Application of evolving Takagi–Sugeno fuzzy model to nonlinear system identification

In this paper, a new encoding scheme is presented for learning the Takagi–Sugeno (T–S) fuzzy model from data by genetic algorithms (GAs). In the proposed encoding scheme, the rule structure (selection of rules and number of rules), the input structure (selection of inputs and number of inputs), and the antecedent membership function (MF) parameters of the T–S fuzzy model are all represented in one chromosome and evolved together such that the optimisation of rule structure, input structure, and MF parameters can be achieved simultaneously. The performance of the developed evolving T–S fuzzy model is first validated by studying the benchmark Box–Jenkins nonlinear system identification problem and nonlinear plant modelling problem, and comparing the obtained results with other existing results. Then, it is applied to approximate the forward and inverse dynamic behaviours of a magneto-rheological (MR) damper of which identification problem is significantly difficult due to its inherently hysteretic and highly nonlinear dynamics. It is shown by the validation applications that the developed evolving T–S fuzzy model can identify the nonlinear system satisfactorily with acceptable number of rules and appropriate inputs.     

Absolute stability analysis for a class of Takagi–Sugeno fuzzy control systems

This article presents absolute stability conditions for a particular class of Takagi–Sugeno fuzzy control systems. Initially, a Takagi–Sugeno fuzzy control system is transformed into a multivariable Lur’e type system. A simple algorithm for checking the absolute stability of this system is then proposed. Since the key of the proposed algorithm is to solve algebraic Riccati equations, software packages such as MATLAB provides a simple means to check the conditions. The proposed approach does not limit the methods of fuzzification and defuzzification. This article presents several analytical examples to verify the simplicity and efficiency of the proposed approach.     

Robust fault diagnosis for a class of nonlinear systems

Robust fault diagnosis based on adaptive observer is studied for a class of nonlinear systems up to output injection. Adaptive fault updating laws are designed to guarantee the stability of the diagnosis system. The upper bounds of the state estimation error and fault estimation error of the adaptive observer are given respectively and the effects of parameter in the adaptive updating laws on fault estimation accuracy are also discussed. Simulation example demonstrates the effectiveness of the proposed methods and the analysis results.     

Structure and stability analysis of a Takagi–Sugeno fuzzy PI controller with application to tissue hyperthermia therapy

 In this paper, we first reveal the analytical structure of a simple Takagi–Sugeno (TS) fuzzy PI controller relative to the linear PI controller. The fuzzy controller consists of two linear input fuzzy sets, four TS fuzzy rules with linear consequent, Zadeh fuzzy logic AND and the centroid defuzzifier. We prove that the fuzzy controller is actually a nonlinear PI controller with the gains changing with process output. Utilizing the well-known small Gain Theorem in control theory, we then derive sufficient conditions for global stability of the fuzzy control systems involving the TS fuzzy PI controller. Finally, as an application demonstration, we apply the fuzzy PI controller to control issue temperature, in computer simulation, during hyperthermia therapy. The relationship between heat energy and tissue temperature is represented by a linear time-varying model with a time delay. The sufficient conditions for global stability are used to design a stable fuzzy control system. Our simulation results show that the fuzzy PI control system achieves satisfactory temperature control performance. The control system is robust and stable even when the model parameters are changed suddenly and significantly.     

A Takagi–Sugeno fuzzy model combined with a support vector regression for stock trading forecasting

The turning points prediction scheme for future time series analysis based on past and present information is widely employed in the field of financial applications. In this research, a novel approach to identify turning points of the trading signal using a fuzzy rule-based model is presented. The Takagi–Sugeno fuzzy rule-based model (the TS model) can accurately identify daily stock trading from sets of technical indicators according to the trading signals learned by a support vector regression (SVR) technique. In addition, when new trading points are created, the structure and parameters of the TS model are constantly inherited and updated. To verify the effectiveness of the proposed TS fuzzy rule-based modeling approach, we have acquired the stock trading data in the US stock market. The TS fuzzy approach with dynamic threshold control is compared with a conventional linear regression model and artificial neural networks. Our result indicates that the TS fuzzy model not only yields more profit than other approaches but also enables stable dynamic identification of the complexities of the stock forecasting system.     

Fouling detection in a heat exchanger by observer of Takagi–Sugeno type for systems with unknown polynomial inputs

This paper proposes a new method for fouling detection in a heat exchanger. It is based on the modeling of the system in a fuzzy Takagi–Sugeno representation derived from a physical model. With this representation, the design of a fuzzy observer with unknown inputs of polynomial types is obtained via a LMI formulation. Main advantages of the proposed method are that neither specific sensor, excepted standard ones, nor special operating conditions such as steady state regime are required. Some realistic simulations show the efficiency of the proposed technique.     

Optimal control for stochastic linear quadratic singular neuro Takagi–Sugeno fuzzy system with singular cost using genetic programming

In this paper, optimal control for stochastic linear quadratic singular neuro Takagi–Sugeno (T-S) fuzzy system with singular cost is obtained using genetic programming(GP). To obtain the optimal control, the solution of matrix Riccati differential equation (MRDE) is computed by solving differential algebraic equation (DAE) using a novel and nontraditional GP approach. The obtained solution in this method is equivalent or very close to the exact solution of the problem. Accuracy of the solution computed by GP approach to the problem is qualitatively better. The solution of this novel method is compared with the traditional Runge–Kutta (RK) method. A numerical example is presented to illustrate the proposed method.     

Safe-by-design planner–tracker synthesis with a hierarchy of system models

We present a safe-by-design trajectory planning and tracking framework for nonlinear dynamical systems using a hierarchy of system models. The planning layer uses a low-fidelity model to plan a feasible trajectory satisfying the planning constraints, and the tracking layer utilizes the high-fidelity model to design a controller that restricts the error states between the low- and high-fidelity models to a bounded set. The simplicity of the low-fidelity model enables the planning to be performed online (e.g. using Model Predictive Control) and the tracking controller and error bound are derived offline (e.g. using sum-of-squares programming). This error bound is then used by the planner to ensure safety for the combined planner–tracker system To provide freedom in the choice of the low-fidelity model, we allow the tracking error to depend on both the states and inputs of the planner. The goal of this article is to provide a tutorial review of this hierarchical framework and to illustrate it with examples, including a design for vehicle obstacle avoidance.     

Application of bifrequency phase equivalent reduction to system synthesis†

The paper discusses a method to synthesize high–order linear systems with the gain cross–over frequency (ω_eg), the phase cross-over frequency (ω_cp)and the phase margin (φm) as the given specifications, using the bifrequency phase equivalent reduction method.     

A fuzzy Lyapunov function approach to estimating the domain of attraction for continuous-time Takagi–Sugeno fuzzy systems

This paper deals with stability analysis and control design problems for continuous-time Takagi–Sugeno (T–S) fuzzy systems. The first aim is to present less conservative linear matrix inequality (LMI) conditions to design controllers and assess the stability. The second relevant contribution is to present a new strategy to find an inner estimate of the domain of attraction (DA) via LMIs. The results are based on the fuzzy Lyapunov functions (FLFs) and non-parallel distributed compensation (non-PDC) approaches. Finally, examples illustrate the effectiveness and merits of the proposed methods.     

Position control of a quadcopter drone using evolutionary algorithms-based self-tuning for first-order Takagi–Sugeno–Kang fuzzy logic autopilots

Trajectory tracking control of a quadcopter drone is a challenging work due to highly-nonlinear dynamics of the system, coupled with uncertainties in the flight environment (e.g. unpredictable wind gusts, measurement noise, modelling errors, etc). This paper addresses the aforementioned research challenges by proposing evolutionary algorithms-based self-tuning for first-order Takagi–Sugeno–Kang-type fuzzy logic controller (FLC). We consider three major state-of-the-art optimisation algorithms, namely, Genetic Algorithm, Particle Swarm Optimisation, and Artificial Bee Colony to facilitate automatic tuning. The effectiveness of the proposed control schemes is tested and compared under several different flight conditions, such as, constant, varying step and sine functions. The results show that the ABC-FLC outperforms the GA-FLC and PSO-FLC in terms of minimising the settling time in the absence of overshoots.     

Distributed fault diagnosis for process and sensor faults in a class of interconnected input–output nonlinear discrete-time systems

This paper presents a distributed fault diagnosis scheme able to deal with process and sensor faults in an integrated way for a class of interconnected input–output nonlinear uncertain discrete-time systems. A robust distributed fault detection scheme is designed, where each interconnected subsystem is monitored by its respective fault detection agent, and according to the decisions of these agents, further information regarding the type of the fault can be deduced. As it is shown, a process fault occurring in one subsystem can only be detected by its corresponding detection agent whereas a sensor fault in a subsystem can be detected by either its corresponding detection agent or the detection agent of another subsystem that is affected by the subsystem where the sensor fault occurred. This discriminating factor is exploited for the derivation of a high-level isolation scheme. Moreover, process and sensor fault detectability conditions characterising quantitatively the class of detectable faults are derived. Finally, a simulation example is used to illustrate the effectiveness of the proposed distributed fault detection scheme.     

Fault-tolerant control of wind turbines with hydrostatic transmission using Takagi–Sugeno and sliding mode techniques

In this paper, a Takagi–Sugeno Sliding Mode Observer for actuator fault diagnosis and fault-tolerant control scheme of wind turbines with hydrostatic transmission are presented. It will be shown that sliding mode techniques have the advantages that several actuator faults of the wind turbine drive train can be simultaneously reconstructed with one and the same observer and directly applied for fault compensation. Furthermore, a simple compensation approach is implemented by subtracting the reconstructed faults obtained from the (faulty) inputs. These corrected inputs act on the system as virtual actuators, such that the originally designed controller for the nominal, i.e. fault-free situation, can still be used. The fault reconstruction and fault tolerant control strategy are tested in simulations with several faults of different types.     

Fault diagnosis for a class of active suspension systems with dynamic actuators’ faults

In this paper, a new fault diagnosis and fault-tolerant control method for a class of active suspension systems with actuator faults is proposed. The considered actuators have uncertain dynamic characteristics, which are the electromagnetic actuators made up with a motor control system and a ball screw transmission mechanism. To detect such suspension system actuator faults, dynamic fault diagnosis observers are designed for the actuators to estimate the possible faults. The actuators are analyzed to first and second order dynamic models, respectively, whose output can be measured but the rate is non-measurable. Then, the fault diagnosis method is developed for these two kinds of models to obtain the fault information. Using the fault estimation and adaptive control technique, a robust fault-tolerant controller is constructed to guarantee the performance of the rail vehicles in the faulty case. Finally, using the parameters of a practical suspension system, a simulation study is conducted to show the effectiveness of the proposed method.