Non-parallel Distributed Compensation Research Articles

Dynamic Event-Triggered Control for Interval Type-2 Fuzzy Systems Under Fading Channel.

This article is to tackle the event-based state-feedback control problem for interval type-2 (IT2) fuzzy systems subject to the fading channel. For saving communication resources, a dynamic event-triggered (ET) mechanism is utilized to decide the data transmission from sensors to the controller. A time-varying random process is employed to characterize the fading phenomenon in the unpredictable communication network. By considering the effect of channel fading, a nonparallel distribution compensation (non-PDC) IT2 fuzzy controller is synthesized and its number of rules and membership functions (MFs) can be freely selected. As a consequence, the closed-loop fuzzy system possesses imperfectly matched MFs. By taking the global membership boundary information into stability analysis, the membership-function-dependent analysis method is employed to handle these imperfectly matched MFs and to obtain relaxed criteria. Besides, sufficient criteria are obtained so that the resulting closed-loop IT2 fuzzy system can achieve stochastic stability despite fading measurements. The effectiveness of the proposed method is illustrated by a mass-spring-damper system and a numerical example.

Velocity control of a two-wheeled inverted pendulum mobile robot: a fuzzy model-based approach

This paper presents the design of a fuzzy tracking controller for balancing and velocity control of a Two-Wheeled Inverted Pendulum (TWIP) mobile robot based on its Takagi-Sugino (T-S) fuzzy model, fuzzy Lyapunov function and non-parallel distributed compensation (non-PDC) control law. The T-S fuzzy model of the TWIP mobile robot was developed from its nonlinear dynamical equations of motion. Stabilization conditions in a form of linear matrix inequalities (LMIs) were derived based on the T-S fuzzy model of the TWIP mobile robot, a fuzzy Lyapunov function and a non-PDC control law. Based on the derived stabilization conditions and the T-S fuzzy model of the TWIP mobile robot, a state feedback velocity tracking controller was then proposed for the TWIP mobile robot. The balancing and velocity tracking performance of the proposed controller was investigated via simulations. The simulation result shows the effectiveness of the proposed control scheme.

Fuzzy model-based controller for blood glucose control in type 1 diabetes: An LMI approach

This paper deals with designing a robust controller with H∞ performance index criteria for regulating the glucose-insulin level in type 1 diabetes. The proposed approach employs a Takagi-Sugeno (TS) fuzzy modeling and fuzzy model-based parallel distributed compensation (PDC) and non-parallel distributed compensation (non-PDC) schemes to design a stabilizing control law for the injecting insulin in silico. Deploying a non-quadratic Lyapunov function (NQLF) candidate, the stabilization conditions are derived in terms of linear matrix inequalities (LMIs) and solved by convex optimization techniques. Furthermore, based on the convex property of the membership functions, a new null term is defined which increases the degree of freedom of the proposed LMI constraints and reduces the stabilization conditions conservativeness. The diabetes models that are considered are nonlinear minimal Bergman and Tolic models that describe the glucose-insulin process in diabetes type 1. Based on the so-called sector nonlinearity approach (SNA), the equivalent TS fuzzy models of the Bergman and Tolic models are obtained. Then, the stabilization LMI conditions are solved and the PDC and non-PDC controllers are designed. Simulation results are obtained with a single patient testing parameters uncertainties and verify the advantages of the proposed robust control technique in dealing with the effects of external meal disturbance and maintaining the blood glucose concentration in the desired region to avoid the hypoglycemia and hyperglycemia disorders.

State and output feedback control for constrained discrete-time nonlinear systems

This paper presents a new systematic controller design approach for disturbed nonlinear time-varying systems subject to input and state constraints in discrete-time case. The Takagi–Sugeno (TS) formalism and fuzzy Lyapunov framework are used to handle the time varying parameters and control input saturation. Moreover, the proposed control method is based on L2 criterion which results in two different control design procedures. Both non-parallel distributed compensation (non-PDC) static state feedback control law and dynamics output feedback controller are proposed. To ensures the closed-loop system stability with respect to the given saturation constraints on the control input different optimization problem are also formulated in terms of linear matrix inequality conditions which can be solved efficiently with available solvers. The proposed techniques are illustrated through numerical examples.

Observer-based dissipative output feedback control for network T–S fuzzy systems under time delays with mismatch premise

This paper deals with the problem of non-parallel distribution compensation networked control systems (NCSs) under event-triggered strategy based on the fuzzy system for a class of nonlinear systems with time-varying delays and mismatching premise membership functions. The T–S fuzzy model under event-triggered strategy is provided in unified framework, in which (1) a delay fuzzy observer-based with the mismatch premise is employed to approximate the immeasurable states of the existing system; (2) a delay fuzzy observer-based controller is constructed, by considering the same premises as in observer; and (3) event-triggered strategy is considered to mitigate the effect of communication burden. Another derivation of this paper is to introduce the notation of extended dissipativity which provides the $$H_{\infty }$$ , $$L_{2}-L_{\infty }$$ and dissipative performances. Furthermore, in this regard, by taking into account a novel fuzzy Lyapunov–Krasovskii functional in conjunction with free weighting matrices, containing mode-dependent integral terms such that the resulting system is stable with the desired performance. Then, desired observer-based controller is presented in the account of LMI. Finally, we validate our results with a truck–trailer example.

TS Fuzzy Model-Based Controller Design for a Class of Nonlinear Systems Including Nonsmooth Functions

This paper proposes a novel robust controller design for a class of nonlinear systems including hard nonlinearity functions. The proposed approach is based on Takagi–Sugeno (TS) fuzzy modeling, nonquadratic Lyapunov function, and nonparallel distributed compensation scheme. In this paper, a novel TS modeling of the nonlinear dynamics with signum functions is proposed. This model can exactly represent the original nonlinear system with hard nonlinearity while the discontinuous signum functions are not approximated. Based on the bounded-input-bounded-output stability scheme and ${L_{1}}$ performance criterion, new robust controller design conditions in terms of linear matrix inequalities are derived. Three practical case studies, electric power steering system, a helicopter model and servo-mechanical system, are presented to demonstrate the importance of such class of nonlinear systems comprising signum function. Furthermore, to show the superiorities of the proposed approach, it is applied to these systems; and, the experimental real-time hardware-in-the-loop results are compared with the published literature with the same topic.

Improved results on stability analysis and controller synthesis for T-S fuzzy systems

ABSTRACTThis paper is concerned with the stability analysis and synthesis issues for T-S fuzzy systems. By fully using the properties of fuzzy weighting functions and matrix inequalities, two improved sufficient stability conditions are derived based on the common Lyapunov function and fuzzy Lyapunov function, respectively. It is not necessary to require every fuzzy subsystem to be stable in these conditions. Following the analysis, both parallel and non-parallel distributed compensation controllers are obtained by solving linear matrix inequalities. Finally, four examples are given to show the effectiveness of our proposed approach and the advantages of the approach over existing methods.

Robust <inline-formula> <tex-math notation="LaTeX">${L_1}$</tex-math> </inline-formula> Observer-Based Non-PDC Controller Design for Persistent Bounded Disturbed TS Fuzzy Systems

This paper proposes a new method for bounded input bounded output stabilization and robust ${{{\bf L}}_1}$ observer-based controller design of a class of nonlinear systems described by Takagi–Sugeno (TS) models. The sufficient conditions of nonparallel distributed compensation (non-PDC) controller design are derived in terms of linear matrix inequalities (LMIs) in a way that the effect of external persistent bounded disturbance is alleviated on the amplitude of the TS system states. The main contributions of this paper can be categorized in two classes. First, a novel method for minimizing the ${{{\bf L}}_1}$ performance upper bound is proposed which leads to less number of pre-fixed scalar terms and less computational time. Second, we utilize nonquadratic Lyapunov function to reduce the conservativeness of proposed conditions and make them applicable to wider classes of TS fuzzy systems. Finally, several numerical examples are presented to test the validity of the proposed approaches of this paper. In particular, TS fuzzy model of a helicopter system is derived and the proposed controller is applied to the original nonlinear plant. Simulation results verify the effectiveness of our approaches, even in the presence of white noise.

Event-based weighted residual generator design via non-PDC scheme for fault diagnosis in T–S fuzzy systems

This paper is concerned with the event-based weighted residual generator design via non-parallel distribution compensation (PDC) scheme for fault diagnosis in discrete-time T–S fuzzy systems, under consideration of the imperfect premise matching membership functions. An event-triggered mechanism is firstly introduced to save communication resources, which leads to the premise variables of the system and observer to be asynchronous. Then, a fuzzy diagnostic observer with mismatched premise variables is designed to estimate the unmeasurable states of the system. Moreover, by using non-PDC method, a diagnostic observer-based weighted residual generator is established to improve the fault detection (FD) performance by using the information provided by each local system, in which the membership functions structure of the diagnostic observer and residual generator need not to be the same as the systems, and the L∞/L2 and L∞ FD scheme is used to optimize the FD performance. Finally, two simulation results are provided to show the efficiency of the proposed non-PDC method.

Design of Robust Double-Fuzzy-Summation Nonparallel Distributed Compensation Controller for Chaotic Power Systems

This paper studies a systematic linear matrix inequality (LMI) approach for controller design of nonlinear chaotic power systems. The presented method is based on a Takagi–Sugeno (TS) fuzzy model, a double-fuzzy-summation nonparallel distributed compensation (non-PDC) controller, and a double-fuzzy-summation nonquadratic Lyapunov function (NQLF). Since time derivatives of fuzzy membership functions (MFs) appear in the NQLF-based controller design conditions, local controller design criteria is considered, and sufficient conditions are formulated in terms of LMIs. Compared with the existing works in hand, the proposed LMI conditions provide less conservative results due to the special structure of the NQLF and the non-PDC controller in which two fuzzy summations are employed. To evaluate the effectiveness of the presented approach, two practical benchmark power systems, which exhibit chaotic behavior, are considered. Simulation results and hardware-in-the-loop illustrate the advantages of the proposed method compared with the recently published works.

Robust Constrained Model Predictive Control for Discrete‐Time Uncertain System in Takagi‐Sugeno's Form

AbstractIn this paper, we investigate a robust constrained model predictive control synthesis approach for discrete‐time Takagi‐Sugeno's (T‐S) fuzzy system with structured uncertainty. The key idea is to determine, at each sampling time, a state feedback fuzzy predictive controller that minimizes the performance objective function in the infinite time horizon by solving a class of linear matrix inequalities (LMIs) optimization problem. To do this, the fuzzy predictive controller is designed on the basis of non‐parallel distributed compensation (non‐PDC) control law, relaxed stability conditions of the closed‐loop fuzzy system are developed by employing an extended nonquadratic Lyapunov function and introducing additional slack and collection matrices. In addition, the presented approach is capable of ensuring the robust asymptotic stability as well as the recursive feasibility of the closed‐loop fuzzy system. Simulations on a highly nonlinear continuous stirred tank reactor (CSTR) are eventually presented to demonstrate the effectiveness of the developed theoretical approach.

Admissibility Analysis and Control Synthesis for T–S Fuzzy Descriptor Systems

The problem of admissibility analysis and control synthesis for Takagi–Sugeno fuzzy descriptor systems is investigated. First, based on Nonquadratic fuzzy Lyapunov function and fully using the information of fuzzy membership functions, a new relaxed sufficient condition ensuring a fuzzy descriptor system to be admissible (regular, impulse-free, and stable) is proposed, in which it is not necessary to require every fuzzy subsystem to be stable. Second, the other sufficient condition for the admissibility is obtained without the information of time derivatives of fuzzy membership functions. Following the analysis, both parallel and nonparallel distributed compensation controllers are designed, linear matrix inequalities conditions are given to construct the controllers. Finally, some examples are provided to illustrate the main results in this paper less conservative than some earlier related results.

An SOS-Based Control Lyapunov Function Design for Polynomial Fuzzy Control of Nonlinear Systems

This paper deals with a sum-of-squares (SOS)-based control Lyapunov function (CLF) design for polynomial fuzzy control of nonlinear systems. The design starts with exactly replacing (smooth) nonlinear systems dynamics with polynomial fuzzy models, which are known as universal approximators. Next, global stabilization conditions represented in terms of SOS are provided in the framework of the CLF design, i.e., a stabilizing controller with nonparallel distributed compensation form is explicitly designed by applying Sontag's control law, once a CLF for a given nonlinear system is constructed. Furthermore, semiglobal stabilization conditions on operation domains are derived in the same fashion as in the global stabilization conditions. Both global and semiglobal stabilization problems are formulated as SOS optimization problems, which reduce to numerical feasibility problems. Five design examples are given to show the effectiveness of our proposed approach over the existing linear matrix inequality and SOS approaches.

Dynamic Model-Based Fuzzy Controller for Maximum Power Point Tracking of Photovoltaic Systems: A Linear Matrix Inequality Approach

In this paper, a new systematic approach for stability analysis and controller design of nonlinear solar photovoltaic (PV) power system is proposed. Based on a nonquadratic Lyapunov function (NQLF), a model-based dynamic nonparallel-distributed compensation (non-PDC) controller and descriptor representation, the problem of the output tracking is formulated in terms of linear matrix inequalities (LMIs). Furthermore, some slack LMI variables are introduced in the problem formulation which lead to more relaxed conditions. Finally, to illustrate the merits of the proposed approach, it is applied to a PV power system in which the reference voltage is calculated from the maximum power point tracking (MPPT) method.

Observer-Based Non-PDC Control for Networked T-S Fuzzy Systems With an Event-Triggered Communication.

This paper addresses the problem of an event-triggered non-parallel distribution compensation (PDC) control for networked Takagi-Sugeno (T-S) fuzzy systems, under consideration of the limited data transmission bandwidth and the imperfect premise matching membership functions. First, a unified event-triggered T-S fuzzy model is provided, in which: 1) a fuzzy observer with the imperfect premise matching is constructed to estimate the unmeasurable states of the studied system; 2) a fuzzy controller is designed following the same premise as the observer; and 3) an output-based event-triggering transmission scheme is designed to economize the restricted network resources. Different from the traditional PDC method, the synchronous premise between the fuzzy observer and the T-S fuzzy system are no longer needed in this paper. Second, by use of Lyapunov theory, a stability criterion and a stabilization condition are obtained for ensuring asymptotically stable of the studied system. On account of the imperfect premise matching conditions are well considered in the derivation of the above criteria, less conservation can be expected to enhance the design flexibility. Compared with some existing emulation-based methods, the controller gains are no longer required to be known a priori. Finally, the availability of proposed non-PDC design scheme is illustrated by the backing-up control of a truck-trailer system.

An improved robust finite-time dissipative control for uncertain fuzzy descriptor systems with disturbance

ABSTRACTIn this paper, finite-time robust control problems are investigated for Takagi– Sugeno fuzzy descriptor systems. We provide a novel sufficient condition for robust finite-time admissibility of Takagi– Sugeno fuzzy descriptor systems, involving a group of coupled linear matrix inequalities (LMIs), which guarantee dissipative performance, reduce conservativeness and improve LMIs forms. Second, corresponding controllers are developed based on both parallel distributed compensation and non-parallel distributed compensation. Simulations demonstrate the effectiveness of the proposed control approach.

New approaches to observer design and stability analysis for T–S fuzzy system with multiplicative noise

The problem of observer design and stability analysis for T–S fuzzy system with multiplicative noise is investigated in this paper. Based on the fuzzy Lyapunov function, a membership function based global stable non-parallel distributed compensation observer is developed for the T–S fuzzy system. Then we give an improved membership function dependent stability analysis approach, which involves the calculated values of the membership function and its derivatives. The conservativeness of stability conditions for the observer is much relaxed than the existing methods, and these conditions can be formulated as LMIs (linear matrix inequalities), which can be effectively solved by convex optimization techniques. An example is provided to illustrate the effectiveness of proposed method.

Stability analysis and state feedback control of continuous-time T–S fuzzy systems via anew switched fuzzy Lyapunov function approach

This paper deals with stability analysis and control design problems for continuous-time Takagi–Sugeno (T–S) fuzzy systems. First, a new membership-function-dependent switching law is proposed and a relaxation parameter is introduced into this switching law to guarantee a minimal dwell time between two consecutive switching. Compared to the existing methods, the most important point is that with the help of the dwell time, the discretized Lyapunov function (DLF) technique can be adopted. Then a new stability criterion of the T–S fuzzy system with less conservatism is derived based on a fuzzy discretized Lyapunov function (FDLF). Second, to estimate the domain of attraction (DA), an algorithm with less iteration steps is proposed. Based on the proposed switching method, sufficient conditions for existence of the state feedback controllers are presented via the switched non-parallel distributed compensation (non-PDC) scheme. The effectiveness of the proposed method is illustrated through three simulation examples.

LMI-based control synthesis of constrained Takagi–Sugeno fuzzy systems subject to [formula omitted] or [formula omitted]∞ disturbances

This paper is devoted to the development of a new saturated non-parallel distributed compensation control law for disturbed Takagi–Sugeno fuzzy systems subject to both control input and state constraints. In order to cover a large range of real-world applications, both L2 and L∞ disturbances are considered which result in two different control design procedures. A parameter-dependent version of the generalized sector condition is effectively exploited in a fuzzy Lyapunov control framework to handle the control input saturation. Moreover, the proposed control method is based on the concept of robust invariant set which is able to provide an explicit characterization of the estimated domain of attraction of the closed-loop system. Different optimization algorithms are also proposed to deal with the trade-off between different closed-loop requirements in a local control context. The design conditions are expressed in terms of linear matrix inequalities which can be solved efficiently with available solvers. The numerical examples illustrate how the proposed methodology leads to less conservative results as well as less computational complexity when compared to very recent works in the literature.

Mean-square admissibility for stochastic T–S fuzzy singular systems based on extended quadratic Lyapunov function approach

The mean-square admissibility problem of stochastic T–S fuzzy singular systems via an extended quadratic Lyapunov function is investigated in this paper. Comparing with the existing quadratic Lyapunov function method, the extended quadratic Lyapunov function method can relax stabilization conditions. Firstly, the sufficient condition is given for the mean-square admissibility of stochastic T–S fuzzy singular systems based on an extended quadratic Lyapunov function approach. Secondly, two sufficient conditions for mean-square admissibility of closed-loop systems via the parallel distributed compensation (PDC) fuzzy controller and non-parallel distributed compensation (non-PDC) fuzzy controller are proposed. Furthermore, through the extended quadratic Lyapunov function method and non-PDC fuzzy controller, the less conservative mean-square admissibility conditions on solving fuzzy controllers are derived in terms of linear matrix inequalities (LMIs). Finally, some simulation examples are given to show the effectiveness and merits of the proposed fuzzy controller design methodology.