of a closed-loop system can be guaranteed and, in particular, by choosing the design parameters and initialising the filters and the update law properly, we show that the ℒ∞ performance of the system-tracking error can be achieved without over-parametrisation. Another advantage of the proposed scheme compared with those traditional backstepping control and current adaptive DSC schemes, whose adaptive control law is obtained through a series of steps recursively, is that the adaptive law is needed only at the first design step, and therefore significantly reduces the design procedure.

Observer-Based Adaptive Fuzzy Backstepping Control for a Class of Stochastic Nonlinear Strict-Feedback Systems

In this paper, two adaptive fuzzy output feedback control approaches are proposed for a class of uncertain stochastic nonlinear strict-feedback systems without the measurements of the states. The fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy state observer is designed for estimating the unmeasured states. On the basis of the fuzzy state observer, and by combining the adaptive backstepping technique with fuzzy adaptive control design, an adaptive fuzzy output feedback control approach is developed. To overcome the problem of "explosion of complexity" inherent in the proposed control method, the dynamic surface control (DSC) technique is incorporated into the first adaptive fuzzy control scheme, and a simplified adaptive fuzzy output feedback DSC approach is developed. It is proved that these two control approaches can guarantee that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) in mean square, and the observer errors and the output of the system converge to a small neighborhood of the origin. A simulation example is provided to show the effectiveness of the proposed approaches.

Adaptive Neural Network Decentralized Backstepping Output-Feedback Control for Nonlinear Large-Scale Systems With Time Delays

In this paper, two adaptive neural network (NN) decentralized output feedback control approaches are proposed for a class of uncertain nonlinear large-scale systems with immeasurable states and unknown time delays. Using NNs to approximate the unknown nonlinear functions, an NN state observer is designed to estimate the immeasurable states. By combining the adaptive backstepping technique with decentralized control design principle, an adaptive NN decentralized output feedback control approach is developed. In order to overcome the problem of "explosion of complexity" inherent in the proposed control approach, the dynamic surface control (DSC) technique is introduced into the first adaptive NN decentralized control scheme, and a simplified adaptive NN decentralized output feedback DSC approach is developed. It is proved that the two proposed control approaches can guarantee that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded, and the observer errors and the tracking errors converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approaches.