This paper is concerned with the problems of state and output feedback control for interval type-2 (IT2) fuzzy systems with mismatched membership functions. The IT2 fuzzy model and the IT2 state and ...output feedback controllers do not share the same membership functions. A novel performance index, which is expressed as an extended dissipativity performance, is introduced to be a generalization of H ∞ , L 2- L ∞ , passive, and dissipativity performances indexes. First, the IT2 Takagi-Sugeno fuzzy model and the controllers are constructed by considering the mismatched membership functions. Second, on the basis of Lyapunov stability theory, the IT2 fuzzy state and output feedback controllers are designed, respectively, to guarantee that the closed-loop system is asymptotically stable with extended dissipativity performance. The existence conditions of the two kinds of controllers are obtained in terms of convex optimization problems, which can be solved by standard software. Finally, simulation results are provided to illustrate the effectiveness of the proposed methods.
In this paper, we consider the performance of exclusive-OR (XOR) rule in detecting the presence or absence of a deterministic signal in bivariate Gaussian noise. Signals, when present at the two ...sensors, are assumed unequal, whereas the noise components have identical marginal distribution but are correlated. The sensors send their one-bit quantized data to a fusion center, which then employs the XOR rule to arrive at the final decision. Here we prove that, in the limit as the correlation coefficient <inline-formula> <tex-math notation="LaTeX">r </tex-math></inline-formula> approaches 1, the optimum fusion rule for both parallel and tandem topologies is XOR with identical, alternating partitions (XORAP) of the observations at the sensors. We further quantify the asymptotic decrease of the Bayes error of XORAP towards zero as a constant multiplied by <inline-formula> <tex-math notation="LaTeX">\sqrt {1-r} </tex-math></inline-formula>, as <inline-formula> <tex-math notation="LaTeX">r </tex-math></inline-formula> approaches 1. When compared to the asymptotic Bayes error of CLRT, which decreases to zero exponentially fast, as a function of <inline-formula> <tex-math notation="LaTeX">1/(1-r) </tex-math></inline-formula>, the Bayes error of XORAP decreases to zero much slower.
This paper is concerned with the sliding mode control of nonlinear singular systems in terms of the interval type-2 (IT2) fuzzy model. To better approximate the nonlinear systems, the modeling errors ...are considered in the IT2 fuzzy model. The uncertainties in membership functions are expressed based on their boundedness. Admissibility conditions are obtained via a linear matrix inequalities approach. A new reaching law-based sliding controller is presented by choosing a typical sliding surface to analyze the sliding motion, such that all of the input gains are allowed to be different and the chattering of the system can be minimized with a guaranteed <inline-formula> <tex-math notation="LaTeX">H_{\infty } </tex-math></inline-formula> performance. The feasibility of the proposed control method is verified by simulation results.
This paper investigates the problem of adaptive <inline-formula> <tex-math notation="LaTeX">{H}_{\infty} </tex-math></inline-formula> sliding mode control (SMC) for a class of nonlinear systems via ...Takagi-Sugeno (T-S) fuzzy model approach. The input matrices and output matrices in all local linear systems are different. A novel observer is designed to estimate the unmeasured states. Based on such an observer, the control input is only appeared in the T-S fuzzy singular system and error system. A new integral sliding surface is put forward to match the characteristic of T-S fuzzy singular system with different input and output matrices. Based on the new integral sliding surface, a new adaptive SMC scheme is designed to guarantee the admissibility of the T-S fuzzy singular system with <inline-formula> <tex-math notation="LaTeX">{H}_{\infty} </tex-math></inline-formula> performance and the reachability of the T-S fuzzy integral sliding surface. A simulation result is presented to illustrate the effectiveness and feasibility of the developed observer-based SMC design method.
In the present study, the adaptive sliding mode control (ASMC) strategy is investigated for a class of complex nonlinear systems with matched and unknown nonlinearities and external disturbances. The ...nonlinearities and external disturbances are approached by a Gaussian radial basic neural network. A Takagi-Sugeno (T-S) fuzzy model based integral switching function is introduced to solve the ASMC problem, which eliminates the constrain that input gains required to share a common matrix in all fuzzy rules. Then, the switching control term is represented as a proportional integral (PI) control format to reduce the chattering phenomenon. Based on the Lyapunov theory, a set of existence conditions of the sliding mode controller are given such that the stability of the control systems can be guaranteed. Finally, a experimental simulation is utilized to verify the effectiveness of the proposed sliding mode control (SMC) strategy.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
This paper considers the admissibility of interval type-2 (IT2) uncertain Itô stochastic descriptor systems. Both membership functions and parametric matrices of considered nonlinear systems contain ...uncertain parameters. An IT2 fuzzy controller is designed such that the closed-loop descriptor systems is admissible. The membership functions of the controller and systems are unmatched. In the control systems, membership functions are represented by a partition method of footprint of uncertainty (FOU). Some conditions dependent on membership functions for the existence of IT2 fuzzy controller are obtained in the form of linear matrix inequality (LMI). In order to verify the effectiveness and feasibility of the proposed method, an IT2 fuzzy controller is designed for inverted pendulum system.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
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.
Do materials prepared from identical compositions of constituting ingredients always exhibit similar mechanical properties? The answer is negative for most structural materials, as has been ...demonstrated by extensive studies on various factors such as the effects of processing and microstructures. However, the same question has seldom been addressed in the case of polymeric gels. In this work, by using a simple chemically crosslinked hydrogel as a model system, the mechanical properties, including elastic stiffness, fracture toughness, and fatigue threshold, of gels with identical chemical compositions are systematically investigated. The distinct material properties are then rationalized and quantitatively correlated to synthesis conditions and manufacture processes through scaling laws derived from basic physics. Different scaling laws are identified between samples prepared from swelling and deswelling. Extreme mechanical properties, such as the remarkable fracture energy of hydrogels prepared by deswelling from highly swollen samples, are observed and attributed to the structural characteristics of the polymer network, and further correlated to the synthesis processes. This study provides insights into the synthesis-property correlations of polymeric gels, which may have profound influences on the design of new polymeric materials and their applications in various fields.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
The point of this article is the sensor fault estimation and fault‐tolerant controller design for IT2 fuzzy systems via sliding mode approach. In order to estimate accurately the system states and ...sensor faults, a novel proportional and derivative sliding mode observer is introduced, which provide more design freedom and eliminate the effects of sensor faults. By splitting the operating domain and estimating the membership functions, a set of relaxation stability conditions subject to the information of membership functions and system states are obtained. Then, a sliding mode controller in form of IT2 fuzzy model is designed to stabilize the closed‐loop systems. An example of bolt‐tightening tool model is considered to demonstrate the validity of the proposed results.
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FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SBCE, SBMB, UL, UM, UPUK
The distributed optimization problem (DOP) of Takagi-Sugeno (T-S) fuzzy cyber-physical systems is studied under the framework of weight-balanced graphs and quasistrongly connected characteristics. ...The objective is to drive the outputs of all agents to the optimal solution of a given global objective function regarded as the desired output, based on the partial information of the local objective functions. To this end, distributed optimal coordinators (DOCs) are used to generate optimal solutions of local objective functions that converge to the desired output, and fuzzy reference-tracking controllers are designed to ensure that all agents can track the optimal solutions. As novel technical results, two Lyapunov-based fuzzy input-to-state stability (ISS) small-gain theorems are proposed for the T-S fuzzy interconnected system. Thus, the overall closed-loop system is an interconnected system involving the modules of optimal coordinators and fuzzy tracking controllers with T-S fuzzy subsystems. The fuzzy ISS cyclic-small-gain theorem is applied to analyze the system stability. The DOP of T-S fuzzy cyber-physical systems is solved using the DOCs and fuzzy reference-tracking controllers through the fuzzy small-gain approach. A numerical example is presented to demonstrate the effectiveness and superiority of the proposed method.
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