### Abstract:

It has been established that bilinear models
occur frequently in nature and offer some important
advantages from the standpoint. of controllability,
optimization and modeling. The estimation of
bilinear systeim models from the Measurements
of input-output data are discussed. In the
first approach a parametric model of a discrete-time
linear system is obtained by correlation analysis. The
method is extended to bilinear systems using higher-
order correlations, It is shown that for a pseudorandom
binary input signal the computations in the estimation
algorithm can be simplified. The estimates are
asymptotically normal unbiased and consistent. The
efficiency of the estimates is improved by least-squares fit on a parametric model involving correlation functions.
A recursive formulation is given which makes the algorithm
attractive for on-line implementation. These methods
are compared with maximum-likelihood and least-squares
parameter estimation for a model of a nuclear fission
process.
An experimental furnace to control the temperature
of a sample is modeled. The power applied. to the furnace
and the rate of air flow inside the chamber are the control
variables. Only one input is perturbed at a time
with a pseudorandom binary sequence and the linear and
the bilinear models of the process are obtained from the
input-output measurements. The identification results
are used to design a feedforward-feedback programmable
controller for the system with constant air flow rates.
The second approach is to estimate the first and
the second-order kernels in a Volterra series expansion
of bilinear systems using correlation analysis. The
kernels are estimated for a simulation model of a nuclear
fission process. It is seen that the correlation method
yields good estimates of the first -order kernel under noisy
input -output measurements, However, the second-order
kernel estimates are not satisfactory. A new approach
to the estimation of the second and the higher-order
kernels is then developed. The input-output relation of the bilinear system is represented by an integral-equation.
A Wiener-Hopf type equation is obtained by crosscorrelation
of the input and the output. An algorithm is given to
estimate the unknown parameters in the bilinear operator.
The estimation of the second-order kernel is significantly
improved.