Immeasurable Premise Variables Research Articles

Observer design based on D-stability and Finsler’s lemma for interconnected Takagi–Sugeno systems with immeasurable premise variables

This paper deals with the observer design for a class of Interconnected Takagi–Sugeno (TS) systems with Immeasurable Premise Variables (IPV). We first investigate the D-stability of Luenberger-like interconnected multiple observers. However, the resulting constraints can be somewhat conservative due to the use of a common Lyapunov matrix. Then, the so-called Finsler’s lemma is used to relax the D-stability conditions through the introduction of additional slack variables providing more flexibility and extra degrees of freedom. The designed conditions are expressed as Linear Matrix Inequalities (LMIs). The proposed approaches are applied in simulation to a Proton Exchange Membrane Fuel Cell (PEMFC) system and a four-tank system.

Event-triggered non-fragile state estimator design for interval type-2 Takagi–Sugeno fuzzy systems with bounded disturbances

In this paper, the state estimator design problem of interval type-2 Takagi–Sugeno fuzzy systems suffering from bounded disturbances is studied. To enhance the resilience of the estimator, a non-fragile design scheme is proposed to tackle the estimator gain variations. Meanwhile, an event-triggered communication mechanism is introduced for relieving the transmission burden over networks. To settle down the non-fragile estimator design issue subject to bounded disturbances and event-induced error, we propose a new definition of quadratic boundedness via the multiple Lyapunov functions. Based on this definition, a novel co-design method of estimator and event generator for fuzzy system models in the presence of both measurable and immeasurable premise variables is presented. In virtue of quadratic boundedness framework, less conservative conditions of the existence and quadratic stability of the fuzzy estimators are obtained, and the upper bound of estimation error is given explicitly. The desired estimator gains are determined by convex optimization technique using slack matrices. Two illustrative examples are exploited to validate the availability and superiority of the addressed design approach.

Positivity and separation principle for observer-based output-feedback disturbance attenuation of uncertain discrete-time fuzzy models with immeasurable premise variables

We propose a robust observer-based output-feedback (OBOF) controller design method for the positive stabilization of discrete-time Takagi–Sugeno (T–S) fuzzy models subject to immeasurable premise variables, parametric uncertainties, and l∞ disturbances. The results of this paper are as follows. First, a new fuzzy OBOF controller structure is used to improve the possibility that the uncertain closed-loop system is positive. Second, the separation principle is demonstrated for the l∞–l∞ disturbance attenuation. Finally, the stability, positivity, and disturbance attenuation of T–S fuzzy closed-loop models are analyzed in the presence of the perturbation caused by the imperfect premise matching by the immeasurable premise variable.

Descriptor-based T–S fuzzy fault-tolerant control for delayed systems with immeasurable premise variables

Descriptor-based T–S fuzzy fault-tolerant control for delayed systems with immeasurable premise variables

Simultaneous Sensor and Actuator Fault Reconstruction by Using a Sliding Mode Observer, Fuzzy Stability Analysis, and a Nonlinear Optimization Tool

This paper proposes a Takagi–Sugeno (TS) fuzzy sliding mode observer (SMO) for simultaneous actuator and sensor fault reconstruction in a class of nonlinear systems subjected to unknown disturbances. First, the nonlinear system is represented by a TS fuzzy model with immeasurable premise variables. By filtering the output of the TS fuzzy model, an augmented system whose actuator fault is a combination of the original actuator and sensor faults is constructed. An performance criteria is considered to minimize the effect of the disturbance on the state estimations. Then, by using two further transformation matrices, a non-quadratic Lyapunov function (NQLF), and fmincon in MATLAB as a nonlinear optimization tool, the gains of the SMO are designed through the stability analysis of the observer. The main advantages of the proposed approach in comparison to the existing methods are using nonlinear optimization tools instead of linear matrix inequalities (LMIs), utilizing NQLF instead of simple quadratic Lyapunov functions (QLF), choosing SMO as the observer, which is robust to the uncertainties, and assuming that the premise variables are immeasurable. Finally, a practical continuous stirred tank reactor (CSTR) is considered as a nonlinear dynamic, and the numerical simulation results illustrate the superiority of the proposed approach compared to the existing methods.

Proportional Observer design based on [formula omitted]-stability and Finsler's Lemma for Takagi-Sugeno systems

This paper concerns Proportional Observer design for Takagi-Sugeno (TS) systems with Immeasurable Premise Variables using D-stability constraints and L2-gain analysis. The D-stability is used to control the dynamics of the designed observer (eigenvalues clustering in a prescribed Linear Matrix Inequality region) while the L2 technique minimizes the effect of Immeasurable Premise Variables on the state estimation error. In addition, Finsler's Lemma provides more flexibility and extra degrees of freedom through slack variables to obtain relaxed stability conditions. Numerical examples are presented to illustrate the effectiveness of the proposed approaches.

Adaptive event-triggered finite-time [formula omitted] control for fuzzy semi-Markovian jump systems with immeasurable premise variables

This paper addresses the adaptive event-triggered finite-time H∞ control problem of Takagi-Sugeno fuzzy semi-Markovian jump systems with immeasurable premise variables. Firstly, different from some existed works, the restrictions of measurable system states and measurable premise variables of nonlinear plant are removed and the fuzzy observer is designed to estimate unmeasurable system states. Then, a novel adaptive event-triggered scheme is firstly proposed to reduce the number of data transmission while ensuring the reliable system performance. Subsequently, the asynchronous problem about premise variables, namely, the premise variables of fuzzy system are not consistent with premise variables of fuzzy event-triggered controller is dealt with by utilizing an asynchronous method. By applying the delay system method, free-weighting matrix approach and slack matrix variables, novel sufficient conditions are derived to guarantee the finite-time H∞ performance of the closed-loop system, where the nonlinear terms caused by network-induced delay and partly unknown transition rates can be tackled by using suitable method. Finally, the single-link robot arm system is presented to affirm the efficiency of the obtained theoretical results.

An improved approach to fuzzy dynamic output feedback H ∞ control of continuous-time Takagi–Sugeno fuzzy systems

This paper studies the problem of dynamic output feedback control for continuous-time Takagi–Sugeno fuzzy systems. Based on the fuzzy Lyapunov functions without the special structure, a controller design method is developed and the relaxed stabilisation conditions are proposed. First, some shortcomings of the existing results are improved and a new approach is proposed for bounding the time derivatives of the membership functions. Then, less conservative conditions are obtained by introducing regulable parameters and applying the matrix decoupling techniques, which guarantee the prescribed performance. Moreover, the relaxation technique proposed in this paper is also suitable for the fuzzy system with immeasurable premise variables. Finally, some examples are provided to demonstrate the validity of the approach.

Sensor and actuator fault-tolerant control based on fuzzy unknown input observer: A polynomial fuzzy approach

This paper studies sensor and actuator Fault-Tolerant Control (FTC) of nonlinear systems. The fault tolerance is necessary to have desired performance and prevent the system from instability. A Polynomial Fuzzy Unknown Input Observer (PFUIO) with immeasurable premise variable is proposed to estimate the states of the system, and sensor and actuator faults; and to use them in the controller to compensate the faults. The essence of the sensor fault necessitates considering the third class of Polynomial Fuzzy Model (PFM) with immeasurable premise variables. This makes the design procedure more complicated. Application of PFM reduces the conservatism and increases modeling accuracy. Moreover, the disturbance and model uncertainties are considered to realize more practical conditions. The polynomiality leads to Sum Of Squares (SOS), which can be solved using existing software. The proposed approach is evaluated by applying it to the inverted pendulum system. Simulating results show better performance of the proposed method as compared with the Linear Matrix Inequality (LMI) approach

Dynamic Output Feedback Controller Design for Uncertain Takagi–Sugeno Fuzzy Systems: A Premise Variable Selection Approach

This article presents new design conditions of full-order dynamic output feedback controllers for continuous-time Takagi–Sugeno (T–S) fuzzy systems allowing the selection of premise variables to be used in the control law. The fuzzy output controller is allowed to have a different number of fuzzy rules and a different set of membership functions from the T–S model. This includes the cases of complete or partial immeasurable premise variables. The main aspect of the proposed methodology is to present conditions such that the control gains are independent of the premise variables that cannot be measured allowing flexibility for the designer in a realistic output feedback context. For this purpose, the design conditions are expressed as linear matrix inequality relaxations combined with scalar parameters that provide extra degrees of freedom. The proposed control methodology also deals with model uncertainties and the use of fuzzy Lyapunov functions. The effectiveness and applicability of the methodology are shown through numerical examples.

Sliding Mode Control for a Class of Nonlinear Singular Systems With Partly Immeasurable Premise Variables

This paper investigates the problem of sliding mode controller design for a class of T-S fuzzy singular systems (TSFSSs) with partly immeasurable premise variables. By analyzing the different cases of immeasurable premise variables, novel state-feedback, and static output-feedback-based sliding mode controllers design methods are first developed. The information of measurable premise variables in TSFSS is utilized to design the controllers. Attention is focused on solving the problem of sliding mode controllers design for TSFSS with immeasurable premise variables related to time and system states. Further, based on the new sliding mode control (SMC) methods, some new convex conditions for designing sliding mode controllers are proposed. It is shown that the proposed sliding mode controllers design approaches have the advantage over existing SMC methods to stabilize the TSFSS with immeasurable premise variables. Finally, two simulation results are given to verify the feasibility and effectiveness of the proposed methods.

Design of a Fault Tolerant Sampled-Data Fuzzy Observer With Exponential Time-Varying Gains

This paper deals with the sampled-data fuzzy observer design problem with time-varying gains under the sensor fault consideration. To this end, a nonlinear system with sensor fault is represented by a Takagi-Sugeno fuzzy model with immeasurable premise variables. The sensor fault considered in this paper is assumed to be a time-varying uncertain matrix included in measurements. The observer is designed to consist of gains varying exponentially between two consecutive sampling instants, by which the equilibrium point of the estimation error dynamics is asymptotically exponentially stabilized. In addition, the observer considered in this paper is assumed not to share the same premise variable with a system. Unlike previous studies, this paper proposes a method handling this mismatched premise problem by using an H-infinity criterion. The proposed observer design condition is formulated in terms of linear matrix inequalities, which is relaxed based on a novel fuzzified Lyapunov-Krasovskii functional and a matrix inequality. Finally, two simulation examples are given to validate the effectiveness of the proposed method.

전반부 불일치 조건에서의 불확실한 시스템의 상태 추정을 위한 샘플데이터 퍼지 관측기 설계

In this paper, we propose a sampled-data fuzzy observer design technique for estimating the state variables of a nonlinear system with model uncertainty. It is assumed that the IF-THEN rules of the fuzzy system contains immeasurable premise variables, which complicates the observer design. In this paper, the observer is assumed not to share the same premise part with that of the system in order to deal with the immeasurable premise condition. After then, the error between the observer and the system including model uncertainty is represented by the Takagi-Sugeno (T-S) fuzzy model. In order to minimize the impact of imperfect premise matching, model uncertainty, and disturbances on the state estimation, an HSUB∞/SUB performance criterion is defined. Based on the fuzzy Lyapunov function, we derive a sufficient condition in the form of linear matrix inequality to ensure that the error dynamics is asymptotically stable and satisfy the HSUB∞/SUB condition. Finally, a simulation example verifies the superiority of the proposed method.

Robust Interval Type-2 Fuzzy Observer for Fault Detection of Networked Control Systems Subject to Immeasurable Premise Variables

In this paper, a novel observer design has been suggested for fault detection of networked control systems under random measurement delays. A randomly varying communication delay structure has been assumed in data transmission between the physical system and the observer. In order to increase the applicability of the proposed Takagi-Sugeno fuzzy observer, it has been contemplated to be under immeasurable premise variables. In addition, time-varying parameter uncertainties are added to the system, which contribute to the system uncertainties. Theoretical materials related to the system and the observer design with a predetermined H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> index are provided resulting in less conservative constraints in the proof of asymptotical mean-square stability of the closed-loop system. Simulation results, which have been applied to a real-world system of tunnel diode circuit, have shown how the proposed observer would benefit from the use of interval type-2 fuzzy sets in dealing with uncertainties of the system.

Controller synthesis for continuous T-S fuzzy systems with partly immeasurable premise variables

In this paper, the controller synthesis problem for continuous T-S fuzzy systems with partly immeasurable premise variables is studied. The objective is to synthesize an observer-based controller to bound the reachable set of the system by an ellipsoid set such that the problem of state bounding can be addressed. First, the measurable premise variables and the estimated immeasurable premise variables are simultaneously utilized to construct the controller. Then, the information of the measurable premise variables is employed for deriving the controller synthesis criterion. In the end, the effectiveness of the presented approach is confirmed by an example.

Takagi–Sugeno Model-Based Sliding Mode Observer Design for Finite-Time Synthesis of Semi-Markovian Jump Systems

This paper is concerned with finite-time sliding mode control (SMC) of continuous-time semi-Markovian jump systems with immeasurable premise variables via fuzzy approach. First, an integral sliding surface is constructed based on fuzzy observer. Second, an observer-based SMC law is synthesized to guarantee finite-time reachability of the predefined sliding surface before the prescribed time. Third, through finite-time boundedness analysis, the required boundedness performance is conducted at the reaching phase first and then the sliding motion phase, respectively. Furthermore, sufficient conditions in terms of linear matrix inequalities (LMIs) are established to guarantee the required boundedness performance of the overall closed-loop controlled system during the two phases with generally uncertain transition rates (TRs) simultaneously. Finally, a practical example is given to show the validity of the established method numerically.

Distributed H∞ filter design for T-S fuzzy systems with Sigma-Delta quantisation via non-PDC scheme

The paper focuses on the distributed filtering problem over wireless sensor networks (WSNs) for a class of discrete-time T-S fuzzy systems with immeasurable premise variables and Sigma-Delta quantiser. Two defectives are considered including packet losses and multiplicative noises, which can be represented by some mutual independent random variables, respectively. Unlike conventional logarithmic quantiser, by utilising the Sigma-Delta dynamic quantiser, the quantised measurement outputs are broadcasted to the distributed filters over WSNs, only requiring a finite number of quantisation levels, and the static errors can be eliminated simultaneously. Using non-PDC scheme, an estimated premise variable-dependent distributed filter is designed over WSNs. Then treating the premise variables as uncertainties, a robust distributed filtering problem is considered for such an uncertain filtering error system. Based on the fuzzy Lyapunov function, the less conservative mean-square stable conditions with a prescribed performance index for the uncertain filtering error dynamical systems are presented. The filter parameters are determined by solving a set of linear matrix inequalities (LMIs). Finally, a tunnel diode circuit model and a numerical example are presented to illustrate the theoretical findings.

Adaptive Control of Nonlinear Semi-Markovian Jump T-S Fuzzy Systems With Immeasurable Premise Variables via Sliding Mode Observer.

The issue of observer-based adaptive sliding mode control of nonlinear Takagi-Sugeno fuzzy systems with semi-Markov switching and immeasurable premise variables is investigated. More general nonlinear systems are described in the model since the selections of premise variables are the states of the system. First, a novel integral sliding surface function is proposed on the observer space, then the sliding mode dynamics and error dynamics are obtained in accordance with estimated premise variables. Second, sufficient conditions for stochastic stability with an H∞ performance disturbance attenuation level γ of the sliding mode dynamics with different input matrices are obtained based on generally uncertain transition rates. Third, an observer-based adaptive controller is synthesized to ensure the finite time reachability of a predefined sliding surface. Finally, the single-link robot arm model is provided to verify the control scheme numerically.

Dynamic output-feedback control for nonlinear continuous-time systems based on parametric uncertain subsystem and interval type-2 fuzzy model

This paper addresses the interval type-2 fuzzy robust dynamic output-feedback control problem for a class of nonlinear continuous-time systems with parametric uncertainties and immeasurable premise variables. First, the parametric uncertainties are assumed to be a subsystem based on the control input matrix and output matrix, and described as a linear fractional. Secondly, the nonlinear continuous-time systems are described by the interval type-2 fuzzy model. Thirdly, the new dynamic output feedback controller is designed based on the interval type-2 fuzzy model and the linear fractional (parametric uncertainties), the sufficient conditions for robust stabilization are given in the form of linear matrix inequalities (LMIs). Compared with previous work, the developed methods not only have abilities to handle the fuzzy system with immeasurable premise variables but also can deal with the parametric uncertainties effectively. The results are further extended to a mobile robot case and a chemical process case. Finally, two simulation examples are performed to show the effectiveness of the propose methods.

State and unknown inputs estimation for Takagi–Sugeno systems with immeasurable premise variables: Proportional Multiple Integral observer design

In this work, we focus on the design of a Proportional Multiple Integral (PMI) observer for Takagi–Sugeno (T–S) fuzzy systems with immeasurable premise variables subjected to unknown inputs. The LMI-based stability conditions are significantly relaxed by the introduction of an output error injection in the premise variable of the PMI observer. The efficiency of the proposed observer is finally illustrated by a simulation example of a chaotic system.