Application of Uncertain Nonlinear Systems Partial State Variables Control to a Class of Pendulum Systems

Because of inaccuracy of modeling and parameters measurement, the controlled systems are subjected by the inaccuracy inevitably and the control of uncertain systems is studied by many researchers. Uncertain nonlinear systems partial state variables control technique is developed, and applied to single pendulum systems. In order to make a certain state variable asymptotically stable and adaptive parameters identify the uncertain parameters, using partial state stability theory and adaptive control method, two controllers and adaptive regulators are designed separately for two state variables and uncertain parameters. Our controllers can guarantee the uniformly ultimate boundedness of the solution of the closed-loop system, and make the tracking error arbitrarily small for uncertain parameters. Numerical simulation results illustrate the effectiveness of the proposed controllers and adaptive regulators.