Synthesis of input signals in parameter identification in static systems

This paper considers the syntheses of optimal input signals for parameter identification in static systems for two types of criteria, i.e. Fisher's information and the mean-square error (MSE). A sufficient condition under which the optimal input signals are comparatively easy to obtain in the form of periodic sequence is derived, particularly for the information criterion. For the MSE criterion, a lower bound on the optimal MSE is obtained in order that information can be given for the construction of desirable sequences. As illustrative examples, unimodal and multimodal Gauss- and Cauchy-type functions are considered, and the effectiveness of the conditions is shown.     

Computational algorithm for input-signal optimization in distributed-parameter systems identification

This paper deals with the problem of optimum choice of testing signals for identification in linear distributed-parameter systems. It is based on earlier theoretical results of one of the authors, which are extended here by investigating the structure of the optimal input signal. These investigations allow the proposal of an efficient computational algorithm. Its convergence is proved and the convergence rate is verified by numerical studies     

Selection of input variables for model identification of static nonlinear systems

System identification can be divided into structure and parameter identification. In most system-identification approaches the structure is presumed and only a parameter identification is performed to obtain the coefficients in the functional system. Yet, often there is little knowledge about the system structure. In such cases, the first step has to be the identification of the decisive input variables. In this paper a black-box input variable identification approach using feedforward neural networks is proposed.     

Constrained multisine input signals for plant-friendly identification of chemical process systems

This paper considers the use of constrained minimum crest factor multisine signals as inputs for plant-friendly identification testing of chemical process systems. The methodology presented here effectively integrates operating restrictions, information-theoretic requirements, and state-of-the-art optimization techniques to design minimum crest factor multisine signals meeting important user-specified time and frequency domain properties. A series of optimization problem formulations relevant to problems in linear, nonlinear, and multivariable system identification are presented; these culminate with their application to the modeling of the Weischedel–McAvoy high-purity distillation column problem, a demanding nonlinear and highly interactive system. The effectiveness of these signals for modeling for control purposes and the ability to incorporate a priori nonlinear models in the signal design procedure are demonstrated in this distillation system case study.     

Comparison of input signals in subspace identification of multivariable ill-conditioned systems

Ill-conditioned processes often produce data of low quality for model identification in general, and for subspace identification in particular, because data vectors of different outputs are typically close to collinearity, being aligned in the “strong” direction. One of the solutions suggested in the literature is the use of appropriate input signals, usually called “rotated” inputs, which must excite sufficiently the process in the “weak” direction. In this paper open-loop (uncorrelated and rotated) random signals are compared against inputs generated in closed-loop operation, with the aim of finding the most appropriate ones to be used in multivariable subspace identification of ill-conditioned processes. Two multivariable ill-conditioned processes are investigated and as a result it is found that closed-loop identification gives superior models, both in the sense of lower error in the frequency response and in terms of higher performance when used to build a model predictive control system.     

Suboptimal state estimation algorithm for non-linear discrete-time distributed-parameter systems

A non-linear discrete-time distributed-parameter system may be described by stochastic partial differential equations. Some state variables are measured at selected points of the system space. For this system a suboptimal state estimation algorithm is proposed. The error covariance matrix is calculated by an approximate approach. This simplification considerably reduces computer calculations in comparison with an optimal algorithm. Finally, the digital simulation of a non-linear DPS demonstrates the effectiveness of the suboptimal estimator.     

Effective approach for the identification of boundary conditions in distributed-parameter systems

This paper is concerned with the identification of boundary conditions in parabolic-type distributed systems with boundaries of irregular shape. In the present approach, finite element discretization in the spatial domain and orthogonal functions expansion in the time domain are adopted to reduce the partial differential equation to a set of algebraic equations. The boundary conditions are then estimated by the method of least squares using state observations taken at a few interior points. The present approach is very straightforward and, at least as shown in illustrative examples, the results are in excellent agreement with exact results.     

Nonparametric identification of quasi-stationary systems

Recursive estimates of a regression function — based on the Parzen-Rosenblatt kernels — are applied for identification of quasi-stationary systems. It is shown that these estimates do not lose their asymptotic properties even if the data are not stationary. Conditions for weak and strong pointwise consistency are given.     

Observer theory for distributed-parameter systems

This paper examines the problem of the approximate reconstruction of the unknown state variables in distributed-parameter systems. New results on the observer theory for important classes of linear and non-linear operator, partial differential, and partial differential-integral equations in describing distributed-parameter systems are presented. The specific developments employ the recent results on Lyapunov stability theory, along with the theory of linear and non-linear semigroup operators, and their infinitesimal generators. The questions of observability, stability of the state reconstruction error dynamics associated with the proposed observer structure are discussed. The theoretical results are illustrated with some applications to problems of the kinetic lumping of complex distributed-parameter chemical reaction systems, as well as the observer design for linear and non-linear distributed-parameter diffusion systems.     

Boundary element approach for identification of boundary conditions of distributed-parameter systems

An identification problem is discussed for the boundary conditions of a deterministic distributed-parameter system governed by a partial differential equation of parabolic type. A method based on the fundamental ideas of the boundary element method is proposed for identification of unknown boundary conditions. The identification problem is formulated by using the ideas of boundary partition and weighted residual expression corresponding to the given partial differential equation. The boundary conditions are estimated by the method of least squares using the state observations taken at the interior points. A numerical example illustrates the applicability of the proposed method for boundary identification.     

Identification of the external input of distributed-parameter systems by the boundary-element approach

An identification method is proposed for the unknown external input of distributed-parameter systems governed by a non-homogeneous partial differential equation of parabolic type. The mathematical formulation of the identification problem is based on a boundary partition and a weighted residual expression corresponding to the given partial differential equation, both of which are fundamental ideas of the boundary-element method. The unknown external input is estimated from state observations taken at points on the boundary by minimizing a suitable criterion function. The applicability of the proposed method is illustrated by a numerical example     

Optimal experiment design for identification of linear distributed-parameter systems: Frequency domain approach

In this paper optimality conditions for experiment design are derived. The experiment is planned for identification of linear time invariant distributed-parameter systems. The determinant of the averaged information matrix is expressed in the terms of input spectral density matrix and spatial density of measurements, and then used as a measure of estimation accuracy. Presented results are applied to find optimal sensors positions and input signals in several examples.     

Nonparametric identification of Wiener systems by orthogonal series

A Wiener system, i.e., a system comprising a linear dynamic and a nonlinear memoryless subsystems connected in a cascade, is identified. Both the input signal and disturbance are random, white, and Gaussian. The unknown nonlinear characteristic is strictly monotonous and differentiable and, therefore, the problem of its recovering from input-output observations of the whole system is nonparametric. It is shown that the inverse of the characteristic is a regression function and a class of orthogonal series nonparametric estimates recovering the regression is proposed and analyzed. The estimates apply the trigonometric, Legendre, and Hermite orthogonal functions. Pointwise consistency of all the algorithms is shown. Under some additional smoothness restrictions, the rates of their convergence are examined and compared. An algorithm to identify the impulse response of the linear subsystem is proposed     

Robust state estimation for uncertain linear systems with deterministic input signals

In this paper, we investigate state estimations of a dynamical system in which not only process and measurement noise, but also parameter uncertainties and deterministic input signals are involved. The sensitivity penalization based robust state estimation is extended to uncertain linear systems with deterministic input signals and parametric uncertainties which may nonlinearly affect a state-space plant model. The form of the derived robust estimator is similar to that of the well-known Kalman filter with a comparable computational complexity. Under a few weak assumptions, it is proved that though the derived state estimator is biased, the bound of estimation errors is finite and the covariance matrix of estimation errors is bounded. Numerical simulations show that the obtained robust filter has relatively nice estimation performances.     

Genetic polynomial regression as input selection algorithm for non-linear identification

The performance of non-linear identification techniques is often determined by the appropriateness of the selected input variables and the corresponding time lags. High correlation coefficients between candidate input variables in addition to a non-linear relation with the output signal induce the need for an appropriate input selection methodology. This paper proposes a genetic polynomial regression technique to select the significant input variables for the identification of non-linear dynamic systems with multiple inputs. Statistical tools are presented to visualize and to process the results from different selection runs. The evolutionary approach can be used for a wide range of identification techniques and only requires a minimal input and a priori knowledge from the user. The evolutionary selection algorithm has been applied on a real-world example to illustrate its performance. The engine load in a combine harvester is highly variable in time and should be kept below an allowable limit during automatic ground speed control mode. The genetic regression process has been used to select those measurement variables that have a significant impact on the engine load and that will act as measurement variables of a non-linear model-based engine load controller.     

A static scheduling algorithm for distributed hard real-time systems

A static scheduling algorithm is presented for off-line scheduling of tasks in distributed hard real-time systems. The tasks considered are instances of periodic jobs and have deadlines, resource requirements and precedence constraints. Tasks are divided into nonpreemptable blocks and all task characteristics are known a priori. The algorithm orders the tasks and iteratively schedules the tasks according to the order. Each task is scheduled globally by selecting a node to which it is assigned. Then, the task is scheduled locally by adding the task to the schedule of the selected node. Heuristics are used for both task ordering and node selection in order to guide the algorithm to a feasible schedule. Whenever local scheduling leads to an infeasible schedule, backtracking is used.Results of simulation studies of randomly generated task sets are presented. Although the scheduling problem is NP-hard, the results show that time performance is acceptable for off-line scheduling, except for extremely difficult task sets which make extensive use of the available resources.     

Adaptive parameter identification in dynamical and static systems

We consider algorithms for adaptive offline identification of deterministic dynamical and static systems tailored for the computer mathematics software suite Matlab+Simulink. The derivation of the adaptive identification algorithm is based on the direct Lyapunov method. A numerical example illustrates the efficiency of the proposed identification algorithm.     

Conditional variational problems of control for distributed-parameter systems

Solved was a number of the classical variational problems of control of the distributed-parameter dynamic systems constrained also by nondifferential and differential equations. The corresponding rules of the Lagrange multipliers were formulated and proved. For the generalized diffusion and generalized wave processes, the results obtained were applied to the conditional variational problems of distributed optimal control. Derivation of the Euler-Poisson and Euler equations as applied to the designed control system was substantiated for these problems.