Frequency identification of Wiener systems with Backlash operators using separable least squares estimators

This paper deals with the identification of Wiener models that involve backlash operators bordered by possibly noninvertible parametric lines. The latter are also allowed to cross each other making possible to account for general-shape static nonlinearities. The linear dynamic subsystem is not-necessarily parametric but is BIBO stable. A frequency identification method is developed that provides estimates of the nonlinear operator parameters as well as estimates of the linear subsystem frequency gain. The method involves standard and separable least squares estimators that all are shown to be consistent. Backlash operators and memoryless nonlinearities are handled within a unified framework.Preprin

Least Squares Based and Two-Stage Least Squares Based Iterative Estimation Algorithms for H-FIR-MA Systems

This paper studies the identification of Hammerstein finite impulse response moving average (H-FIR-MA for short) systems. A new two-stage least squares iterative algorithm is developed to identify the parameters of the H-FIR-MA systems. The simulation cases indicate the efficiency of the proposed algorithms

The recursive neural network

This paper describes a special type of dynamic neural network called the Recursive Neural Network (RNN). The RNN is a single-input single-output nonlinear dynamical system with three subnets, a nonrecursive subnet and two recursive subnets. The nonrecursive subnet feeds current and previous input samples through a multi-layer perceptron with second order input units (SOMLP) [9]. In a similar fashion the two recursive subnets feed back previous output signals through SOMLPs. The outputs of the three subnets are summed to form the overall network output. The purpose of this paper is to describe the architecture of the RNN, to derive a learning algorithm for the network based on a gradient search, and to provide some examples of its use. The work in this paper is an extension of previous work on the RNN [10]. In previous work the RNN contained only two subnets, a nonrecursive subnet and a recursive subnet. Here we have added a second recursive subnet. In addition, both of the subnets in the previous RNN had linear input units. Here all three of the subnets have second order input units. In many cases this allows the RNN to solve problems more efficiently, that is with a smaller overall network. In addition, the use of the RNN for inverse modeling and control was never fully developed in the past. Here, for the first time, we derive the complete learning algorithm for the case where the RNN is used in the general model following configuration. This configuration includes the following as special cases: system modeling, nonlinear filtering, inverse modeling, nonlinear prediction and control

Combined Parameter and State Estimation Algorithms for Multivariable Nonlinear Systems Using MIMO Wiener Models

This paper deals with the parameter estimation problem for multivariable nonlinear systems described by MIMO state-space Wiener models. Recursive parameters and state estimation algorithms are presented using the least squares technique, the adjustable model, and the Kalman filter theory. The basic idea is to estimate jointly the parameters, the state vector, and the internal variables of MIMO Wiener models based on a specific decomposition technique to extract the internal vector and avoid problems related to invertibility assumption. The effectiveness of the proposed algorithms is shown by an illustrative simulation example

A unified framework for solving a general class of conditional and robust set-membership estimation problems

In this paper we present a unified framework for solving a general class of problems arising in the context of set-membership estimation/identification theory. More precisely, the paper aims at providing an original approach for the computation of optimal conditional and robust projection estimates in a nonlinear estimation setting where the operator relating the data and the parameter to be estimated is assumed to be a generic multivariate polynomial function and the uncertainties affecting the data are assumed to belong to semialgebraic sets. By noticing that the computation of both the conditional and the robust projection optimal estimators requires the solution to min-max optimization problems that share the same structure, we propose a unified two-stage approach based on semidefinite-relaxation techniques for solving such estimation problems. The key idea of the proposed procedure is to recognize that the optimal functional of the inner optimization problems can be approximated to any desired precision by a multivariate polynomial function by suitably exploiting recently proposed results in the field of parametric optimization. Two simulation examples are reported to show the effectiveness of the proposed approach.Comment: Accpeted for publication in the IEEE Transactions on Automatic Control (2014

Control of Inverse Response Process using Model Predictive Controller (Simulation)

Model predictive control is an important model-based control strategy devised for large multiple-input, multiple-output control problems with inequality constraints on the input and outputs. Applications typically involve two types of calculations: (1) a steady-state optimization to determine the optimum set points for the control calculations, and (2) control calculations to determine the input changes that will drive the process to the set points. The success of model-based control strategies such as MPC depends strongly on the availability of a reasonably accurate process model. Consequently, model development is the most critical step in applying MPC. As Rawlings (2000) has noted, “feedback can overcome some effects of poor model, but starting with a poor process model is a kind to driving a car at night without headlight.” Finally the MPC design should be chosen carefully. Model predictive control has had a major impact on industrial practice, with over 4500 applications worldwide. MPC has become the method of choice for difficult control problems in the oil refining and petrochemical industries. However, it is not a panacea for all difficult control problem(Shinkey, 1994; Hugo, 2000). Furthermore, MPC has had much less impact in the order process industries. Performance monitoring of MPC systems is an important topic of current research interest

Improved techniques for bispectral reconstruction of signals

Higher order cumulants and spectra have found a variety of uses in many areas of digital signal processing. The third order spectrum, or bispectrum, is of specific interest to researchers because of some of its properties. The Bispectrum is defined as the fourier transform of the third order cumulant se quence for stochastic processes, and as a triple product of fourier transforms for deterministic signals. In the past, bispectral analysis has been used in applications such as identification of linear filters, quadratic phase coupling problems and detection of deviations from normality. This work is aimed at developing techniques for reconstructing deterministic signals in noise us ing the bispectrum. The bispectrum is zero for many noise processes, and is insensitive to linear phase shifts. The main motivation of this work is to exploit these properties of bispectrum that are potentially useful in signal re covery. The existing bispectral recovery techniques are discussed in the signal reconstruction frame work and their main limitation in handling noisy de terministic signals is brought out. New robust reconstruction procedures are provided in order to use bispectrum in such cases. The developed algorithms are tested over a range of simulated applications to bring out their robustness in handling both deterministic and stochastic signals. The new techniques are compared with existing bispectral methods in various problems. This thesis also discusses some of the tradeoffs involved in using bispectrum based reconstruction approaches against non-bispectral methods

Adaptive Input Reconstruction with Application to Model Refinement, State Estimation, and Adaptive Control.

Input reconstruction is the process of using the output of a system to estimate its input. In some cases, input reconstruction can be accomplished by determining the output of the inverse of a model of the system whose input is the output of the original system. Inversion, however, requires an exact and fully known analytical model, and is limited by instabilities arising from nonminimum-phase zeros. The main contribution of this work is a novel technique for input reconstruction that does not require model inversion. This technique is based on a retrospective cost, which requires a limited number of Markov parameters. Retrospective cost input reconstruction (RCIR) does not require knowledge of nonminimum-phase zero locations or an analytical model of the system. RCIR provides a technique that can be used for model refinement, state estimation, and adaptive control. In the model refinement application, data are used to refine or improve a model of a system. It is assumed that the difference between the model output and the data is due to an unmodeled subsystem whose interconnection with the modeled system is inaccessible, that is, the interconnection signals cannot be measured and thus standard system identification techniques cannot be used. Using input reconstruction, these inaccessible signals can be estimated, and the inaccessible subsystem can be fitted. We demonstrate input reconstruction in a model refinement framework by identifying unknown physics in a space weather model and by estimating an unknown film growth in a lithium ion battery. The same technique can be used to obtain estimates of states that cannot be directly measured. Adaptive control can be formulated as a model-refinement problem, where the unknown subsystem is the idealized controller that minimizes a measured performance variable. Minimal modeling input reconstruction for adaptive control is useful for applications where modeling information may be difficult to obtain. We demonstrate adaptive control of a seeker-guided missile with unknown aerodynamics.Ph.D.Aerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91520/1/amdamato_1.pd

Control of Inverse Response Process using Model Predictive Controller (Simulation)

Model predictive control is an important model-based control strategy devised for large multiple-input, multiple-output control problems with inequality constraints on the input and outputs. Applications typically involve two types of calculations: (1) a steady-state optimization to determine the optimum set points for the control calculations, and (2) control calculations to determine the input changes that will drive the process to the set points. The success of model-based control strategies such as MPC depends strongly on the availability of a reasonably accurate process model. Consequently, model development is the most critical step in applying MPC. As Rawlings (2000) has noted, “feedback can overcome some effects of poor model, but starting with a poor process model is a kind to driving a car at night without headlight.” Finally the MPC design should be chosen carefully. Model predictive control has had a major impact on industrial practice, with over 4500 applications worldwide. MPC has become the method of choice for difficult control problems in the oil refining and petrochemical industries. However, it is not a panacea for all difficult control problem(Shinkey, 1994; Hugo, 2000). Furthermore, MPC has had much less impact in the order process industries. Performance monitoring of MPC systems is an important topic of current research interest