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

A methodology for airplane parameter estimation and confidence interval determination in nonlinear estimation problems

An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. With the fitted surface, sensitivity information can be updated at each iteration with less computational effort than that required by either a finite-difference method or integration of the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, and thus provides flexibility to use model equations in any convenient format. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. The degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels and to predict the degree of agreement between CR bounds and search estimates

Performance analysis of least squares algorithm for multivariable stochastic systems

summary:In this paper, we consider the parameter estimation problem for the multivariable system. A recursive least squares algorithm is studied by minimizing the accumulative prediction error. By employing the stochastic Lyapunov function and the martingale estimate methods, we provide the weakest possible data conditions for convergence analysis. The upper bound of accumulative regret is also provided. Various simulation examples are given, and the results demonstrate that the convergence rate of the algorithm depends on the parameter dimension and output dimension

Data-based mechanistic modelling, forecasting, and control.

This article briefly reviews the main aspects of the generic data based mechanistic (DBM) approach to modeling stochastic dynamic systems and shown how it is being applied to the analysis, forecasting, and control of environmental and agricultural systems. The advantages of this inductive approach to modeling lie in its wide range of applicability. It can be used to model linear, nonstationary, and nonlinear stochastic systems, and its exploitation of recursive estimation means that the modeling results are useful for both online and offline applications. To demonstrate the practical utility of the various methodological tools that underpin the DBM approach, the article also outlines several typical, practical examples in the area of environmental and agricultural systems analysis, where DBM models have formed the basis for simulation model reduction, control system design, and forecastin

System identification, time series analysis and forecasting:The Captain Toolbox handbook.

CAPTAIN is a MATLAB compatible toolbox for non stationary time series analysis, system identification, signal processing and forecasting, using unobserved components models, time variable parameter models, state dependent parameter models and multiple input transfer function models. CAPTAIN also includes functions for true digital control

Self-tuning controllers via the state space

Imperial Users onl

An algorithm for maximum likelihood estimation using an efficient method for approximating sensitivities

An algorithm for maximum likelihood (ML) estimation is developed primarily for multivariable dynamic systems. The algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). The method determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort compared with integrating the analytically determined sensitivity equations or using a finite-difference method. Different surface-fitting methods are discussed and demonstrated. Aircraft estimation problems are solved by using both simulated and real-flight data to compare MNRES with commonly used methods; in these solutions MNRES is found to be equally accurate and substantially faster. MNRES eliminates the need to derive sensitivity equations, thus producing a more generally applicable algorithm