Filtering And Control For Singularly Perturbed Systems With Incomplete Measurements

Singularly perturbed systems(SPSs)are effective tools to describe multi-time-scale coupled systems,which are widely used in process industry,smart grid,intelligent robot and other fields.The difficulty is that the existence of singular perturbation parameter?will lead to ill-conditioned numerical problems in traditional analysis and design methods.In addition,the complete measurement is a basic condition to guarantee the safe and efficient operation of the controlled systems.However,in the actual transmission process,the factors of large sampling period,high transmission frequency and limited network bandwidth cause the incomplete measurements,which may lead to the deterioration of the system performance,and even cause the instability of systems.Therefore,it is of great practical significance to study the design method of filter and controller for SPSs with incomplete measurements to achieve the required system performance index.This dissertation studies the filter and controller design problems of SPSs with incomplete measurements by using singular perturbation technology and singular system method.Meanwhile,a series of design and analysis methods are proposed to overcome the ill-conditioned numerical problems and reduce the conservatism of designed methods.The main results of this dissertation are given as follows:(1)H_?filter design methods for SPSs with incomplete measurements are proposed.For two typical cases of incomplete measurement information,an independent random variable obeying Bernoulli distribution and an event-triggered mechanism(ETM)with large thresholds are used to describe the characteristics of random loss and active rejection of measurement data respectively.At the same time,the input delay term is adopted to deal with the hybrid characteristics of continuous and discrete dynamics coexisting in systems.By constructing an?-dependent Lyapunov-Krasovskii functional(LKF),the methods of H_?filter design based on sampled-data and ETMs are proposed.On the basis of the designed scheme,the filtering error systems can meet the expected H_?performance.And the ill-conditioned numerical problems and Zeno phenomenon are avoided in the design process.Finally,the circuit systems show that the proposed methods can obtain better disturbance rejection ability and a larger average triggering time interval.(2)Sampled-data H_?controller design methods for SPSs with incomplete measurements are proposed.For the phenomenon of actively discarding measurement data existed in the process of data acquisition and transmission,a non-uniform sampling and an ETM based on multi-rate sampled-data are respectively used to describe the features of incomplete measurement information.And an input delay term is used to analyze and deal with the hybrid characteristics of the closed-loop systems.Based on the two-time-scale feature of SPSs,an improved asynchronous ETM is constructed by using the multi-rate sampled-data to realize the independent transmission and update of the measurements for fast and slow subsystems.By constructing an LKF including the parameter?and sampling periods,the methods of H_?controller design based on a large sampling period and an asynchronous ETM are proposed,which can ensure the desired performance of the closed-loop systems.And the ill-conditioned numerical problems and Zeno phenomenon are avoided in the design process.Finally,the inverted pendulum systems verify that the proposed methods can obtain a larger stability bound and a smaller triggering number.(3)Observer-based controller design methods for SPSs with incomplete measurements and actuator saturation are proposed.For the situation of actively discarding the measurement data,a non-uniform sampling and an ETM are used to describe the features of incomplete measurement information.In addition,considering that the state information of the system is not completely measurable,a controller structure based on state estimator is proposed.By establishing an LKF based on the parameter?and a dwell time h,using the input delay method and co-design method to deal with the hybrid characteristics and the strong coupling existed in the process of controller design,the design methods of sampled-data observer-based anti-windup controller and observer-based event-triggered controller are proposed,which are free of the ill-conditioned numerical problems and Zeno phenomenon,guarantee the stability of systems,and estimate the basin of attraction.Finally,the circuit systems show that the results can efficiently reduce the load of network,get a larger basin of attraction and a lower data transmission frequency.(4)Fuzzy controller design method for coal-fired power generation systems(CFPGSs)based on the singular perturbation theory is proposed.By analyzing the characteristics of two-time-scale,nonlinearity and input saturation for CFPGSs,and using the singular perturbation theory and fuzzy control theory,the CFPGSs are modeled as fuzzy SPSs with actuator saturation.In addition,considering the factors of the unavailable information on some state variables(such as inlet steam mass flow)and the limited bandwidth of network,the event-triggered observer-based controller structure is constructed.Based on the previous design idea,a design method of event-triggered observer-based anti-windup controller is proposed by establishing an LKF which depends on the parameter?and the upper bound of time-delay,such that the closed-loop systems are asymptotically stable.And the ill-conditioned numerical problems and Zeno phenomenon are avoided in the design process.Finally,a simulation verifies the effectiveness of the proposed method,that is,the system outputs(electric power and main steam pressure)tend to the reference value.This dissertation consists of 42 figures,6 tables and 161 references.