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In this paper we describe an efficient computational algorithm for estimating the coefficients of the characteristic polynomial of a linear time-invariant multi-output dynamic system, using only output observations, for qualitative analysis of the transition matrix or for evaluating its eigenvalues. We also give some computational results of the identification of those systems using the Ho-Kalman approach. Furthermore, an identification scheme for high-frequency periodic systems of unknown periods is described in detail.

A computer code is described which is used for the off-line analysis of detector telescope data. The code extracts yield spectra and energy spectra of nuclear reaction products observed with a three-detector counter-telescope. The code contains an identification scheme which allows identification of detected reaction products over a wide energy range.

A study of four techniques is examined to determine which method has the greater overall utility. An iterative least-squares error minimization method provides the greatest accuracy, while a linear algebraic method is accurate only for two-exponential data with small error. Consequently, a three-method sequential identification scheme is devised utilizing a graphical method, a transform method, and an iterative method. This scheme is successfully applied to physiological data containing three and four exponents.

The identification of a random compartmental model from kinetic data in pharmacokinetics is considered, where the randomness arises due to uncertainties in our knowledge of the rate constants. An identification scheme together with computational algorithms for estimating the properties of the random rate constants is presented. A two-compartment model is used as an example, and the problem of identification based upon incompletely observed data is commented upon. The results also show that, if the underlying model is actually random, serious degradation in results can be expected if it is incorrectly modeled as deterministic.

A discrete linear stationary system is considered for which the input noise covariance Q and the output noise covariance R are unknown. A stable filter with a suboptimal gain is assumed. An identification scheme is presented which uses the autocorrelation functions of the innovations sequence of the suboptimal filter to determine the optimum filter steady state gain \Gamma directly without the intermediate determination of the unknown covariances Q and R . The approach used is to identify an output equivalent representation of the original system which does not involve the unknown covariances directly.

The possibility of estimating process parameters using input-output data collected when the system operates in closed loop is discussed in this paper. Concepts that are useful for a systematic treatment of the problem are introduced. The results refer to the case where the regulator is a linear feedback law or alternates between several such laws. It is shown that a straightforwardly applied identification scheme has the same identifiability properties as the more complex method in which the parameters of the closed-loop system are estimated first. It is also shown that it is always possible to achieve the same identifiability properties as for open-loop systems by shifting between different linear regulators. The required number of regulators depends only on the number of inputs and outputs. The results obtained are illustrated by a numerical example.

The pressure distribution in an underground reservoir is modeled by a linear partial differential equation of parabolic type with space-varying coefficients. The distributed parameters, storage and transmissibility, are identified by minimizing a norm dependent upon observed and model-derived pressures. These distributed parameters are approximated by ''average'' values over discrete portions of the reservoir. Thus, the number of parameters to be identified may be quite large. In this paper, two different models for an underground reservoir are developed. An identification scheme based on decomposition techniques is derived to identify the unknown parameters. An important feature of the identification procedure is that it identifies automatically the areas of the reservoir having similar ''average'' properties. In this way a partitioning of the reservoir spatial region is accomplished along with the parameter identification. The method is based on concepts of decomposition and multi-level optimization and is specifically designed to accommodate the high-dimensional systems involved. The theoretical development of the identification scheme is given for each of the system models considered. A computational example is included and the effect of ''modeling'' on the results is illustrated. In addition, the computational algorithm is examined and numerical results are given.

It has been shown in several cases that linear stochastic control theory can be used successfully to design regulators for the steady state control of industrial processes. To use this theory it is necessary to have mathematical models of the system dynamics and the disturbances. In practice it is thus necessary to go through the steps of identification, computation of control strategies and implementation. It might also be necessary to repeat the identification if the system dynamics or the disturbances are changing. In this paper we discuss algorithms that combine the steps of identification and control. The special case of discrete time single-input single-output systems is considered. It is assumed that the disturbances can be characterized as filtered white noise. The main result is a theorem which states that if the algorithm converges it will in fact converge to a minimum variance regulator. The behaviour of the algorithm is illustrated with several examples which indicate that it has nice convergence properties. The result has several practical implications. It can be used to construct self-adjusting regulators for direct digital control. It can be interpreted as a real-time maximum likelihood identification scheme. If the control problem discussed is reformulated as a stochastic control problem the theorem implies that asymptotically there is a finite dimensional sufficient statistic. The implementation of the algorithm on process computers is also discussed. It is shown that it is feasible to implement it on snail computers.

Particle identification schemes for heavy ions have been tested using the semiempirical range-energy calculations of Northcliffe and Schilling as primary data. A new scheme is suggested in which the particle identifying output (PIO) may be calculated from the relationship PIO = mET + b, where ET is the total energy of the particle and m and b are functions of ΔE/ET, the ratio of the energy loss in the front detector of a detector telescope to the total energy of the particle. Functions for determining m and b are generated using the range-energy tables. The scheme has been compared with other techniques and found to be useful for ions Z≥4.

An identification scheme for surface-active agents is given which enables these agents or their mixtures to be detected in commercial products. Use is made of the acid resistance of the various types, which make it possible to separate the different compounds step by step from the mixture.

This paper explores the possibility of using the instrumental variable method to estimate the parameters of linear time-invariant discrete-time systems. The existence of optimal estimates is established, methods for their approximate computation are given, and an on-line identification scheme based on recursive computation is proposed. Experimental results are included.

For a rotary lime kiln used in the recausticizing process of a (kraft) paper mill, R mathematical model is presented. The form of the mathematical description is obtained on the basis of the mass and energy balances. The unknown coefficients in the mathematical model are determined by applying the stochastic approximation method. The identification scheme yields the optimal values of the parameters such that the best fit to the available discrete measurements is attained.

This paper reports on an investigation of the effect of adaptive control on a closed-loop chemical plant. The plant controlled was a simple closed-loop feedback system, the elements of which were a proportional controller and an elementary continuous stirred-tank reactor. The reaction involved was an exothermic, single-reactant decomposition, with the control criterion being the integral of the square of the deviation of the output composition from a value determined by a reference model. The adaptive control system incorporated an automatic identification scheme and a decision process, and operated in the presence of disturbances in cooling water temperature and/or catalyst activity. The adaptive control system yielded excellent results. For all disturbances, the output of the adaptive controlled plant remained much closer to the reference model output than did the output of the simply controlled plant. Inclusion of an adaptive capability in a control system thus appears to be desirable and often feasible.

In a companion paper to the present, a model is derived to predict human reflex motion. This model contains a set of seven neuromuscular parameters which are evaluated in the present paper on the basis of results obtained from experiments performed on the human forearm. In these experiments, forearm position is studied following an abrupt change in load and the parameters are evaluated using an identification scheme which minimizes an error function containing forearm position. The relative importance of the various parameters is discussed as well as the relation between the proposed model and previous models in this field.

A paremeter identification scheme was applied to the study of the dynamic properties of resting (nonstimulated) striated muscle. This method makes it possible to study muscle dynamics by performing simple experiments and provides an analytical method for evaluating nonlinearities. This approach revealed the presence of a “tension feedback” component in resting muscle. In addition, certain dynamic characteristics of striated muscles were correlated with their structure.

An interesting identification scheme for scalar-input-scalar-output linear systems, proposed by Lion in [1], is investigated for a wide class of random inputs. The inputs include the class of functions u(t) = \Sigma k_{i}\bar{u}_{i}(t) , where \{\bar{u}_{1}(t),..,\bar{u}_{k}(t)\} is a Markov process which is asymptotically stationary. An invariant set theorem for random systems [2] is used to prove convergence (in probability) of the identification algorithm proposed in [1]. Indeed, in view of the power of the deterministic invariant set theorem, it is of great interest to study methods of useful application of the stochastic analogy. One of the main contributions is the illustration of its potential power, via the vehicle of the identification problem.

This paper discusses the discrete version of the adaptive observer problem. First, a stable identification scheme for a linear discrete multivariable system when all its state variables are accessible is presented. The scheme is then extended to obtain stable identification laws for a single variable system using only input-output data.

The multivariable nonlinear system considered here is assumed to be characterized by a truncated functional power series. The system is to be identified under normal operating conditions. Least square error criterion is used to estimate the system weighting function matrix and a steepest descent method is employed for solving this problem. A recursive estimation scheme is devised for up-dating its estimation. An “Adjoint Space Approach”, which has the advartage of reducing the dimensionality of the identification problem is explored.

Summary By testing some of the many methods that have been described for the identification of Ps. aeruginosa with a series of typical strains an identification scheme was evolved and subsequently applied in an epidemiological investigation of Ps. aeruginosa respiratory tract infections. Its use led to the rapid identification of typical strains, but even atypical strains were usually identified within 48 hr of their isolation. The scheme has been evolved with the needs of the routine medical diagnostic laboratory in mind.

Publisher Summary This chapter discusses the adaptive optimal steady state control of nonlinear systems. If the plant dynamics are unknown and vary from time to time in an unpredictable manner, it is evident that some type of identification scheme must be incorporated into the system operation to achieve and maintain optimal performance in any meaningful sense. The techniques which have been proposed to cope with this problem, often referred to as an adaptive or adaptive-optimal control problem, usually require some a priori information of the plant dynamic characteristics, for example, the order and form of the differential equations may be known though some of the coefficients may be unknown. Such techniques are useful when the order and form of the plant differential equations are known. An adaptive optimal control scheme which does not rely upon a priori knowledge of the order or form of the plant differential equations is the Draper and Li extremum or peak holding controller.

It is suggested that the identification scheme proposed in a paper by Papoulis has very limited usefulness.