Unknown dynamics estimator-based output-feedback control for nonlinear pure-feedback systems

Most existing adaptive control designs for nonlinear pure-feedback systems have been derived based on backstepping or dynamic surface control (DSC) methods, requiring full system states to be measurable. The neural networks (NNs) or fuzzy logic systems (FLSs) used to accommodate uncertainties also impose demanding computational cost and sluggish convergence. To address these issues, this paper proposes a new output-feedback control for uncertain pure-feedback systems without using backstepping and function approximator. A coordinate transform is first used to represent the pure-feedback system in a canonical form to evade using the backstepping or DSC scheme. Then the Levant's differentiator is used to reconstruct the unknown states of the derived canonical system. Finally, a new unknown system dynamics estimator with only one tuning parameter is developed to compensate for the lumped unknown dynamics in the feedback control. This leads to an alternative, simple approximation-free control method for pure-feedback systems, where only the system output needs to be measured. The stability of the closed-loop control system, including the unknown dynamics estimator and the feedback control is proved. Comparative simulations and experiments based on a PMSM test-rig are carried out to test and validate the effectiveness of the proposed method

Hierarchical modeling of multi-scale dynamical systems using adaptive radial basis function neural networks: application to synthetic jet actuator wing

To obtain a suitable mathematical model of the input-output behavior of highly nonlinear, multi-scale, nonparametric phenomena, we introduce an adaptive radial basis function approximation approach. We use this approach to estimate the discrepancy between traditional model areas and the multiscale physics of systems involving distributed sensing and technology. Radial Basis Function Networks offers the possible approach to nonparametric multi-scale modeling for dynamical systems like the adaptive wing with the Synthetic Jet Actuator (SJA). We use the Regularized Orthogonal Least Square method (Mark, 1996) and the RAN-EKF (Resource Allocating Network-Extended Kalman Filter) as a reference approach. The first part of the algorithm determines the location of centers one by one until the error goal is met and regularization is achieved. The second process includes an algorithm for the adaptation of all the parameters in the Radial Basis Function Network, centers, variances (shapes) and weights. To demonstrate the effectiveness of these algorithms, SJA wind tunnel data are modeled using this approach. Good performance is obtained compared with conventional neural networks like the multi layer neural network and least square algorithm. Following this work, we establish Model Reference Adaptive Control (MRAC) formulations using an off-line Radial Basis Function Networks (RBFN). We introduce the adaptive control law using a RBFN. A theory that combines RBFN and adaptive control is demonstrated through the simple numerical simulation of the SJA wing. It is expected that these studies will provide a basis for achieving an intelligent control structure for future active wing aircraft

System Identification for Nonlinear Control Using Neural Networks

An approach to incorporating artificial neural networks in nonlinear, adaptive control systems is described. The controller contains three principal elements: a nonlinear inverse dynamic control law whose coefficients depend on a comprehensive model of the plant, a neural network that models system dynamics, and a state estimator whose outputs drive the control law and train the neural network. Attention is focused on the system identification task, which combines an extended Kalman filter with generalized spline function approximation. Continual learning is possible during normal operation, without taking the system off line for specialized training. Nonlinear inverse dynamic control requires smooth derivatives as well as function estimates, imposing stringent goals on the approximating technique

Matrix formulation of fuzzy rule-based systems

In this paper, a matrix formulation of fuzzy rule based systems is introduced. A gradient descent training algorithm for the determination of the unknown parameters can also be expressed in a matrix form for various adaptive fuzzy networks. When converting a rule-based system to the proposed matrix formulation, only three sets of linear/nonlinear equations are required instead of set of rules and an inference mechanism. There are a number of advantages which the matrix formulation has compared with the linguistic approach. Firstly, it obviates the differences among the various architectures; and secondly, it is much easier to organize data in the implementation or simulation of the fuzzy system. The formulation will be illustrated by a number of examples