Feedback Linearization Optimal Control Of Bilinear Systems

In the real world, the ideal linear system does not exist, most practical systems are nonlinear systems, and all work with external disturbance and time-delay. The traditional method is linearization. However, with the development of control theory, the limitation of linear model is recognized. In order to describe the actual object better, the researchers constructed a nonlinear system that the state variable and control variable are linear, the whole is nonlinear, this system is the bilinear system. A bilinear system is a nonlinear system which is the simplest in form and most approximate to a linear system. Bilinear system is applied in many practise and it can describe many plants in engineering, for example, the society economy, zoology, biology, etc. This makes that the research of bilinear systems become more and more important.The major results are shown as follows:1. First, give a brief overview of nonlinear systems and current domestic; Introduce the bilinear system, including its mathematical model and current status. And give a brief description of the feedback linearization of nonlinear systems, optimal control systems and time delay. Consider the optimal control problem for the bilinear system based on state feedback, give the mathematical model of the bilinear system and the optimal control law. Then consider the optimal control problem for the bilinear system affected by measurable disturbances, by solving the Riccati equation and the Sylvester equation, a feedforword/feedback transformation is designed which is used to eliminate the influence of the disturbances.2. For the bilinear systems with time-delay, optimal controller design method is proposed based on state feedback linearization and model transformation. Researching the bilinear system with time-delay and external disturbance, through the conversion, we change it to a time-delay pseudo linear system, a linear controllable system without with time-delay is obtained by exact delay-free transformation using integral transformation with memory control. Then based on the theory of linear quadratic optimal control, a feedforword/feedback optimal disturbances rejection control law is designed which is used to eliminate the influence of the disturbances.3. Based on the knowledge of relation in nonlinear systems, we make the partial coordinate alterlate to the uncertain bilinear system with time delay and external disturbance, and the partial linearization to the system. The optimal control problem is transformed into the optimal control problem of linear system with disturbance rejection. Using the exist conclusion, the original optimal control problem is solved at 1ast. Asimulation result demonstrates the effect of the proposed method.