Observer-based adaptive fuzzy backstepping control of MIMO stochastic nonlinear strict-feedback systems

In this paper, an adaptive fuzzy output feedback control approach is proposed for a class of multiinput and multioutput (MIMO) 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. Utilizing the designed the fuzzy state observer and by combining the adaptive backstepping control design, an adaptive fuzzy output feedback control approach is developed. It is proved that the proposed control approach can guarantee that all the signals of the closed-loop 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 by appropriate choice of the design parameters. A simulation example is provided to show the effectiveness of the proposed approach.     

A new adaptive fuzzy sliding mode observer for a class of MIMO nonlinear systems

In this paper, a new adaptive fuzzy sliding mode (AFSM) observer is proposed which can be used for a class of MIMO nonlinear systems. In the proposed algorithm, the zero-input dynamics of the plant could be unknown. In this method, a fuzzy system is designed to estimate the nonlinear behavior of the observer. The output of fuzzy rules are tuned adaptively, based on the observer error. The output connection matrix is used to combine the observer errors of individual subsystems. A robust term, which is designed based on the sliding mode theory, is added to the observer to compensate the fuzzy estimation error. The estimation error bound is adjusted by an adaptive law. The main advantage of the proposed observer is that, unlike many of the previous works, the measured outputs is not limited to the first entries of a canonical-form state vector. The proposed observer estimates the closed-loop state tracking error asymptotically, provided that the output gain matrix includes Hurwitz coefficients. The chattering is eliminated by using boundary layers around the sliding surfaces and the observer convergence is proved using a Lyapunov-based approach. The proposed method is applied on a real multilink robot manipulator. The performance of the observer shows its effectiveness in the real world.     

Observer-based fractional-order adaptive type-2 fuzzy backstepping control of uncertain nonlinear MIMO systems with unknown dead-zone

Nonlinear Dynamics - A new problem of observer-based fractional adaptive type-2 fuzzy backstepping control for a class of fractional-order MIMO nonlinear dynamic systems with dead-zone input...     

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.     

Response analysis of fuzzy nonlinear dynamical systems

The transient and steady-state membership distribution functions (MDFs) of fuzzy response of a Duffing–Van der Pol oscillator with fuzzy uncertainty are studied by means of the fuzzy generalized cell mapping (FGCM) method. A rigorous mathematical foundation of the FGCM is established with a discrete representation of the fuzzy master equation for the possibility transition of continuous fuzzy processes. Fuzzy response is characterized by its topology in the state space and its possibility measure of MDFs. The evolutionary orientation of MDFs is in accordance with invariant manifolds toward invariant sets. In the evolutionary process of a steady-state fuzzy response with an increase of the intensity of fuzzy noise, a merging bifurcation is observed in a sudden change of MDFs from two sharp peaks of maximum possibility to one peak band around unstable manifolds.     

Command filter-based adaptive fuzzy decentralized control for large-scale nonlinear systems

Nonlinear Dynamics - This paper focuses on the decentralized finite-time prescribed performance control problem for a class of large-scale nonlinear interconnected systems with input dead zone...     

Adaptive fuzzy control of MIMO nonstrict-feedback nonlinear systems with fuzzy dead zones and time delays

Nonlinear Dynamics - This paper addresses an adaptive fuzzy control for a class of multi-input and multi-output nonlinear nonstrict-feedback systems with fuzzy dead zones, time delays and...     

Distributed adaptive fuzzy control approach for prescribed-time containment of uncertain nonlinear multi-agent systems with unknown hysteresis

Nonlinear Dynamics - Unknown hysteresis cannot be ignored in containment control, but the problem of prescribed-time containment for uncertain nonlinear multi-agent systems with unknown hysteresis...     

Robust control for MIMO hybrid dynamical system of underwater vehicles by composite adaptive fuzzy estimation of uncertainties

An organization structure of global oscillation with respect to a cracked rotor system with oil-film force is investigated in this paper. We profit from GPU cluster parallel computing to present a number of high-quality phase diagrams, and exhibit global dynamic characteristics of the system. An interesting scenario, “eye” of chaos, is discovered in this cracked rotor system, emerging as the accumulation limit of forward and reverse period-doubling bifurcation cascades. In this system, it is a common phenomenon that the vibration response of the rotor presents three typical characteristics in parameter space with the rotation speed increasing. Moreover, these phase diagrams assist us to identify multi-attractor coexisting that makes the dynamics behavior of this system become more enrich and complex. These results we represent get us better to understand the nonlinear response of the cracked rotor system and are beneficial to control and diagnose the crack.     

Fuzzy adaptive high-gain-based observer backstepping control for SISO nonlinear systems with dynamical uncertainties

In this paper, a fuzzy adaptive output feedback control approach is developed for a class of SISO strict-feedback nonlinear systems with unmeasured states, unmodeled dynamics, and dynamical disturbances. In the backstepping recursive design, fuzzy logic systems are used to approximate the unknown nonlinear functions, a fuzzy adaptive high-gain observer is designed to estimate the unmeasured states; a dynamic signal is incorporated into the control scheme to dominate the dynamic uncertainties. Using the states estimates and combining the backstepping design technique, a fuzzy adaptive output feedback control is constructed recursively. It is proved that the proposed fuzzy adaptive output feedback control scheme can guarantee the all signals in the closed-loop system are semiglobally uniformly ultimately bounded (SUUB), and the observer and tracking error converges to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated via an example.     

Prescribed performance adaptive fuzzy output-feedback control of uncertain nonlinear systems with unmodeled dynamics

In this paper, an adaptive fuzzy output-feedback control approach is proposed for a class of uncertain nonlinear systems with unknown nonlinear functions, unmodeled dynamics, and 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. To solve the problem of unmodeled dynamics, the dynamical signal combined with changing supply function is incorporated into the backstepping recursive design technique. Under the framework of the backstepping control design technique and incorporated by the predefined performance technique, a new robust adaptive fuzzy output feedback control scheme is constructed. It is shown that all the signals of the resulting closed-loop system are bounded, and the system output remains an adjustable neighborhood of the origin with the prescribed performance bounds. A simulation example and comparison with the previous control methods are provided to show the effectiveness of the proposed control approach.     

A linear approach to generalized minimum variance controller design for MIMO nonlinear systems

Designing minimum variance controllers (MVC) for nonlinear systems is confronted with many difficulties. The methods which are able to identify MIMO nonlinear systems are scarce, and linear models are not accurate in modeling nonlinear systems. In this paper, Vector ARX (VARX) models are proposed for designing MVC and generalized minimum variance controller (GMVC) for linear and nonlinear systems, and the accuracy of these models in approximating the nonlinear MIMO system is studied. However, the VARX is a linear model. It is shown that this model can identify some kinds of nonlinear systems with any desired accuracy. Therefore, the controller designed by the VARX is accurate, even for these nonlinear systems. The proposed controller is tested on a both linear system and a nonlinear four-tank benchmark process. In spite of the simplicity of designing GMVCs for the VARX models, the results show that the proposed method is accurate and implementable.     

Finite-time adaptive fuzzy command filtered control for nonlinear systems with indifferentiable non-affine functions

Nonlinear Dynamics - This paper mainly addresses the finite-time tracking problem of pure-feedback systems with indifferentiable non-affine functions. A novel adaptive fuzzy finite-time command...     

Event-triggered fixed-time adaptive fuzzy control for state-constrained stochastic nonlinear systems without feasibility conditions

Nonlinear Dynamics - The problem of event-triggered fixed-time control for state-constrained stochastic nonlinear systems is discussed in this article. Different from the barrier Lyapunov function...     

Extended state observer-based adaptive prescribed performance control for a class of nonlinear systems with full-state constraints and uncertainties

Nonlinear Dynamics - In this paper, an extended state observer-based adaptive prescribed performance control technique is proposed for a class of nonlinear systems with full-state constraints and...     

Decentralized adaptive fuzzy control of large-scale nonaffine nonlinear systems by state and output feedback

This paper develops two novel decentralized adaptive fuzzy control methods of large-scale nonaffine uncertain nonlinear systems. By using a fuzzy inference system and implicit function theorem, a decentralized direct adaptive state feedback fuzzy control algorithm is firstly presented for a class of large-scale nonaffine continuous-time systems. By using a high-gain observer to reconstruct the system states, an extension is made to a decentralized output feedback control of unmeasurable interactive nonaffine systems. The decentralized adaptive fuzzy control schemes via state and output feedback guarantee the stability of the closed-loop large-scale systems. The effectiveness of the developed approaches is demonstrated through simulation results of a platoon of vehicles within an automated highway system.     

Active disturbance rejection adaptive control of uncertain nonlinear systems: theory and application

This paper proposes an active disturbance rejection adaptive controller for tracking control of a class of uncertain nonlinear systems with consideration of both parametric uncertainties and uncertain nonlinearities by effectively integrating adaptive control with extended state observer via backstepping method. Parametric uncertainties are handled by the synthesized adaptive law and the remaining uncertainties are estimated by extended state observer and then compensated in a feedforward way. Moreover, both matched uncertainties and unmatched uncertainties can be estimated by constructing an extended state observer for each channel of the considered nonlinear plant. Since parametric uncertainties can be reduced by parameter adaptation, the learning burden of extended state observer is much reduced. Consequently, high-gain feedback is avoided and improved tracking performance can be expected. The proposed controller theoretically guarantees a prescribed transient tracking performance and final tracking accuracy in general while achieving asymptotic tracking when the uncertain nonlinearities are not time-variant. The motion control of a motor-driven robot manipulator is investigated as an application example with some suitable modifications and improvements, and comparative simulation results are obtained to verify the high tracking performance nature of the proposed control strategy.     

Reduced-order observer-based backstepping tracking control for a class of stochastic nonlinear systems

In this paper, an output feedback tracking control scheme is put forwarded for a class of stochastic nonlinear systems, whose dynamics involve not only unknown parameters but also unmeasured states multiplied by output nonlinearities. A type of reduced-order observer is first developed. By adding some output related items in the observer, the estimation error realize global asymptotic convergence under disturbance free condition, and global bounded convergence when considering disturbance. Besides, the dimension of the closed-loop system is reduced, and the update law of this observer gain is beneficial for steady tracking. After the observer was established, the controller is constructed by employing the adaptive backstepping approach, and a smooth nonsingular robust item is proposed to handle the influence of stochastic disturbance. All the signals in the closed system is proved to be globally bounded in probability. Moreover the output tracking error converges to an arbitrary small neighborhood of the origin by proper choosing of the design parameters. The simulation results based on current control scheme and the comparison with the previous method illustrate that the proposed output feedback scheme realizes good tracking performance and strong ability on stochastic disturbance attenuation.