On-line modeling and control via T-S fuzzy models for nonaffine nonlinear systems using a second type adaptive fuzzy approach

[[abstract]]This paper proposes a novel method for on-line modeling and robust adaptive control via Takagi-Sugeno (T-S) fuzzy models for nonaffine nonlinear systems, with external disturbances. The T-S fuzzy model is established to approximate the nonaffine nonlinear dynamic system in a linearized way. The so-called second type adaptive law is adopted, where not only the consequent part (the weighting factors) of fuzzy implications but also the antecedent part (the membership functions) of fuzzy implications are adjusted. Fuzzy B-spline membership functions (BMFs) are used for on-line tuning. Furthermore, the effect of all the unmodeled dynamics, BMF modeling errors and external disturbances on the tracking error is attenuated by a fuzzy error compensator which is also constructed from the T-S fuzzy model. In this paper, we can prove that the closed-loop system which is controlled by the proposed controller is stable and the tracking error will converge to zero. Three examples are simulated in order to confirm the effectiveness and applicability of the proposed methods in this paper.[[notice]]補正完

Adaptive Predictive Control Using Neural Network for a Class of Pure-feedback Systems in Discrete-time

10.1109/TNN.2008.2000446IEEE Transactions on Neural Networks1991599-1614ITNN

Output feedback NN control for two classes of discrete-time systems with unknown control directions in a unified approach

10.1109/TNN.2008.2003290IEEE Transactions on Neural Networks19111873-1886ITNN

Control of Nonaffine Nonlinear Discrete Time Systems using Reinforcement-learning-Based Linearly Parameterized Neural Networks

A nonaffine discrete-time system represented by the nonlinear autoregressive moving average with eXogenous input (NARMAX) representation with unknown nonlinear system dynamics is considered. An equivalent affinelike representation in terms of the tracking error dynamics is first obtained from the original nonaffine nonlinear discrete-time system so that reinforcement-learning-based near-optimal neural network (NN) controller can be developed. The control scheme consists of two linearly parameterized NNs. One NN is designated as the critic NN, which approximates a predefined long-term cost function, and an action NN is employed to derive a near-optimal control signal for the system to track a desired trajectory while minimizing the cost function simultaneously. The NN weights are tuned online. by using the standard Lyapunov approach, the stability of the closed-loop system is shown. The net result is a supervised actor-critic NN controller scheme which can be applied to a general nonaffine nonlinear discrete-time system without needing the affinelike representation. Simulation results demonstrate satisfactory performance of the controlle

Online Reinforcement Learning Control of Unknown Nonaffine Nonlinear Discrete Time Systems

In this paper, a novel neural network (NN) based online reinforcement learning controller is designed for nonaffine nonlinear discrete-time systems with bounded disturbances. The nonaffine systems are represented by nonlinear auto regressive moving average with exogenous input (NARMAX) model with unknown nonlinear functions. An equivalent affine-like representation for the tracking error dynamics is developed first from the original nonaffine system. Subsequently, a reinforcement learning-based neural network (NN) controller is proposed for the affine-like nonlinear error dynamic system. The control scheme consists of two NNs. One NN is designated as the critic, which approximates a predefined long-term cost function, whereas an action NN is employed to derive a control signal for the system to track a desired trajectory while minimizing the cost function simultaneously. Offline NN training is not required and online NN weight tuning rules are derived. By using the standard Lyapunov approach, the uniformly ultimate boundedness (UUB) of the tracking error and weight estimates is demonstrated

Adaptive Tracking of Angular Velocity for a Planar Rigid Body With Unknown Models for Inertia and Input Nonlinearity

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57795/1/AdaptiveTrackingTACTTCST1D.pd

Lyapunov based optimal control of a class of nonlinear systems

Optimal control of nonlinear systems is in fact difficult since it requires the solution to the Hamilton-Jacobi-Bellman (HJB) equation which has no closed-form solution. In contrast to offline and/or online iterative schemes for optimal control, this dissertation in the form of five papers focuses on the design of iteration free, online optimal adaptive controllers for nonlinear discrete and continuous-time systems whose dynamics are completely or partially unknown even when the states not measurable. Thus, in Paper I, motivated by homogeneous charge compression ignition (HCCI) engine dynamics, a neural network-based infinite horizon robust optimal controller is introduced for uncertain nonaffine nonlinear discrete-time systems. First, the nonaffine system is transformed into an affine-like representation while the resulting higher order terms are mitigated by using a robust term. The optimal adaptive controller for the affinelike system solves HJB equation and identifies the system dynamics provided a target set point is given. Since it is difficult to define the set point a priori in Paper II, an extremum seeking control loop is designed while maximizing an uncertain output function. On the other hand, Paper III focuses on the infinite horizon online optimal tracking control of known nonlinear continuous-time systems in strict feedback form by using state and output feedback by relaxing the initial admissible controller requirement. Paper IV applies the optimal controller from Paper III to an underactuated helicopter attitude and position tracking problem. In Paper V, the optimal control of nonlinear continuous-time systems in strict feedback form from Paper III is revisited by using state and output feedback when the internal dynamics are unknown. Closed-loop stability is demonstrated for all the controller designs developed in this dissertation by using Lyapunov analysis --Abstract, page iv

Equivalence between Approximate Dynamic Inversion and Proportion-Integral Control

Approximate Dynamic Inversion (ADI) has been established as a method to control minimum-phase, nonaffine-in-control systems. Previous results have shown that for single-input nonaffine-in-control systems, every ADI controller admits a linear Proportional-Integral (PI) realization that is largely independent of the nonlinear function that defines the system. In this report, we first present an extension of the ADI method for single-input nonaffine-in-control systems that renders the closed-loop error dynamics independent of the reference model dynamics. The equivalent PI controller will be derived and both of these results are then extended to multi-input nonaffine-in-control systems.DSO National Laboratories (Singapore), AFOSR grant FA9550-08-1-0086