Payman Sadegh

Constrained optimization via stochastic approximation with a simultaneous perturbation gradient approximation

This paper deals with a projection algorithm for stochastic approximation using simultaneous perturbation gradient approximation for optimization under inequality constraints where no direct gradient of the loss function is available and the inequality constraints are given as explicit functions of the optimization parameters. It is shown that, under application of the projection algorithm, the parameter iterate converges almost surely to a Kuhn-Tucker point. The procedure is illustrated by a numerical example.

Optimal experiment design for identification of grey-box models

Optimal experiment design is investigated for stochastic dynamic systems where the prior partial information about the system is given as a probability distribution function in the system parameters. The concept of information is related to entropy reduction in the system through Lindleys measure of average information, and the relationship between the choice of information related criteria and some estimators (MAP and MLE) is established. A continuous time physical model of the heat dynamics of a building is considered and the results show that performing an optimal experiment corresponding to a MAP estimation results in a considerable reduction of the experimental length. Besides, it is established that the physical knowledge of the system enables us to design experiments, with the goal of maximizing information about the physical parameters of interest.

Experiment Design for Grey-Box Models

Abstract In this paper, design methods are presented, where information related criteria for optimality of the precision of the resulting parameter estimates are extended with prior information, corresponding to the available physical knowledge about the system, and with cost related loss function elements, reflecting the importance of the obtained parameter estimates. Bayesian as well as non-Bayesian techniques are discussed. An example is given on the grey-box approach for optimal design of a power constrained input sequence.

On the Usefulness of Grey-box Information when doing Experiment Design for System Modeling and Identification

Abstract In this paper, the usefulness of performing optimal experiments for stochastic dynamic models is investigated. The prior partial information about the parameters of the model is given as probability distribution functions in the system parameters. The concept of information is related to entropy reduction in the parameters through Lindley’s measure of average information, and the relationship between the choice of information related criteria and some estimators (MAP and MLE) is established. Bayesian as well as non-Bayesian techniques are considered and compared using numerical methods and geometrical interpretations and the importance of employing partial prior information in design methods is discussed. The role of prior physical knowledge has also been investigated in experiment design for a continuous time model. The results show that introducing prior information in experimental design methods enables us to reach a more efficient identification especially in terms of a reduction of the experimental length. Besides, it is established that the physical knowledge of system enables us to design experiments which are informative about the physical parameters of interest.

Globally Constrained Local Function Approximations via Hierarchical Modeling; A Framework for System Modeling Under Partial Information

Abstract Local function approximations concern fitting low order models to weighted data in neighborhoods of the points where the approximations are desired. Despite their generality and convenience of use, local models typically suffer, among others, from difficulties arising in physical interpretation of the parameters and data sparsity in high dimensional situations (or the so called curse of dimensionality). While estimation in parametric globed models, on the other hand, may eliminate the majority of these problems, it generally raises other important issues such as trade off between selecting an appropriate model structure and preserving good local properties. This paper presents a new approach for system modeling under partial (global) information (or the so called gray-box modeling) that seeks to preserve the benefits of the globed as well as local methodologies within a unified framework. While the proposed technique relies on local approximations, constraints are introduced to ensure the conformity of the estimates to a given global structure. Hierarchical models are then utilized as a tool to accommodate global model uncertainties via parametric variabilities within this structure. The globed parameters and their associated uncertainties are estimated simultaneously with the (local estimates of) function values. The approach is applied to modeling of a linear time varying dynamic system under prior linear time invariant structure where local regression fails as a result of high dimensionality

Input design for linear dynamic systems using maxmin criteria

Abstract This paper considers the problem of input design for maximizing the smallest eigenvalue of the information matrix for linear dynamic systems. The optimization of the smallest eigenvalue is of interest in parameter estimation and parameter change detection problems. We describe a simple cutting plane algorithm to determine the optimal frequency power weights of the input, using successive solutions to linear programs. We present a case study related to estimation of thermal parameters of a building.

Maxmin Input Design for Linear Dynamic Systems

Abstract This paper considers the problem of input design for maximizing the smallest eigenvalue of the information matrix for linear dynamic systems. The optimization of the smallest eigenvalue is of interest in parameter estimation and parameter change detection problems. We describe a simple cutting plane algorithm to determine the optimal frequency power weights of the input, using successive solutions to linear programs.

Constrained Optimization via Stochastic Approximation with a Simultaneous Perturbation Gradient Approximation

Abstract The paper deals with a projection algorithm for stochastic approximation using simultaneous perturbation gradient approximation for optimization under inequality constraints where no direct gradient of the loss function is available and the inequality constraints are given as explicit functions of the optimization parameters. It is shown that under application of the projection algorithm, the parameter iterate converges almost surely to a Kuhn-Tucker point. The procedure is illustrated by a numerical example.

Optimal input design for fault detection and diagnosis

In the paper, the design of optimal input signals for detection and diagnosis in a stochastic dynamical system is investigated. The design is based on maximization of Kullback measure between the model under fault and the model under normal operation conditions. It is established that the optimal input design for change detection when the magnitude of change is small is equivalent to optimal input design for parameter estimation.