Robust nonlinear control: The extended linearization

We categorize nonlinear systems with parameter uncertainties into 4 classes according to the effect of parameter uncertainties on the equilibrium manifold and the variation rate of scheduling signal. A system in CLASS 1 is that the equilibrium manifold is independent upon parameter uncertainties and the scheduling signal is slowly varying. A system in CLASS 2 is that the scheduling signal is sufficiently slowly varying, the equilibrium manifold depends upon both the scheduling signal and parameter uncertainties. A system in CLASS 3 is that the equilibrium manifold is independent of parameter uncertainties and the scheduling signal is fast varying. A system in CLASS 4 is that the scheduling signal is fast varying, the equilibrium manifold depends on the scheduling signal and parameter uncertainties.; For a system in CLASS 1, we develop a control law for the output regulation and investigate stability. The control law whose linearization around the equilibrium manifold is characterized by a constant feedback gain matrix is proposed. We address ultimate boundedness of the state and the output of the nonlinear closed loop system.; Next, we address the control law design for the output regulation and stability analysis for a system in a subclass of CLASS 2. We propose a two loop control law. The inner loop control law design is based on the nominal equilibrium manifold and makes use of extended linearization. We complete the two loop control law design by the outer loop control law which is a non-identifier-based adaptive control law. Based upon Lyapunov stability, we prove ultimate boundedness of the state and the output. Also, we prove that the two loop control law achieves {dollar}lambda{dollar}-regulation of the output.; For a system in CLASS 3, we develop a state feedback control law and investigate stability. Since the perturbed equilibrium manifold has the derivative of the scheduling signal as its argument, we achieve the improved performance of the output regulation for fast varying scheduling signal. We obtain ultimate boundedness of the state and the output of the nonlinear closed loop system.; Finally, we address the control law design for the output regulation and stability analysis for a system in a subclass of CLASS 4. A system in the subclass is assumed that the linearization family of the system satisfies the relaxed conditions of almost strict positive realness. In order to achieve the control objective, we couple the idea of the two loop control law as proposed in the case of the second class and the idea of the control law design as proposed in the case of the third class. Here, the inner loop control law makes use of the scheduling signal and its derivative as well. By a non-identifier-based adaptive control law we complete the two loop control law. We investigate stability and {dollar}lambda{dollar}-regulation of the output. (Abstract shortened by UMI.)...