Research On The H_∞Control Of Interconnected Large-Scale System Based On Fuzzy Models

With the rapid development of modern science and technology, many practi-cal control systems can be seen as nonlinear interconnected large-scale systems, so the decentralized control theory of interconnected large-scale systems has attracted great attentions in both academic research and industrial applications. The precise state model is required in classical nonlinear control theory and the design process is also very complicated. An effective method dealing with the above problem is fusing fuzzy control and the decentralized control theory of interconnected large-scale systems to develop the effective methodology that guaranteeing some basic requirements, such as stability and H∞performance, for nonlinear interconnected large-scale systems based on Takagi-Sugeno (T-S) fuzzy models or fuzzy hyperbolic models(FHM). The main contents of the dissertation can be briefly described as follows:1. Based on T-S fuzzy model, firstly decentralized state feedback H∞controllers are designed for homogeneous fuzzy interconnected large-scale systems. If states of the system are not all available, the decentralized fuzzy observers are proposed to estimate the states of each subsystem for decentralized control. Consequently, the fuzzy observer-based state feedback decentralized fuzzy controllers are proposed to solve H∞control problem. Secondly, non-fragile state feedback H∞controllers are designed for affine fuzzy interconnected large-scale systems. The corresponding sufficient conditions in the terms of linear matrix inequalities (LMIs) are proposed to guarantee the fuzzy interconnected large-scale systems are asymptotically stable with the H∞performance.2. Reliable H∞controllers are designed for descriptor interconnected large-scale system with time-delay based on T-S model, and the sufficient conditions using LMIs for the existence of state feedback controllers and observer-based state feedback controllers respectively, which enable the systems to satisfy H∞performance are provided.3. Based on T-S fuzzy model, robust and reliable decentralized H∞tracking control issue is considered for the fuzzy large-scale interconnected systems with time-varying delay. Firstly, the ordinary fuzzy interconnected systems are equivalently transformed to the fuzzy descriptor systems, then new LMIs-based conditions with some free variables are derived to guarantee the H∞tracking performance not only when all control components are operating well, but also in the presence of some possible actuator failures. Moreover, the precise failure parameters of the actuators are not required, and the requirements are only the lower and upper bounds of failure parameters. Therefore, obtained results are less conservative.4. The problem of stabilizing the fuzzy interconnected bilinear systems via the state-feedback controllers with actuator saturation is dealt. Firstly, the nonlinear interconnected systems with the additive disturbance inputs are represented into the bilinear interconnected systems via Taylor’s series expansion and then the T-S fuzzy modeling technique is adopted to construct the fuzzy bilinear models. Secondly, the saturated linear state-feedback controllers for fuzzy interconnected bilinear systems are presented. An ellipsoid is the contractively invariant set of the fuzzy intercon-nected bilinear systems. The LMI-based conditions are proposed such that the fuzzy interconnected bilinear systems are asymptotically stable with the H∞performance with the ellipsoid contained in the region of attraction. Moreover, an assigned poly-topic region of the state space, containing the equilibrium, is enclosed into the region of attraction of the equilibrium itself.5. Firstly, the FHM is used to establish the model for certain large-scale sys-tems, then using a new Lyapunov function, the sufficient condition in the terms of LMIs which guarantee the existence of the state feedback H∞control even in the presence of some possible actuator failures is proposed. Secondly, delay-dependent robust and reliable H∞fuzzy hyperbolic control for nonlinear large-scale intercon-nected systems with parameter uncertainties is developed. The modeling method of FHM is given for the general large-scale interconnected systems with time-delay, then LMIs-based conditions with some free weighting matrices are derived, which guarantee the closed-loop interconnected systems to be robustly stable with the H∞performance even in the presence of some possible actuator failures.6. Sampled-data reliable H∞, hyperbolic control for uncertain continuous-time fuzzy large-scale systems with time-varying delay is developed. Firstly, FHM is used to establish the model for certain complex large-scale systems, then LMIs-based conditions are derived to guarantee the H∞performance not only when all control components are operating well, but also in the presence of some possible actuator failures. The conditions are dependent on the upper bound of time-delay, and not dependent on the derivative of time-varying delay. Moreover, we do not require the sampling to be periodic, and the only requirement is that the maximum sampled-data interval is less than a given bound. Two examples are provided to illustrate the effectiveness of FHM-based control, and the comparison between the FHM and T-S model are provided.