Delay-dependent T–S fuzzy control for nonlinear interconnected systems: Using dithers as auxiliaries

A robustness design of fuzzy control is proposed in this paper to overcome the effect of modeling error between nonlinear system and Takagi-Sugeno (T-S) fuzzy model. In terms of Lyapunov's direct method, a stability criterion is derived to guarantee the asymptotic stability of nonlinear interconnected systems. Based on the decentralized control scheme and this criterion, a set of model-based fuzzy controllers is then synthesized via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear interconnected systems. Finally, an example is given to illustrate the concepts discussed throughout the paper.

This chapter investigates the problem of stabilization of nonlinear discrete-time networked control systems (NCS) with event-triggering communication scheme in the presence of signal transmission delay. A Takagi–Sugeno (T–S) fuzzy model and parallel-distributed compensation (PDC) scheme are first employed to design a nonlinear fuzzy event-triggered controller for the stabilization of nonlinear discrete-time NCS. The idea of the event-triggering communication scheme (a soft computation algorithm) under consideration is that the current sensor data is transmitted only when the current sensor data and the previously transmitted one satisfy a certain state-dependent trigger condition. By taking the signal transmission delay into consideration and using delay system approach, a T–S fuzzy delay system model is established to describe the nonlinear discrete-time NCSs with event-triggering communication scheme. Attention is focused on the design of fuzzy event-triggered controller which ensures asymptotic stability of the closed-loop fuzzy systems. Linear matrix inequality- (LMI-) based conditions are formulated for the existence of admissible fuzzy event-triggered controller. If these conditions are feasible, a desired fuzzy event-triggered controller can be readily constructed. A nonlinear mass-spring-damper mechanical system is presented to demonstrate the effectiveness of the proposed method.

Adaptive fuzzy decentralized optimal control for interconnected nonlinear systems with unmodeled dynamics via mixed data and event driven method

The present work is concerned to solve the problem of nonlinear robotic control systems on the basis of Takagi- Sugeno (T-S) fuzzy models. In addition, controllability and observability studies for T-S fuzzy model systems are considered for Single-Input Single-Output (SISO) and Multiple-Input Multiple-Output (MIMO) systems. In particular, the robust pole assignment approach is extended to the fuzzy field. This approach is used to design fuzzy stabilizers and fuzzy observers directly on the overall T-S fuzzy system. The latter one is the representation of the nonlinear robotic system, which is linearized around certain operation regions. The suggested method is considered for either SISO or MIMO systems. Furthermore, the method allows inducing an arbitrary behavior into the fuzzy plant in a relatively easy way. Two examples are used to verify the effectiveness of the proposed approach. The results are compared with the well-known Parallel Distributed Compensation (PDC) method, which is designed on the basis of Linear Matrix Inequalities (LMIs).

Over the past two decades, there has been a rapidly growing interest in approximating a nonlinear system by a Takagi-Sugeno (T-S) fuzzy model (Takagi & Sugeno, 1985). In general, this model is represented by using a set of fuzzy rules to describe a global nonlinear system in terms of a set of local linear models which are smoothly connected by fuzzy membership functions. Based on the T-S fuzzy model, recently, various fuzzy controllers have been developed under the so-called parallel-distributed compensation (PDC) scheme (in which each control rule is distributively designed for the corresponding rule of a T-S fuzzy model) and have been widely and successfully applied in fields ranging from aerospace to process control. The reason is because the fuzzy model-based control method provides a natural, simple and effective design approach to complement other nonlinear control techniques that require special and rather involved knowledge. Below are listed the main features of T-S model-based fuzzy control method: 1. It does not require severe structural assumptions on the plant model. 2. It preserves well-understood linear intuition. 3. It is naturally compatible with decompositions of the overall control problem. The decompositions are typically not hierarchical, and the interactions of sub-problems are captured by physical variables that are typically state variables in a more complete model of the overall system. 4. It enables control systems to respond rapidly to changing operating conditions. For this reason, it is important that the selected physical variables reflect changes in plant dynamics as operating conditions change. In fact, the T-S model-based fuzzy control method (of divide and conquer type) constructs a nonlinear controller, with certain required dynamic properties, by combining, in some sense, the members of appropriate family of linear time-invariant controllers. Here, nonlinear control design task is broken into a number of linear sub-problems, which enable linear design methods to be applied to nonlinear problems. Within the general framework of the T-S fuzzy model-based control method, a flurry of research activities have quickly yielded many important results on the design of fuzzy control systems by means of the following Lyapunov function approaches: 1. Common quadratic Lyapunov function approach (Tanaka & Sugeno, 1992; Tanaka et al, 1996; Wang et al, 1996; Cao & Frank, 2000; Assawinchaichote, 2004).

This paper addresses the analysis and design of fuzzy control systems for a class of complex uncertain single input single output nonlinear systems. In the design procedure, we represent the nonlinear system using a Takagi-Sugeno fuzzy model and construct a global fuzzy logic controller by blending all local state feedback controllers with a sliding mode controller. Unlike the commonly used parallel distributed compensation technique, we can design a global stable fuzzy controller without finding a common Lyapunov function for all local control systems, and can obtain a good tracking performance. Furthermore, a stability analysis is carried out not for the fuzzy model but for a real nonlinear system with uncertainties. One simulation example is given to show the effectiveness and feasibility of the proposed fuzzy controller design method.

This paper proposed a method of improved genetic algorithm (IGA)-based secure communications in multiple time delay chaotic (MTDC) systems with optimal H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sup> performance and advanced encryption standard (AES). First, we apply an initial round key via AES encryption function to acquire the encrypted message. The encrypted message is used to carry out double encryption by chaotic synchronization. A robust fuzzy control design is then presented to address the effects of modeling errors between the MTDC systems and Takagi-Sugeno (T-S) fuzzy models. Next, in terms of Lyapunov's direct method, a delay dependent exponential stability criterion is derived to guarantee that the trajectories of the slave system can approach those of the master system. Subsequently, the stability conditions of this criterion are transformed into linear matrix inequalities (LMIs). In addition, the genetic algorithm (GA) has drawn great attention from researchers due to the capability of GA in random search for achieving near-optimal solutions. The lower and upper bounds of the search space based on the LMI approach can be set so that the GA will seek better feedback gains of fuzzy controllers in order to speed up the synchronization. However, the GA has the shortcomings of premature convergence and local search. Therefore, an improved genetic algorithm (IGA) is proposed in this study to effectively overcome the weakness of the traditional GA. On the basis of the IGA, a fuzzy controller is synthesized to not only realize the exponential synchronization, but also achieve optimal H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sup> performance by minimizing the disturbance attenuation level. Finally, a numerical example with simulations is given to demonstrate the effectiveness of our approach.

This paper proposes an integral fuzzy control strategy to solve output regulation problem for the micro unmanned helicopter. In order to eliminate the system's bias and guarantee the zero-offset output regulation performance, we firstly take coordinate translation at equilibrium point and introduce an added integral state of output regulation error, and then the resulting augmented system is represented into a Takagi-Sugeno fuzzy model. Next, utilizing parallel distributed compensation (PDC) technique and direct Lyapunov method, an integral state feedback control law for output regulation is established by solving a set of linear matrix inequalities (LMIs). Moreover, the proposed controller design has following merits: i) capability to dealing with nonlinear affine system; ii) giving the exponential stability in the presence of model uncertainty; iii) possessing a piecewise constant output regulation performance. Finally, a micro unmanned helicopter dynamic model is presented to demonstrate the validity of the proposed integral fuzzy controller.

Exponential small-gain theorem and fault tolerant safe control of interconnected nonlinear systems

Modeling and stabilization for a class of nonlinear networked control systems: A T-S fuzzy approach

Non-fragile fuzzy mobile control for nonlinear parabolic distributed parameter processes with random packet losses

This paper investigates the Static Output (SO) control issue of the disturbed nonlinear stochastic system, which achieves passivity. Through the application of fuzzy sets and the stochastic differential equation, a Takagi–Sugeno (T-S) fuzzy model with the terms of multiplicative noise and external disturbance can be constructed to describe the considered systems. Furthermore, the Parallel Distributed Compensation (PDC) concept is used to design a fuzzy controller exhibiting an SO feedback scheme structure. To attenuate the effect of external disturbance, the PDC-based SO fuzzy controller is designed to exhibit passivity. During the derivation of some sufficient conditions, a line-integral Lyapunov function is utilized to avoid the conservative term produced using the derivative membership function. Using converting technologies, a stability criterion belonging to Linear Matrix Inequality (LMI) forms is proposed such that the derived conditions are convex hull problems and are solved through an optimization algorithm. Then, the proposed criterion is used to discuss the problem of SO controller design of ship fin stabilizing systems with added disturbance and noise.

Fuzzy logic control based on the Takagi–Sugeno inference method has been applied for the yeast alcoholic fermentation running in a continuous-time biochemical reactor in this paper. A type-1 fuzzy PID controller was designed to temperature control in a biochemical reactor. The fuzzy PID controller was also designed using type-2 fuzzy sets. The advantage of the fuzzy control is that it can be used very successfully for control of strongly non-linear processes and processes that are difficult to model because of complicated reaction kinetics. Obtained simulation results confirm this fact. The disadvantage of the fuzzy control design lies in the time-consuming tuning of controllers. The subtractive clustering method was used to identify the rule base. This approach was chosen to minimize the number of rules of the designed fuzzy logic controllers and to simplify the fuzzy controller design. Simulation results confirm that fuzzy PID controllers can assure better performance than conventional PID controllers. Yeast alcoholic fermentation is an exothermic process and the cooling is necessary to maintain the optimal temperature in the reactor. Fuzzy PID control reduces coolant consumption in comparison with conventional PID control and so it assures energy-efficient control of continuous-time alcoholic fermentation. Using type-2 fuzzy sets in the fuzzy PID controller design is very promising as the type-2 fuzzy controller offers even better results than the type-1 fuzzy controller.

This paper discusses the problem of suboptimal local piecewise H ∞ fuzzy control of quasi-linear spatiotemporal dynamic systems with control magnitude constraints. A Takagi-Sugeno fuzzy partial differential equation (PDE) model with space-varying coefficient matrices is first assumed to be derived for exactly describing nonlinear system dynamics. In the light of the fuzzy model, a local piecewise fuzzy feedback controller is then constructed to guarantee the exponential stability with a prescribed H ∞ disturbance attenuation level for the resulting closed-loop system, while the control constraints are also ensured. A sufficient condition on the existence of such fuzzy controller is developed by the Lyapunov direct method and an integral inequality and presented in terms of space algebraic linear matrix inequalities (LMIs) coupled with LMIs. By virtue of extreme value theorem, a suboptimal-constrained local piecewise H ∞ fuzzy control design in the sense of minimizing the disturbance attenuation level is formulated as a minimization optimization problem with LMI constraints. Finally, the proposed method is applied to solve the feedback control of a quasi-linear FitzHugh-Nagumo equation with space-varying coefficients, and simulation results show its effectiveness and merit.

This paper reviews the development of fuzzy systems and the problem of time delay control in nonlinear systems. Based on this review, a fuzzy Lyapunov method defined in fuzzy blending quadratic Lyapunov functions is proposed from which to derive stability conditions. In the controller procedure, a parallel distributed compensation (PDC) scheme is utilized to construct a global fuzzy logic controller (FLC) by blending all linear local state feedback controllers. Furthermore, the multiple time-delay interconnected systems are considered in the nonlinear fuzzy systems. Key words: Interconnected systems, fuzzy Lyapunov method, linear matrix inequality.