Sampled-data Feedback Optimal Control For A Class Of Switched Systems With Unknown Parameter

ABSTRACT:As a typical hybrid system theory model, the switched system consists of a number of continuous and discrete dynamic subsystems and switching rules. During the process of switched control, there exists a unique subsystem that is activated, and this activation depends on the switching rules. Generally, the switching rule is regarded as the vital part of the switched system. If the switching rule contains unknown parameter or the switching signal, it will become more difficult to analysis and design.In this thesis, we present a quadratic optimal control approach for a class of switched systems with unknown parameter using sampled-data feedback method. In addition, the possibility of applying to practical systems is studied as well. To estimate the unknown parameter, we use the identification algorithm and calculate the state errors caused by identification in the presence of unknown parameter. Based on the method of sampled-data feedback control, we proposed the optimal feedback control scheme to optimize the linear switching system performance. Moreover, a sufficient condition for the sampling period is obtained for the optimal performance index.The rest of the thesis is organized as follows:First, on the condition that the switching signal is unknown, the Least Matching Error Estimation algorithm is adopted to identify the unknown parameter and state errors with only one step in the switched interval. Considering the negative effects of the stochastic disturbances on the parameter identification, the system states at the end of the identification interval are analyzed and mathematically described.Second, the optimal control problem for switching systems with unknown parameter is studied in detail. The sampled-data feedback is blended with the quadratic optimization theory for designing the optimal controller. The sufficient condition of the sampling period that ensures the optimal performance is analyzed as well.Third, the train model with three switching subsystems is established. Using the MATLAB software, the effectiveness of the proposed system scheme is validated with different sampling periods. Simulation results demonstrate that the system can be optimized with improved performance and stability when the condition of sampling period is satisfied.