Parameter estimation and control of nonlinearly parameterized systems

Abstract

Parameter estimation in nonlinear systems is an important issue in measurement, diagnosis and modeling. The goal is to find a differentiator free on-line adaptive estimation algorithm which can estimate the internal unknown parameters of dynamic systems using its inputs and outputs. This thesis provides new algorithms for adaptive estimation and control of nonlinearly parameterized (NLP) systems. First, a Hierarchical Min-max algorithm is invented to estimate unknown parameters in NLP systems. To relax the strong condition needed for the convergence in Hierarchical Min-max algorithm, a new Polynomial Adaptive Estimator (PAE) is invented and the Nonlinearly Persistent Excitation Condition for NLP systems, which is no more restrictive than LPE for linear systems, is established for the first time. To reduce computation complexity of PAE, a Hierarchical PAE is proposed. Its performance in the presence of noise is evaluated and is shown to lead to bounded errors. A dead-zone based adaptive filter is also proposed and is shown to accurately estimate the unknown parameters under some conditions. Based on the adaptive estimation algorithms above, a Continuous Polynomial Adaptive Controller (CPAC) is developed and is shown to control systems with nonlinearities that have piece-wise linear parameterizations. Since large classes of nonlinear systems can be approximated by piece-wise linear functions through local linearization, it opens the door for adaptive control of general NLP systems. The robustness of CPAC under bounded output noise and disturbances is also established.