Unmeasurable Premise Variables Research Articles

Robust Observer-Based Controller Design for Constrained Takagi-Sugeno Systems

This work concerns a descriptor Takagi-Sugeno (T-S) fuzzy system. The system is subject to disturbances, sensor faults, the presence of unmeasurable premise variables, and input saturation which the latter are considered uncertainties of the system. First, the considered system is transformed into the polytopic representation, and then, a robust Proportional-Integral (PI) observer-based controller is designed. This observer-based controller, can estimate both the system states, and the faults, and stabilize closed-loop state trajectories. An integrated robust controller strategy is adopted by a novel structure of non-Parallel Distributed Compensation (non-PDC) control law. furthermore, the proposed approach expresses the stability conditions of controller design are expressed in terms of Linear Matrix Inequalities (LMIs) constrained optimization problem. Using LMI TOOLBOX in MATLAB, we can easily design the type PI observer for efficient robust state/fault estimation and solve the observer-based controller design problem of discrete-time T-S fuzzy systems. Finally, an application to a rolling disc process is given to illustrate the effectiveness of the proposed method.

Proportional multi-integral observer design for Takagi–Sugeno systems with unmeasurable premise variables: Conservatism reduction via polyquadratic Lyapunov function

In this paper, we present the design of a new unknown-input observer for Takagi–Sugeno fuzzy systems with unmeasurable premise variables. The work proposes an improvement of the simultaneous state and unknown-input observer. The main idea is to consider a non-quadratic Lyapunov function in order to reduce the conservatism of its quadratic counterpart. Moreover, the mean value theorem is used to express the error dynamics in a way that reduces the conservatism of the bounded terms assumptions. The stability conditions are formulated as Bilinear Matrix Inequalities. To address these, we propose an iterative algorithm based on linear matrix inequalities, which transforms the Bilinear form into a sets of linear matrix inequalities. Finally, two examples are given to highlight the performance of the proposed observer.

Observer-Based Security Fuzzy Control for Nonlinear Networked Systems Under Weighted Try-Once-Discard Protocol

This paper is concerned with the observer-based security fuzzy control problem for a class of nonlinear networked systems with imperfectly matched membership functions (MFs) under weighted try-once-discard (WTOD) protocol. The nonlinear networked system is constructed based on interval type-2 (IT2) Takagi-Sugeno (T-S) model, which can properly handle parameter uncertainties via lower and upper MFs. To mitigate the communication load, WTOD protocol is exploited to schedule the transmission order of the signals, in which those signals may be subjected to randomly occurring deception attacks. The observer is constructed under unmeasurable premise variables, and then the controller with imperfect matching MFs is designed according to the estimated states. Moreover, the observer-based controller is derived with Lyapunov stability theory such that the stochastic stability of the augmented closed-loop system with predefined disturbance attenuation performance can be guaranteed. Subsequently, sufficient conditions are provided for the desired observer and controller gain matrices based on linear matrix inequalities (LMIs) technique. Numerical simulation example demonstrates the validity of the proposed observer-based security fuzzy control design scheme.

Robust state and sensor fault estimation for switched nonlinear systems based on asynchronous switched fuzzy observers

SummaryThis article aims to address state and sensor fault estimation issue for a class of continuous‐time nonlinear switched systems, modelled as Takagi‐Sugeno (T‐S) models with nonlinear consequent parts and subject to norm bounded disturbances. This modelling approach helps to prevent Unmeasured Premise Variables (UPVs) problem. The primary contribution of this study consists of proposing robust asynchronous switched observers to simultaneously estimate state and sensor faults under state‐dependent switching. Based on a candidate multiple Lyapunov function, the design of the proposed observer is formulated in terms of Linear Matrix Inequalities (LMIs) conditions. These conditions are dwell‐time‐independent and less conservative compared with similar previous studies, thanks to some usual relaxation techniques and the incremental quadratic constraints applied on unmeasured nonlinear consequent parts. Another contribution consists to perform the estimation of the attraction domain of the estimation error using an optimization procedure. In order to illustrate the effectiveness of the proposed design approach, two simulation examples are considered. The first one concerns the conservatism reduction brought by our proposal compared with previous studies, while the second one is dedicated to show through an illustrative example the performance of the proposed switched T‐S observers under mismatching switching laws.

Unknown input observer for Takagi-Sugeno implicit models with unmeasurable premise variables

<p>Recent years have seen a great deal of interest in implicit nonlinear systems, which are used in many different engineering applications. This study is dedicated to presenting a new method of fuzzy unknown inputs observer design to estimate simultaneously both non-measurable states and unknown inputs of continuous-time nonlinear implicit systems defined by Takagi-Sugeno (T-S) models with unmeasurable premise variables. The suggested observer is based on the singular value decomposition approach and rewritten the continuous-time T-S implicit models into an augmented fuzzy system, which gathers the unknown inputs and the state vector. The exponential convergence condition of the observer is established by using the Lyapunov theory and linear matrix inequalities are solved to determine the gains of the observer. Finally, the effectiveness of the suggested method is then assessed using a numerical application. It demonstrates that the estimated variables and the unknown input converge to the real variables accurately and quickly (less than 0.5 s).</p>

Active Adaptive Observer-Based Fault-Tolerant Control Strategy for a Class of T–S Fuzzy Systems With Unmeasurable Premise Variables

This paper addresses the problem of fault-tolerant output tracking control for a class of Takagi-Sugeno (T-S) fuzzy systems with unmeasurable premise variables subject to additive and multiplicative actuator faults and external disturbances. In nominal conditions, utilizing a quadratic Lyapunov function and non-parallel distributed compensation (non-PDC) technique, the suggested strategy delivers linear matrix inequality (LMI)-based constraints. Simultaneously design of the proportional-integral (PI)-like state feedback controller and fuzzy anti-windup compensator is achieved with the aim of output tracking. In the faulty case, by considering the nominal system as a reference model, a direct adaptive projection-based approach is developed using the T-S fuzzy modeling and control techniques to supply the adaptive fault-tolerant controller components. An enhanced proportional-integral (PI) state/fault observer with unmeasurable premise variables is introduced only to provide the estimation of states to be used in the proposed controller. The overall closed-loop system ensures the uniformly ultimately bounded (u.u.b) solutions for error dynamics. Two examples, subsuming an inverted pendulum and a chaotic power system, have been used to present the merits and efficiency of the suggested approach persuasively.

Dissipativity-Based Integrated Fault Estimation and Fault Tolerant Control for IT2 Polynomial Fuzzy Systems With Sensor and Actuator Faults

The integrated fault estimation and fault-tolerant control scheme is developed in this paper for a series of interval type-2 polynomial fuzzy systems with both sensor faults and actuator faults, where the bi-directional influence between fault estimation unit and fault-tolerant control unit is investigated. Considering the existence of sensor faults, unmeasurable premise variables are investigated for more general situations and Class III state/fault estimation observers are established for the final fault estimation and fault-tolerant control purposes. To increase design flexibility and reduce physical implementation complexity, the proposed method allows the observer and original system to share asynchronous membership functions and a different number of fuzzy rules. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(\mathcal{Q,S,R}) \,-\, \alpha$</tex-math></inline-formula> dissipative performance index is also introduced to fulfill a wider vary of perfor-mance requirements. Membership-function-dependent stability constraints are given in the format of bi-linear polynomial matrix inequalities to obtain less conservative results, which are computed by a two-step path-following method. Superiority and validity are demonstrated by an inverted pendulum example in terms of estimation errors, fault-tolerant control performance and control inputs.

Observer design for Takagi–Sugeno fuzzy systems with unmeasured premise variables: Conservatism reduction using line integral Lyapunov function

In this paper, a non-quadratic Lyapunov function is employed to reduce conservatism in a nonlinear observer designed for a class of continuous-time Takagi–Sugeno fuzzy systems with unmeasurable premise variables. This structure presents greater challenges compared to systems with measured variables. To overcome this issue, we utilize the mean value theorem and the sector nonlinearity transformation to convert the nonlinear error dynamics into a linear parameter-varying system. Moreover, we introduce the line integral Lyapunov function, which based on the integral of the membership functions, in order to ensure the global stability of the fuzzy systems under consideration. The use of this function offers several notable advantages over conventional quadratic forms, including a reduction in conservatism. Additionally, this type of functions constructed in a manner that eliminates the need for generating time derivatives of the membership functions, thereby simplifying calculations and analysis in comparison to other nonquadratic functions. Furthermore, it also enables capturing the system’s behavior along a trajectory. The stability conditions are more relaxed and expressed as linear matrix inequalities, which can be solved using a linear programming approach through specialized software tools. To validate the effectiveness of the proposed methodology, we conducted a hardware-in-the-loop test using a flexible joint robot. The obtained results clearly underscore the success of the proposed approach.

Robust observer design for T-S fuzzy singular systems with unmeasurable premise variables and partially decoupled disturbances

Robust observer design for T-S fuzzy singular systems with unmeasurable premise variables and partially decoupled disturbances

Robust PI multiobserver for discrete nonlinear singularly perturbed system with unmeasurable premise variables

This article deals with the observability bound problem of a discrete-time nonlinear singularly perturbed systems (SPSs) subject to disturbances and noises. This nonlinear SPS is represented by a coupled state multimodel (MM) with unmeasurable premise variables. A [Formula: see text] proportional-integral multiobserver ([Formula: see text] PI multiobserver), known by its robustness, is designed to accomplish this task. The proposed method is based on the [Formula: see text] technique to minimize the effect of the disturbances, the noises, and all the unmeasurable premise variables. To design this observer, sufficient conditions expressed in terms of linear matrix inequalities (LMIs) are developed as a first step to ensure the robust stability bound of the considered system represented by a coupled MM for a bound of the singular perturbation parameter based on a quadratic Lyapunov function and the [Formula: see text] gain. Then, sufficient conditions are developed to ensure the robust stability bound of the state estimation error between the MM and the PI multiobserver for a bound of the singular perturbation parameter that is less than or equal to the considered system’s robust stability bound. Hence, the observability bound of the considered system represented by a coupled state MM is determined. Two simulation examples are then given to validate the proposed strategy.

Unknown input observers for time-varying delay Takagi–Sugeno fuzzy systems with unmeasured nonlinear consequents

This paper investigates the problem of unknown input observer (UIO) design for Takagi–Sugeno (TS) fuzzy systems with time-varying delay. For observer design, all the unmeasured nonlinearities are isolated in the nonlinear consequent parts of TS fuzzy systems. This allows dealing with the well-known issue related to unmeasured premise variables for TS fuzzy observer design in a more effective fashion via the mean value theorem. Using the unknown input (UI) decoupling technique, no a priori information on the UI is needed for the proposed TS fuzzy observer design, which can guarantee the asymptotic estimations of both the system state and the unknown input. Employing a fuzzy Lyapunov–Krasovskii functional with a suitable augmented vector, the effect of time-varying delay on the estimation error dynamics is taken into account in the observer design. Numerical examples are presented to demonstrate the effectiveness of the proposed fuzzy UIO design method for nonlinear time-varying delay systems.

Robust [formula omitted]-dissipative event-triggered sliding mode control of discrete T-S fuzzy descriptor systems with partial unmeasurable premise variables

In this paper, the admissibility analysis and dissipative sliding mode control (SMC) based on event-triggered mechanism (ETM) are studied for discrete T-S fuzzy descriptor systems (D-TSFDS). The problem of partial unmeasurable premise variables in D-TSFDS is dealt with by nonlinear dynamic programming. Based on ETM, a sliding mode surface based on measurable premise variables is proposed for the first time. Since the delay between the sensor and the controller in ETM, a Lyapunov-Krasovskii function is used to acquire the sufficient conditions for the closed-loop system to be admissible with dissipative performance. A new SMC law is given to ensure the reachability conation. The simulation results demonstrate the effectiveness of the proposed method.

Design of asynchronous switched Takagi–Sugeno model‐based H∞ filters with nonlinear consequent parts for switched nonlinear systems

SummaryThis paper investigates the design of asynchronous switched nonlinear filters for a class of continuous‐time nonlinear switched systems with mismatching switching laws and norm‐bounded disturbances. In this context, the switched nonlinear system is modelled as a switched Takagi–Sugeno (T‐S) model with nonlinear consequent parts, that is, where unmeasured nonlinear terms are kept in the nonlinear consequent parts in order to circumvent the occurrence of unmeasured premise variables, which is usually faced in conventional T‐S modeling without nonlinear consequent parts. In this framework, asynchronous switched T‐S filters with unmeasured nonlinear consequent parts are proposed to estimate unmeasured and/or disturbed system's outputs, even when the filter's switching law mismatches the switched nonlinear system's one, which can be in practice unknown or imprecisely measured. Based on a candidate multiple Lyapunov function, combined with a criterion, conditions are proposed in terms of Linear Matrix Inequalities for the design of the considered asynchronous switched T‐S filters with unmeasured nonlinear consequent parts. Compared with previous related works, these conditions have the advantage of being dwell‐time‐independent and less conservative, thanks to the incremental quadratic constraints employed to deal with the unmeasured nonlinear consequent parts. Furthermore, acknowledging that T‐S models are only representing nonlinear ones on subsets of their state space, an optimization procedure to estimate the filtering error's domain of attraction is developed. Two illustrative examples are considered to validate the proposed results. An academic one is presented to illustrate the improvements brought in terms of conservatism by the proposed switched T‐S filter design methodology with regards to previous related studies. Then, a case study illustrates the effectiveness of this proposal from a switched nonlinear mass‐spring system inspired from related literature.

Observer-Based Controller Using Line Integral Lyapunov Fuzzy Function for TS Fuzzy Systems: Application to Induction Motors

This paper deals with the stabilization problem of a nonlinear system described by a Takagi–Sugeno fuzzy (TSF) model with unmeasurable premise variables via a robust controller. Applying the sector nonlinearity techniques, the nonlinear system is represented by a decoupled fuzzy model. Then, we design a robust observer-based controller for the obtained fuzzy system by utilizing the differential mean value approach. The observer and controller gains are obtained by the separation principle, in which the problem is solved in the sum of linear matrix inequalities (LMIs). The paper presents two main contributions: A state feedback controller is designed using differential mean value (DMVT) which ensures robust stabilization of the nonlinear system. Additionally, the Luenberger observer is extended to the Takagi–Sugeno fuzzy models. The second contribution is to reduce conservatism in the obtained conditions, a non-quadratic Lyapunov function (known as the line integral Lyapunov fuzzy candidate (LILF)) is employed. Two examples are provided to further illustrate the efficiency and robustness of the proposed approach; specifically, the Takagi–Sugeno fuzzy descriptor of an induction motor is derived and a robust observer-based controller applied to the original nonlinear system.

A fuzzy observer synthesis to state and fault estimation for Takagi-Sugeno implicit systems

&lt;p&gt;The present paper inquire a fuzzy observer design issue for continuous time Takagi-Sugeno aiming at estimating both of fault and state in case of unmeasurable premise variables. Thanks to singular value decomposition (SVD) approach, the fuzzy observer is synthesized in explicit form. The developed method is based on augmented structure that assemble state and actuator fault, sensor fault as well as their sequential derivatives is enjoined to institute the destined observer. The Lyapunov function is analyzed to assume the exponential stability of the studied observer, furthermore convergence conditions are expressed as linear matrix inequalities (LMIs) form. The applicability of the nominated theoritical result is elucidated and confiremed through numerical simulation using an example of an implicit fuzzy model.&lt;/p&gt;

Anti-disturbance attitude quantized control of flexible spacecraft via a triggering and quantization joint dynamic event-triggered mechanism

This article investigates the problem of dynamic event-triggered anti-disturbance attitude quantized control based on the Takagi-Sugeno fuzzy method for flexible spacecraft, where multiple disturbances and parameter uncertainties are simultaneously considered. First, by employing the Takagi-Sugeno fuzzy model to represent the nonlinear disturbances with additional disturbance, a disturbance observer based on the Takagi-Sugeno fuzzy model is constructed under the unmeasurable premise variables to estimate the unknown nonlinear disturbances. Furthermore, a flexible vibration observer is formatted. Subsequently, a dynamic event-triggered mechanism with the quantization parameter is introduced, which can obtain a trade-off between quantization density and event-triggered frequency on the condition that the system stability is ensured. And an event-triggered anti-disturbance quantized controller is constructed, which can make up for Takagi-Sugeno fuzzy modeling disturbances and reject parameter uncertainties and other bounded disturbances. To guarantee the bound of the closed-loop signals, some sufficient conditions are obtained. At last, the efficiency of the suggested control strategy is illustrated via the simulation results.

Design of unknown input observer for discrete-time Takagi Sugeno implicit systems with unmeasurable premise variables

In this study, an unknown input observer (UIO) is developed in explicit form to estimate unmeasurable states and unknown inputs (UIs) for nonlinear implicit systems represented by the discrete-time Takagi-Sugeno implicit systems (DTSIS) in the case of unmeasurable premise variables. The method employed is based on singular value decomposition (SVD) and augmenting the state vector, which is formed partly by the system state and partly by the UIs. The convergence of the augmented state estimation error is provided by a Lyapunov function ending with solving the linear matrix inequalities (LMI). An application to a model of the rolling disc is considered to evaluate the effectiveness of the developed approach. It appears that estimated variables converge to the true variables quickly and accurately.

Interval type-2 polynomial fuzzy fault detection scheme with a multi-order homogeneous polynomial Lyapunov functions considering unmeasurable premise variables

A polynomial fuzzy fault detection scheme for sampled-output-measurements-based interval type-2 (IT2) polynomial-fuzzy-model-based (PFMB) systems is investigated in this paper, where the uncertainties in the premise variables (PVs) and membership functions (MFs) are described by IT2 fuzzy sets. Fully or partially unmeasurable PVs cause the parameter matrices of the polynomial fuzzy fault detection observer (PFFDO) to rely on the estimated states and the corresponding mismatching problems are further considered. Lyapunov stability theory is carried out with a novel multi-order homogenous polynomial Lyapunov functions (MHPLF) to introduce more information of the states when eliminating the partial derivatives, and the time-delays introduced by sampled-output measurements are handled by L-K functions. Unlike the membership-function-independent (MFI) approaches, the membership-function-dependent (MFD) approaches carry the information of the MFs for the relaxation of the stability constraints. Corresponding stable constraints in sum-of-squares (SOS) form are given to hold the asymptotic stability of the fault detection system with H∞ performance γ. A numerical example with many cases illustrates the effectiveness of the proposed techniques in uncertainty handling and conservativeness reduction, while an inverted pendulum example verifies the feasibility of the method on physical systems.

Dynamic Event-Triggered Antidisturbance Control for Flexible Spacecraft Systems

This study develops a dynamic event-triggered anti-disturbance (DETAD) controller to solve attitude control problem for flexible spacecraft systems with multiple disturbances. The disturbances involve two aspects: one belongs to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{2}$</tex-math></inline-formula> space, and the other is described by an exogenous nonlinear system. Two sets of Takagi–Sugeno (T–S) fuzzy models are employed to model the flexible spacecraft systems and an exogenous nonlinear system, respectively. Moreover, a flexible vibration observer (FVO) is introduced to estimate the flexible modes. And a fuzzy disturbance observer (FDO) is designed to estimate the T–S fuzzy modeling disturbance in the case of the unmeasurable premise variables. By utilizing the estimations of two observers, a DETAD controller is constructed, where a dynamic event-triggered mechanism is implemented to reduce communication transmission. Additionally, new sufficient conditions for the closed-loop system to be asymptotically stable with strict dissipative performance are formed using linear matrix inequality techniques. Simulations are also provided to verify the advantages of the proposed scheme for flexible spacecraft systems subject to different types of disturbances.

Unknown Input Functional Observer Design for Discrete-Time Interval Type-2 Takagi–Sugeno Fuzzy Systems

This article proposes a novel unknown input functional observer design approach toward discrete-time interval type-2 Takagi–Sugeno fuzzy system models subject to measurable and unmeasurable premise variables. By constructing a new state vector that contains both the unknown inputs and the system states, functional observers are proposed for the cases with measurable and unmeasurable premise variables to estimate this new state vector for unknown input and/or state estimation. The observer design problem is converted into the solvability issue of a linear matrix equation involving observer gain matrices, and the existence conditions of the observers are explicitly obtained based on matrix rank analysis. Meanwhile, instead of solving the intricate Sylvester equation directly, the solution of the simplified matrix equation is employed to derive the observer gains. Moreover, the effectiveness and the superiority of the presented method are demonstrated via two illustrative examples.