Stability analysis and robust controller design for a class of uncertain nonlinear systems

Abstract

With the rapid industrialization of human societies, demands for more sophisticated controllers to not only achieve higher performance but handle uncertainties have been increased. Traditional linear control theory, which relies on the assumptions that the system model is well known and linearizable, has provided powerful tools for the design of simple controllers capable of meeting performance specifications. However in practical situation physical systems are inherently nonlinear and therefore the linear control methods may exhibit significant performance degradation or even instability for their limitations. Thus, the topic of nonlinear control design to meet high speed, high accuracy, high performance, and robustness requirements has been occupied the attention of system theorists, and various schemes are developed. They can be categorized into the three approaches, feedback linearization techniques, robust control approach, and adaptive control approach. Generally speaking, robust controllers are simpler to implement and do not need any time to tune to parameter variations while adaptive controllers are applicable to a wider range of uncertainties. However, the most methods are based on the assumptions that the full state of the actual systems should be available directly and that the control variables are not bounded. In practical implementation, the control input variables are bounded because of physical constraints. And, in practical applications to control of mechanical dynamic systems, the velocity measurements are typically obtained through tachometers and contaminated by noise while the position measurement are obtained very accurately through encoders. The problem of designing observers for uncertain nonlinear systems and showing that a given state feedback controller will guarantee the robust stability through the estimated state in place of the true one is very complex due to the nonlinearity of closed-loop control systems and uncertainties. Thus...