Recursive bayesian identification of nonlinear autonomous systems

This paper concerns the recursive identification of nonlinear discrete-time systems for which the original equations of motion are not known. Since the true model structure is not available, we replace it with a generic nonlinear model. This generic model discretizes the state space into a finite grid and associates a set of velocity vectors to the nodes of the grid. The velocity vectors are then interpolated to define a vector field on the complete state space. The proposed method follows a Bayesian framework where the identified velocity vectors are selected by the maximum a posteriori (MAP) criterion. The resulting algorithms allow a recursive update of the velocity vectors as new data is obtained. Simulation examples using the recursive algorithm are presented

Recursive least square and fuzzy modelling using genetic algorithm for process control application

A technique for the modelling of nonlinear process control using Recursive Least Square and Takagi-Sugeno Fuzzy System with Genetic Algorithm topology is described. This paper discusses the identification of parameters of the fuzzy sets at the antecedent part and linear model at the consequent part of fuzzy model within an application to process control. The key issues of finding the best model of the process are described. Results show that fuzzy model with genetic algorithm gives minimum mean squared error compare with recursive least square

Online identification and nonlinear control of the electrically stimulated quadriceps muscle

A new approach for estimating nonlinear models of the electrically stimulated quadriceps muscle group under nonisometric conditions is investigated. The model can be used for designing controlled neuro-prostheses. In order to identify the muscle dynamics (stimulation pulsewidth-active knee moment relation) from discrete-time angle measurements only, a hybrid model structure is postulated for the shank-quadriceps dynamics. The model consists of a relatively well known time-invariant passive component and an uncertain time-variant active component. Rigid body dynamics, described by the Equation of Motion (EoM), and passive joint properties form the time-invariant part. The actuator, i.e. the electrically stimulated muscle group, represents the uncertain time-varying section. A recursive algorithm is outlined for identifying online the stimulated quadriceps muscle group. The algorithm requires EoM and passive joint characteristics to be known a priori. The muscle dynamics represent the product of a continuous-time nonlinear activation dynamics and a nonlinear static contraction function described by a Normalised Radial Basis Function (NRBF) network which has knee-joint angle and angular velocity as input arguments. An Extended Kalman Filter (EKF) approach is chosen to estimate muscle dynamics parameters and to obtain full state estimates of the shank-quadriceps dynamics simultaneously. The latter is important for implementing state feedback controllers. A nonlinear state feedback controller using the backstepping method is explicitly designed whereas the model was identified a priori using the developed identification procedure

On-Line Identification of Nonlinear Systems Using Volterra Polynomial Basis Function Neural Networks

An on-line identification scheme using Volterra polynomial basis function (VPBF) neural networks is considered for nonlinear control systems. This comprises of a structure selection procedure and a recursive weight learning algorithm. The orthogonal least squares algorithm is introduced for off-line structure selection and the growing network technique is used for on-line structure selection. An on-line recursive weight learning algorithm is developed to adjust the weights so that the identified model can adapt to variations of the characteristics and operating points in the nonlinear systems. The convergence f both the weights and estimation errors is established using a Lyapunov technique. The identification procedure is illustrated using simulated examples

Identification of multivariable high performance turbofan engine dynamics from closed loop data

The multivariable instrumental variable/approximate maximum likelihood (IV/AML) method or recursive time-series analysis is used to identify the multivariable (four inputs-three outputs) dynamics of the Pratt and Whitney F100 engine. A detailed nonlinear engine simulation is used to determine linear engine model structures and parameters at an operating point using open loop data. Also, the IV/AML method is used in a direct identification mode to identify models from actual closed loop engine test data. Models identified from simulated and test data are compared to determine a final model structure and parameterization that can predict engine response for a wide class of inputs. The ability of the IV/AML algorithm to identify useful dynamic models from engine test data is assessed

Identification of nonlinear time-varying systems using an online sliding-window and common model structure selection (CMSS) approach with applications to EEG

The identification of nonlinear time-varying systems using linear-in-the-parameter models is investigated. A new efficient Common Model Structure Selection (CMSS) algorithm is proposed to select a common model structure. The main idea and key procedure is: First, generate K 1 data sets (the first K data sets are used for training, and theK 1 th one is used for testing) using an online sliding window method; then detect significant model terms to form a common model structure which fits over all the K training data sets using the new proposed CMSS approach. Finally, estimate and refine the time-varying parameters for the identified common-structured model using a Recursive Least Squares (RLS) parameter estimation method. The new method can effectively detect and adaptively track the transient variation of nonstationary signals. Two examples are presented to illustrate the effectiveness of the new approach including an application to an EEG data set