Numerical methods of stabilizer construction via guidance control

作者：Miranda Francisco^*

来源：Mathematical Methods in the Applied Sciences, 2012, 35(14): 1670-1680.

DOI：10.1002/mma.2545

• non-autonomous control systems
• guidance stabilization
• global stabilization and control
• global guidance stabilizers

This work concerns guidance stabilization of non-autonomous control systems. Global stabilization problem is usually quite complex and difficult to solve. To overcome this difficulty, guidance control is used. A guidance stabilizer uses a trajectory of a globally asymptotically stable auxiliary system as a guide. A local stabilizer keeps the trajectory of the system in a neighborhood of a solution of the auxiliary system. In this way, the trajectory of the system tends to the equilibrium position. The main idea of this method is to solve the global stabilization problem by applying local stabilization methods. The presented procedure also yields additional possibilities for the design of a stabilizer that eliminates the peak effect, that is, the large deviation of the solutions from the equilibrium position at the beginning of the stabilization process. This effect represents a serious obstacle to the design of cascade control systems and to guidance stabilization. The optimal control problem used in this paper eliminates this effect that we have when we apply known construction methods of local stabilizers to obtain a high speed of damping of the control systems trajectories. According to this approach and using e-strategies introduced by Pontryagin in the frame of differential games theory, the stabilizing control is constructed as a function of time defined in a small time interval and not as a feedback. An application to a mechanical stabilization problem is provided here.

• 出版日期2012-9-30