Finite-Time Controllability of Fractional-Order Systems

In this paper, the conditions that lead to a system output remaining at zero with zero input are considered. It is shown that the initialization of fractional-order integrators plays a key role in determining whether the integrator output will remain at a zero with zero input. Three examples are given that demonstrate the importance of initialization for integrators of order less than unity, inclusive. Two examples give a concrete illustration of the role that initialization plays in keeping the output of a fractional-order integrator at zero once it has been driven to zero. The implications of these results are considered, with special consideration given to the formulation of the fractional-order optimal control problem.

Finite-Time Controllability of Fractional-Order Systems

In this paper the conditions that lead to a system output remaining at zero with zero input are considered. It is shown that the initialization of fractional-order integrators plays a key role in determining whether the integrator output will remain at a zero with zero input. Three examples are given that demonstrate the importance of initialization for integrators of order less than unity, inclusive. Two examples give a concrete illustration of the role that initialization plays in keeping the output of a fractional-order integrator at zero once it has been driven to zero. The implications of these results are considered, with special consideration given to the formulation of the fractional-order optimal control problem.

An Expression for the Variance of Abundance Estimates Using a Fish Echo Integrator

A mathematical model of the fish echo integrator, an acoustic device for measuring the abundance of pelagic fish, is presented. This model is analyzed and general expressions for the mean and variance of the integrator output are obtained. The integrator output can be scaled to provide an estimate of the total number of fish in the volume of water surveyed. The effect of each system parameter on the variance of the estimate is investigated and optimum operational procedures are suggested.