An Interval Type-2 (IT-2) fuzzy control approach is proposed to solve the Formation-Containment (F-C) problem for nonlinear multiple Autonomous Ship (AS) systems with the consideration of uncertainties and multiplicative noises. Based on the IT-2 Takagi-Sugeno Fuzzy Model (T-SFM), the nonlinear control problem can be recast into a linear problem. Different from the existing F-C control research, the formation problem is solved by the individual IT-2 fuzzy tracking controller of each leader. As a result, the information communication between leaders, who are farthest from each other, is needless. Moreover, other valuable functions such as the avoidance of known obstacles and time-varying formation can also be accomplished by designing the proper target trajectories for the tracking of leaders. By virtue of the IT-2 T-SFM, the analysis methods for linear Multi-Agent Control Systems (MACSs) can be utilized to solve the containment analysis problem, which is caused by the leaders' control input. Finally, the simulation results of multiple ASs are provided to demonstrate the advantage of the IT-2 fuzzy controller design approach in the F-C problem.

A Fuzzy Sliding Mode (FSM) tracking approach is proposed via Interval Type-2 (IT-2) Takagi-Sugeno Fuzzy Model (T-SFM) to complete Formation and Containment (F-and-C) tasks for Nonlinear Multi-Agent Systems (NMASs) with uncertainties and disturbances. Using Imperfect Premise Matching (IPM) approach, the IT-2 F-and-C Fuzzy Controllers (FCs) are designed in accordance with the IT-2 T-SFM. Different from the existing research, the individual tracking FC for each leader is proposed to complete the formation tasks and assignment of whole system dynamics. The stability analysis process is also simplified for ensuring the formation purpose. Benefiting from the advantage, the FSM control is conveniently combined into the FC design to upgrade the performance of leaders. For followers, the analysis methods of linear Multi-Agent (M-A) systems are extended to solve the containment analysis problem without the additional assumption by virtue of the IT-2 T-SFM representation. To deal with the disturbance effect, the passive constraints are combined into the analysis process. Finally, the proposed F-and-C FCs design method is applied to a Nonlinear Multi-Ships System (NMSS) to illustrate the advantage.

In this paper, the multiple performance problems including the stochastic behaviors, perturbations, and transient behaviors of time response are considered for the discrete-time nonlinear systems. Based on the Takagi-Sugeno fuzzy model, a robust fuzzy controller design method is proposed to achieve the requirements of the above performances. Firstly, the covariance control theory is applied to achieve stability and also suppress the energy of the system under the effects of stochastic behaviors. Secondly, the robust control theory is applied to deal with the perturbations in the system state and input. Thirdly, the pole placement theory is applied to obtain better transient behaviors by locating the closed-loop poles in the given region. Moreover, all the theories are combined into each other such that the multiple performance requirements can be satisfied, simultaneously. To verify the proposed robust fuzzy controller design method, a numerical example for the control of a nonlinear discrete-time stochastic system is provided.

In this paper, a fuzzy controller design problem for continuous perturbed nonlinear stochastic systems with state multiplicative noises is investigated. In order to simultaneously achieve variance and passivity constrained performances, some sufficient conditions are derived based on the Lyapunov theory. These sufficient conditions are in term of the linear matrix inequality forms that can be solved by the convex optimal programming algorithm. Besides, the parallel distributed compensation concept is employed to construct the fuzzy controllers. Finally, a numerical simulation example is given to show the effectiveness and applicability of the proposed fuzzy control methodology.

This paper presents a passive fuzzy controller design method for stabilizing the uncertain nonlinear stochastic inverted pendulum robot system. Through Takagi-Sugeno (T-S) fuzzy modeling approach, the complex nonlinear properties can be described by combining several linear sub-systems and determined membership functions. The Ito stochastic differential equation is employed to represent dynamics of systems in this paper. Applying the modeling approach, the T-S fuzzy model with multiplicative noise can be built for describing the nonlinear stochastic system. Besides, the uncertainties of the controlled system are considered in this paper for dealing with molding errors and varying parameters. Hence, the robust control problem is also discussed and investigated in this paper. Finally, the numerical simulations are proposed to show the effectiveness of the present design approach.

This paper studies the stabilization problem of a kind of large-scale fuzzy system. The large-scale fuzzy system consists of a large number of nonlinear subsystems which are linked through time-varying interconnections. Furthermore, S-procedure is used to solve the transformation from non-LMI problem to LMI problem. Finally, a numerical simulation for a large-scale fuzzy system is given to show the applications of the present approach.

A stability analysis and controller synthesis methodology for an inverted robot arm system is proposed in this paper. This uncertain system is modeled by a state space Takagi-Sugeno (T-S) fuzzy model with linear nominal part and structure bounded parameter uncertainties in the state equations of each fuzzy rule. First, a sufficient condition on robust stability of the continuous perturbed time-delay affine T-S (CPTDATS) fuzzy models of inverted robot arm is proposed. Then, Hinfin-disturbance attenuation performance of the fuzzy models is analyzed. At last, a numerical example shows the use of the proposed approach on the stabilization and Hinfin-disturbance attenuation for the inverted robot arm systems.

A parallel distributed compensation (PDC) based fuzzy controller design issue to discrete time-delay affine Takagi-Sugeno (T-S) fuzzy systems is considered. It is noted that the discrete time-delay affine T-S fuzzy systems stabilization matrix inequalities belong to a class of bilinear matrix inequalities (BMI) and cannot be solved by a convex optimization algorithm. Due to this reason, an iterative linear matrix inequality (ILMI) algorithm is used to represent the BMI problem into a linear matrix inequality (LMI) problem and to obtain the feasible solution for the synthesis of the discrete time-delay affine T-S fuzzy systems. Finally, a numerical simulation is given to show the applications of the present approach.

This paper presents a model-based fuzzy control of translational oscillations with a proof mass actuator (TORA), which is well known as a nonlinear control benchmark problem. In this paper, the nonlinear TORA system is modeled by the Takagi-Sugeno (T-S) fuzzy stochastic system. For this TS type fuzzy model, we design the T-S fuzzy controller which not only ensure the stability of the closed-loop system, but also minimize the control input energy with state variance constraints. The present method uses Linear Matrix Inequalities (LMI) approach to find the common positive definite covariance matrix and feedback gains for each rule of the TORA TS fuzzy stochastic systems.

For the design problem of active suspension systems, the purpose of compensator is to suppress the road disturbances and to tolerate the different body mass. From the control viewpoints, this kind of compensators is equal to the robust controller for which the H/sub 2/ norm is minimized. In this paper, we attempt to use a Simple Genetic Algorithm (SGA) to find out the compensator. The notion is that all elements of compensator are randomly given. The compensator is determined by use of the fitness function which is composed of stability conditions, i.e., we determine the compensator according to the grade of stability. Thus we derive new stability conditions and convert them into numerals. To enhance the computing speed, we propose a Hierarchical Fitness Function Structure (HFFS) to merge these numerals into a unique fitness value. Based on these quantified stability conditions, HFFS and SGA, we can find the compensator without using complex mathematical derivation. Besides, we derive the new stability conditions by using the concept of family of polynomials, the generalized edge theorem, Hurwitz testing matrix and some simple control concept rather than using Lyapunov stability criteria. The purpose is to relax the stability constraints.

Subject to assign a common covariance matrix, the motivation of this paper is to find discrete fuzzy controllers for discrete Takagi-Sugeno (T-S) fuzzy stochastic systems. The approach developed in this paper is based on the concept of parallel distributed compensation (PDC). For each rule of the discrete Takagi-Sugeno fuzzy stochastic model, it shows how to parameterize the static linear feedback control gain to achieve a common covariance matrix for each subsystem.

Considers continuous fuzzy stochastic systems with structured perturbations, which are controlled by the covariance control method. The purpose of the paper is to develop a useful methodology, which is based on the theory of covariance control, to assign a common positive definite covariance matrix and to solve feedback gains for each rule of the continuous Takagi-Sugeno (T-S) fuzzy stochastic systems. Finally, we provide a simple example to show the result of the recommended method.

A simple Takagi-Sugeno (TS) fuzzy controller design method is proposed, which is based on the genetic algorithm (GA) and generalized inverse theory. The eigenvalues problems of LMI could be implemented by this approach. The proposed method can automatically seek the feedback gains without complex mathematical derivations. In this paper, we implement the TS fuzzy controller design problems in an alternative way.