Finite-Time Decentralized Control of IT2 T-S Fuzzy Interconnected Systems With Discontinuous Interconnections

This paper investigates the finite-time decentralized control problem for interconnected systems with discontinuous interconnections. By using the interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy model, a unified IT2 T-S fuzzy interconnected system is provided, in which the global system is described as a fuzzy blending of local subsystems under IF-THEN rules. In addition, based on the differential inclusion theory, the solutions of such discontinuous system are defined in the sense of Filippov. In order to stabilize the considered system in finite time, several decentralized discontinuous state feedback controllers are proposed. Furthermore, by the finite-time stabilization theory and generalized Lyapunov functional method, decentralized control is carried out and several sufficient criteria are derived to ensure the finite-time stabilization of the concerned system. Correspondingly, the settling times for stabilization are given. Finally, the proposed methodology is illustrated by an example.

Adaptive Fault Estimation for T-S Fuzzy Interconnected Systems Based on Persistent Excitation Condition via Reference Signals

This paper is concerned with the fault estimation (FE) problem for a class of interconnected nonlinear systems described by Takagi-Sugeno fuzzy models. Different from the existing FE approaches, where the reference inputs are always viewed as external disturbances, the considered reference signals are injected directly in the controller to excite the system states to ensure persistent excitation condition. Within this framework, a bank of distributed adaptive observers are then designed to effectively estimate the actuator fault parameters even in the presence of nonlinear interconnections. Moreover, in the disturbance-free case, by employing graph theory, a global Lyapunov function is constructed such that the corresponding fault parameter estimate errors are proved to be asymptotically convergent provided that the interconnected strengths are less than a given constant. Finally, two simulation examples are provided to demonstrate the validity of the presented FE scheme.

Minimal-Approximation-Based Decentralized Backstepping Control of Interconnected Time-Delay Systems

A decentralized adaptive backstepping control design using minimal function approximators is proposed for nonlinear large-scale systems with unknown unmatched time-varying delayed interactions and unknown backlash-like hysteresis nonlinearities. Compared with existing decentralized backstepping methods, the contribution of this paper is to design a simple local control law for each subsystem, consisting of an actual control with one adaptive function approximator, without requiring the use of multiple function approximators and regardless of the order of each subsystem. The virtual controllers for each subsystem are used as intermediate signals for designing a local actual control at the last step. For each subsystem, a lumped unknown function including the unknown nonlinear terms and the hysteresis nonlinearities is derived at the last step and is estimated by one function approximator. Thus, the proposed approach only uses one function approximator to implement each local controller, while existing decentralized backstepping control methods require the number of function approximators equal to the order of each subsystem and a calculation of virtual controllers to implement each local actual controller. The stability of the total controlled closed-loop system is analyzed using the Lyapunov stability theorem.

Adaptive Fault-Tolerant Control of Uncertain Nonlinear Large-Scale Systems With Unknown Dead Zone

In this paper, an adaptive neural fault-tolerant control scheme is proposed and analyzed for a class of uncertain nonlinear large-scale systems with unknown dead zone and external disturbances. To tackle the unknown nonlinear interaction functions in the large-scale system, the radial basis function neural network (RBFNN) is employed to approximate them. To further handle the unknown approximation errors and the effects of the unknown dead zone and external disturbances, integrated as the compounded disturbances, the corresponding disturbance observers are developed for their estimations. Based on the outputs of the RBFNN and the disturbance observer, the adaptive neural fault-tolerant control scheme is designed for uncertain nonlinear large-scale systems by using a decentralized backstepping technique. The closed-loop stability of the adaptive control system is rigorously proved via Lyapunov analysis and the satisfactory tracking performance is achieved under the integrated effects of unknown dead zone, actuator fault, and unknown external disturbances. Simulation results of a mass-spring-damper system are given to illustrate the effectiveness of the proposed adaptive neural fault-tolerant control scheme for uncertain nonlinear large-scale systems.

INDIRECT ADAPTIVE CONTROL OF UNKNOWN MULTI VARIABLE NONLINEAR SYSTEMS WITH PARAMETRIC AND DYNAMIC UNCERTAINTIES USING A NEW NEURO-FUZZY SYSTEM DESCRIPTION

The indirect adaptive regulation of unknown nonlinear dynamical systems with multiple inputs and states (MIMS) under the presence of dynamic and parameter uncertainties, is considered in this paper. The method is based on a new neuro-fuzzy dynamical systems description, which uses the fuzzy partitioning of an underlying fuzzy systems outputs and high order neural networks (HONN's) associated with the centers of these partitions. Every high order neural network approximates a group of fuzzy rules associated with each center. The indirect regulation is achieved by first identifying the system around the current operation point, and then using its parameters to device the control law. Weight updating laws for the involved HONN's are provided, which guarantee that, under the presence of both parameter and dynamic uncertainties, both the identification error and the system states reach zero, while keeping all signals in the closed loop bounded. The control signal is constructed to be valid for both square and non square systems by using a pseudoinverse, in Moore-Penrose sense. The existence of the control signal is always assured by employing a novel method of parameter hopping instead of the conventional projection method. The applicability is tested on well known benchmarks.