Immeasurable States Research Articles

Robust dissipative filtering for a kind of T-S fuzzy descriptor system with immeasurable premise variables

The problem of delay-dependent robust dissipative filtering is investigated for a kind of Takagi–Sugeno (T-S) fuzzy descriptor system with immeasurable premise variables. By utilising the free-weighting matrix approach and combining them with the structural characteristics of the error system, we propose the solvable conditions of the dissipative filter that ensure an error system with immeasurable states is admissible and strictly dissipative. This implies that it is not necessary to assume that the error systems are regular and impulse-free prior to designing filters. The derived method can be applied broadly to nonlinear systems. Also, the solvable condition of the dissipative filter with measurable states is a special case of this study. We also elicit the design methods of the H∞ and passive filters, which could potentially reduce the cost and time spent on the filter design. Finally, we perform simulations to validate the derived methods for two kinds of nonlinear descriptor systems.

Output feedback dynamic surface controller design for airbreathing hypersonic flight vehicle

This paper addresses issues related to nonlinear robust output feedback controller design for a nonlinear model of airbreathing hypersonic vehicle. The control objective is to realize robust tracking of velocity and altitude in the presence of immeasurable states, uncertainties and varying flight conditions. A novel reduced order fuzzy observer is proposed to estimate the immeasurable states. Based on the information of observer and the measured states, a new robust output feedback controller combining dynamic surface theory and fuzzy logic system is proposed for airbreathing hypersonic vehicle. The closedloop system is proved to be semi-globally uniformly ultimately bounded (SUUB), and the tracking error can be made small enough by choosing proper gains of the controller, filter and observer. Simulation results from the full nonlinear vehicle model illustrate the effectiveness and good performance of the proposed control scheme.

Observer-Based Adaptive Neural Network Control for Nonlinear Systems in Nonstrict-Feedback Form.

This paper focuses on the problem of adaptive neural network (NN) control for a class of nonlinear nonstrict-feedback systems via output feedback. A novel adaptive NN backstepping output-feedback control approach is first proposed for nonlinear nonstrict-feedback systems. The monotonicity of system bounding functions and the structure character of radial basis function (RBF) NNs are used to overcome the difficulties that arise from nonstrict-feedback structure. A state observer is constructed to estimate the immeasurable state variables. By combining adaptive backstepping technique with approximation capability of radial basis function NNs, an output-feedback adaptive NN controller is designed through backstepping approach. It is shown that the proposed controller guarantees semiglobal boundedness of all the signals in the closed-loop systems. Two examples are used to illustrate the effectiveness of the proposed approach.

Output feedback robust stabilization of switched fuzzy systems with time-delay and actuator saturation

This paper investigates the output feedback robust stabilization problem of a class of switched fuzzy systems with immeasurable states and actuator saturation. A switched state observer is designed to obtain the estimations of the unmeasured states. By using parallel compensation design (PDC) scheme, a robust fuzzy output feedback control law and the signal switching law are constructed, respectively. The sufficient conditions of ensuring the switched fuzzy control system asymptotic stabilization are proposed and formulated in the form of linear matrix inequalities (LMIs). It is proved that proposed control scheme can guarantee that whole closed-loop system is asymptotically stable in the sense of the Lyapunov function. One numerical example and a practical example are given to illustrate the effectiveness of the proposed control method.

Decentralized adaptive neural output feedback control of a class of large-scale time-delay systems with input saturation

A decentralized adaptive neural output feedback control scheme is presented for a class of large-scale time-delay systems with saturating inputs. The observer is constructed to estimate the immeasurable states of the system and the auxiliary system is designed to compensate the nonsmooth nonlinearities of input saturation constraints. Also, the control strategy is developed by the backstepping recursive method combining with neural networks (NNs) for the approximation of the unknown functions and dynamic surface control (DSC) technique for the well known ‘explosion of complexity’ problem. The advantage of this scheme is that it only relies on the output information of the system and there is no requirement for exact priori knowledge about the system parameters. It is proved that the control approach guarantees all signals in the closed-loop system uniformly ultimately bounded. Simulation results are provided to demonstrate the effectiveness and usefulness of the proposed strategy.

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.

Adaptive Tracking Control for A Class of Nonlinear Systems With a Fuzzy Dead-Zone Input

This paper focuses on a problem of adaptive control for a class of nonlinear strict-feedback systems with a fuzzy dead zone and immeasurable states. By using the adaptive backstepping technique, an adaptive fuzzy output-feedback controller is constructed. The proposed control method requires only one adaptive law for an nth-order system. Compared with the conventional deterministic dead-zone models in previous articles, the main advantage of this paper is that the proposed dead-zone model is uncertain and fuzzy. By defuzzifying for fuzzy dead zone ~Γ(u) and employing an integrated design, an integrated fuzzy controller is constructed. It is proved that, even though the dead-zone input ~Γ(u) is fuzzy, the integrated fuzzy controller can make the closed-loop system semiglobally uniformly ultimately bounded and the tracking error converge to a small neighborhood of the origin. Finally, simulation results are provided to show the effectiveness of the proposed approach.

Adaptive fuzzy output feedback tracking control with prescribed performance for chemical reactor of MIMO nonlinear systems

In this paper, a fuzzy adaptive control approach with prescribed performance is developed for a chemical reactor of multi-input and multi-output nonlinear systems with unmeasured states. Using fuzzy logic systems to model the uncertain nonlinear systems, a fuzzy adaptive observer is designed for immeasurable states estimations. Under the framework of the backstepping design and incorporated by the predefined performance technique, a new fuzzy adaptive output feedback control is developed. It is shown that all the signals of the resulting closed-loop systems are bounded, and the tracking errors remain within an adjustable neighborhood of the origin with the prescribed performance bounds. The detailed simulation results and performance comparisons are provided to demonstrate the effectiveness of the proposed control approach.

Observed-Based Adaptive Fuzzy Tracking Control for Switched Nonlinear Systems With Dead-Zone.

In this paper, the problem of adaptive fuzzy output-feedback control is investigated for a class of uncertain switched nonlinear systems in strict-feedback form. The considered switched systems contain unknown nonlinearities, dead-zone, and immeasurable states. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, a switched fuzzy state observer is designed and thus the immeasurable states are obtained by it. By applying the adaptive backstepping design principle and the average dwell time method, an adaptive fuzzy output-feedback tracking control approach is developed. It is proved that the proposed control approach can guarantee that all the variables in the closed-loop system are bounded under a class of switching signals with average dwell time, and also that the system output can track a given reference signal as closely as possible. The simulation results are given to check the effectiveness of the proposed approach.

Adaptive fuzzy output feedback control for a class of nonaffine nonlinear systems with unknown dead-zone input

In this paper, an adaptive fuzzy backstepping output feedback control approach is developed for a class of SISO nonaffine nonlinear systems with unknown dead-zone input and immeasurable states. Within this scheme, the original nonaffine system is firstly transformed into an affine-like form by using Taylor series expansion, the unknown dead-zone input is treated as a combination of a linear and a bounded disturbance-like term, and a state observer is introduced to estimate the system states. The fuzzy logic systems are utilized to directly approximate the desire virtual control law, and a novel adaptive fuzzy output feedback controller is designed via backstepping. A main advantage of the proposed controller is that only one adaptive parameter needs to be updated online in backstepping design process. Theoretically, it is proved that the presented adaptive fuzzy controller can guarantee that the tracking error converges to a small neighborhood of the origin and all signals in closed-loop are bounded. Finally, the simulation results validate the effectiveness of the proposed scheme.

Adaptive Fuzzy Output-Feedback Control of Pure-Feedback Uncertain Nonlinear Systems With Unknown Dead Zone

In this paper, an adaptive fuzzy output-feedback control is investigated for a class of pure-feedback uncertain nonlinear systems with unknown dead-zone inputs and immeasurable states. In this research, fuzzy logic systems are used to identify the unknown nonlinear functions, and a state filter observer is designed to estimate the unmeasured states. Based on the information of the dead-zone slopes as well as treating the unknown inputs coefficients as a system uncertainty, a new adaptive fuzzy output feedback control approach is developed via the backstepping recursive design technique. The stability of the resulting closed-loop system is proved and a simulation example is provided to show the effectiveness of the proposed control approach. The important feature of the proposed adaptive fuzzy controller is that it can solve the states immeasurable and the unknown dead-zone problems that exist in the previous publications and extends the existing results on strict-feedback control to the counterpart on pure-feedback control.

Adaptive Neural Stabilizing Controller for a Class of Mismatched Uncertain Nonlinear Systems by State and Output Feedback.

In this paper, first, an adaptive neural network (NN) state-feedback controller for a class of nonlinear systems with mismatched uncertainties is proposed. By using a radial basis function NN (RBFNN), a bound of unknown nonlinear functions is approximated so that no information about the upper bound of mismatched uncertainties is required. Then, an observer-based adaptive controller based on RBFNN is designed to stabilize uncertain nonlinear systems with immeasurable states. The state-feedback and observer-based controllers are based on Lyapunov and strictly positive real-Lyapunov stability theory, respectively, and it is shown that the asymptotic convergence of the closed-loop system to zero is achieved while maintaining bounded states at the same time. The presented methods are more general than the previous approaches, handling systems with no restriction on the dimension of the system and the number of inputs. Simulation results confirm the effectiveness of the proposed methods in the stabilization of mismatched nonlinear systems.

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.

Adaptive fuzzy decentralized tracking fault-tolerant control for stochastic nonlinear large-scale systems with unmodeled dynamics

This paper studies the adaptive fuzzy decentralized tracking fault-tolerant control design problem for a class of unknown stochastic nonlinear strict-feedback systems with actuator faults. The stochastic systems under study have the characterizations of unknown functions, unmodeled dynamics and without the direct measurements of state variables. Fuzzy logic systems are employed to identify the unknown stochastic nonlinear systems, and a fuzzy state observer is established for estimating the immeasurable states. The dynamic surface control (DSC) design approach based on the backstepping technique is presented to design adaptive decentralized tracking fault-tolerant controller. It is proved that proposed control approach guarantees that all the variables of the closed-loop system are bounded in probability, and also that the tracking errors converge to an adjustable neighborhood of the origin regardless of actuator faults and unmodeled dynamics. The simulation results are provided to illustrate the effectiveness of the proposed control approach.

A Neural Network Combined Inverse Controller for a Two-Rear-Wheel Independently Driven Electric Vehicle

Vehicle active safety control is attracting ever increasing attention in the attempt to improve the stability and the maneuverability of electric vehicles. In this paper, a neural network combined inverse (NNCI) controller is proposed, incorporating the merits of left-inversion and right-inversion. As the left-inversion soft-sensor can estimate the sideslip angle, while the right-inversion is utilized to decouple control. Then, the proposed NNCI controller not only linearizes and decouples the original nonlinear system, but also directly obtains immeasurable state feedback in constructing the right-inversion. Hence, the proposed controller is very practical in engineering applications. The proposed system is co-simulated based on the vehicle simulation package CarSim in connection with Matlab/Simulink. The results verify the effectiveness of the proposed control strategy.

Adaptive fuzzy output feedback dynamic surface control of interconnected nonlinear pure-feedback systems.

In this paper, an adaptive fuzzy decentralized output feedback control design is presented for a class of interconnected nonlinear pure-feedback systems. The considered nonlinear systems contain unknown nonlinear uncertainties and the states are not necessary to be measured directly. Fuzzy logic systems are employed to approximate the unknown nonlinear functions, and then a fuzzy state observer is designed and the estimations of the immeasurable state variables are obtained. Based on the adaptive backstepping dynamic surface control design technique, an adaptive fuzzy decentralized output feedback control scheme is developed. It is proved that all the variables of the resulting closed-loop system are semi-globally uniformly ultimately bounded, and also that the observer and tracking errors are guaranteed to converge to a small neighborhood of the origin. Some simulation results and comparisons with the existing results are provided to illustrate the effectiveness and merits of the proposed approach.

Reduced Parameter Sensitivity Stator Flux Linkage Observer in Deadbeat-Direct Torque and Flux Control for IPMSMs

Direct torque control (DTC) has become a widely acceptable alternative to field-oriented control. Deadbeat-direct torque and flux control (DB-DTFC) is a significant improvement over the classical DTC methods and provides opportunities for fast simultaneous control of torque and dynamic loss minimization. DB-DTFC uses estimated torque and stator flux magnitude from a stator flux observer as feedback. The constant parameter state observer utilizes the system model to estimate immeasurable physical states or dynamics of the real system. However, the constant parameter stator flux observer is parameter sensitive at low frequencies. This paper presents a flux observer that utilizes disturbance input decoupling (DID) so that even under varying or inaccurately identified machine parameters, stator flux linkage and torque can be accurately estimated. The structure of the DID flux observer is theoretically derived and discussed. The flux estimation error due to the parameter variations is decoupled through the disturbance information from a stator current observer. Comparative evaluation of the DID flux observer versus the constant parameter flux observer has been performed via both simulation and experiments.

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.

Attitude control of a small-scale helicopter based on backstepping

In this paper, the attitude control of a small-scale helicopter is investigated. The main rotor flapping dynamics is explicitly explored to improve the control performance. Backstepping technique is adopted to derive the control law, and extended state observer is applied to estimate the immeasurable states and disturbance. Together with these two approaches, sliding mode controller is designed to force the actual attitude of the closed-loop system to converge to the reference attitude. Simulation and experimental results show that the proposed controller yields excellent performance and robustness.

Adaptive fuzzy decentralised output feedback control of pure‐feedback large‐scale stochastic non‐linear systems with unknown dead zone

In this study, a robust adaptive fuzzy decentralised backstepping output feedback control approach is proposed for a class of uncertain non-linear stochastic large-scale systems in pure-feedback form. The non-linear large-scale systems under study have unknown non-linear functions, unknown dead-zone and immeasurable states. Fuzzy logic systems are used to approximate the unknown non-linear functions, and a K-filters state observer is designed for estimating the unmeasured states. Based on the information of the bounds of the dead-zone slopes as well as treating the time-varying inputs coefficients as a system uncertainty, a robust adaptive fuzzy decentralised output feedback control approach is constructed via the backstepping recursive design technique. It is shown that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded in probability, and the observer errors and the output of the system can be regulated to a small neighbourhood of the origin by choosing design parameters appropriately. A simulation example is provided to show the effectiveness of the proposed approach.