Robust Adaptive Control Of Nonlinear Systems Based On Backstepping

The past decade has witnessed a rapid growth of research efforts aimed at the development of systematic design methods for global adaptive control of nonlinear systems with parametric uncertainty. As evidence, a large number of papers published in the literature have been dedicatedin the field of nonlinear control . However much of the researches have focused on adaptive control of feedback linearizable systems with linear parameterization. By comparison, little effort has been made to the development of adaptive control schemes of nonlinearly parameterized systems. As indicated in , nonlinear parametric systems can be found in various practical control problems. For instance, it arises naturally in physical systems such as biochemical processes and machines with friction. Dealing with this type of nonlinearly parameterized dynamic systems is not only interesting theoretically, but also important from a viewpoint of practical applications. Two recentpapers, and , solved this challenging adaptive stabilization problem by using a new parameter separation technique and the tool of adding a power integrator. Simulation results show their controllers work very well. However there are always all kinds of unknown disturbances and unmodeled dynamics exiting in the practical systems. If we consider those[2] [3]uncertainties which were not considered in and in the simulations, the states of the systems become unstable.In this paper, we present a robust adaptive control scheme for a class of nonlinear parametric systems with unmodeled dynamics and unknown bounded disturbances. With the proposed control scheme, all the variables in the closed-loop systems are bounded in the presence of unmodeled dynamics and bounded disturbances. Our design is based on the Lyapunov theory. We use a new parameter separation technique to solve the problem of nonlinear parameters, use a dynamic signal to restrain the unmodeled dynamics, and use adaptive nonlinear damping terms to counteract the effects of the uncertainties. By using backstepping method, we can get robust adaptive scheme step by step. Simulation results show that our control scheme works very well.