A minimum principle for stochastic control problems with output feedback

A minimum principle for stochastic control problems with output feedback is derived by applying Bismut's minimum principle for stochastic control problems with full information about the past to the Kushner-Stratonovitch equation describing the controlled evolution of the conditional density of the state. The well-known solution of the linear-quadratic Gaussian problem is obtained from the principle

Minimax frequency domain performance and robustness optimization of linear feedback systems

It is shown that feedback system design objectives, such as disturbance attenuation and rejection, power and bandwidth limitation, and robustness, may be expressed in terms of required bounds of the sensitivity function and its complement on the imaginary axis. This leads to a minimax frequency domain optimization problem, whose solution is reduced to the solution of a polynomial equation

Estimation of pulse heights and arrival times

The problem is studied of estimating the arrival times and heights of pulses of known shape observed with white additive noise. The main difficulty is estimating the number of pulses. When a maximum likelihood formulation is employed for the estimation problem, difficulties similar to the problem of estimating the order of an unknown system arise. The problem may be overcome using Rissanen's shortest data description approach. An estimation algorithm is described, and its consistency is proved. The results are illustrated by a simulation study using an example from seismic data processing also studied by Mendel

Polynomial computation of Hankel singular values

A revised and improved version of a polynomial algorithm is presented. It was published by N.J. Young (1990) for the computation of the singular values and vectors of the Hankel operator defined by a linear time-invariant system with a rotational transfer matrix. Tentative numerical experiments indicate that for high-order systems, scaling of the polynomial matrices N and D (so that the constant and leading coefficient matrices are of the same order of magnitude) is mandatory, and that solution of bilateral linear polynomial matrix equations by coefficient expansion is highly inefficien

Rating and ranking of multiple-aspect alternatives using fuzzy sets

A method is proposed to deal with multiple-alternative decision problems under uncertainty. It is assumed that all the alternatives in the choice set can be characterized by a number of aspects, and that information is available to assign weights to these aspects and to construct a rating scheme for the various aspects of each alternative. The method basically consists of computing weighted final ratings for each alternative and comparing the weighted final ratings. The uncertainty that is assumed to be inherent in the assessments of the ratings and weights is accounted for by considering each of these variables as fuzzy quantities, characterized by appropriate membership functions. Accordingly, the final evaluation of the alternatives consists of a degree of membership in the fuzzy set of alternatives ranking first. A practical method is given to compute membership functions of fuzzy sets induced by mappings, and applied to the problem at hand. A number of examples are worked out. The method is compared to another one proposed by Kahne who approaches the problem probabilistically