초록/요약

Although considering the uncertainties and constraints is very important, it is very hard to consider them by using the previous control methods due to the difficulty of the controller design and analysis. On the other hand, the recently developed SOS-based control methods provided the motivation to study the systems with the uncertainties and constraints. By using the numerical analysis, SOS approach can not only construct the controller but also can show the stability for the systems with the uncertainties and constraints. With this in mind, SOS-based control methods against the uncertainties and constraints for nonlinear systems are proposed and the practical problem in the control area such as the synchronization of chaotic system, tracking control of wheeled mobile robot, and range estimation of camera system will be studied in this dissertation. Firstly, the synchronization problem for unified chaotic system with mismatched parameters are handled. The error dynamics are expressed in the form of polynomial and the controller is designed to stabilize the error dynamics by SOS approach. The mismatched parameters which can be considered as the system uncertainties are compensated by the adaptive law. Secondly, the range estimation problem for camera system is solved by using the camera dynamics unlike the previous linear algebraic methods. Based on the camera dynamics which can be represented as the polynomial form, SOS-based state observer is designed to estimate the distance between the camera and the object along Z axis. Thirdly, the trajectory tracking control method of the wheeled mobile robot in presence of the input constraints are proposed. The tracking problem is transformed as the stabilization problem by dividing the control inputs as the feedforward and the feedback terms. The control inputs to stabilize the error are obtained by the SOS approach. In this procedure, the fuzzy method is employed to consider the input constraints of the wheeled mobile robot in analytic way. Finally, the controller considering the input rate constraints in the systems are proposed. To this end, a new state variable which consists of the system states and the control input is defined and the augmented polynomial model is derived. In this augmented model, the input magnitude and rate constraints in the original system can be considered as the state and input magnitude constraints, respectively. In this way, we can consider the system state, input magnitude, and input rate constraints.