Control Theoretic Concepts Research Articles

On integral inequalities associated with a linear operator equation

In this paper we apply control theoretic concepts to formulate and solve a generalized problem for the determination of best possible constants in integral inequalities. We investigate the problem of existence of functions for which the best constant is attained, and also the conditions satisfied by these functions.

Control theoretic concepts and motor control

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Optimal receiver design for convolutional codes and channels with memory via control theoretical concepts

The optimum maximum likelihood receiver for estimating the information sequence that passes through a convolutional encoder and a channel with a known finite memory part followed by a noisy memoryless part is derived using control theoretic concepts. The problem is modeled as a regulator control problem in which the plant under consideration is a finite state machine with the information symbols as inputs. It is in a form in which dynamic programming can be applied to obtain a general solution. The case of sending pulse amplitude modulated (PAM) signals over a linear channel with additive white Gaussian noise is analyzed in detail and upper and lower bounds are derived for the performance criterion, the probability of an information sequence error. Applying the coding concept of concatenation, a suboptimum solution for overcoming the “curse of dimensionality” is discussed.

State space evaluation of the Bhattacharyya distance between two Gaussian processes

One measure of the distance between two Gaussian processes is the Bhattacharyya distance. State space techniques are used to express this measure in terms of a matrix Riccati differential equation. This formulation is well suited to numerical evaluation for nonstationary processes and also enables the design of optimal modulations (signals) using control theoretic concepts. Such applications are discussed in general terms.

Optimal waveform design via control theoretic concepts

This paper presents the formulation of a class of optimal signal design problems; in particular, the design of optimal “modulation≓ waveforms (under amplitude and energy constraints) to be used for the optimal estimation or prediction of the state of a linear dynamical system in the presence of Markov and white noise. The Kalman-Bucy theory is used to formulate an optimization problem in which the “state of the plant≓ is given by the elements of covariance matrices (which satisfy matrix Riccati differential equations), the “control≓ is related to the modulation signal, and the “cost≓ is a linear functional of the covariance matrix. The problem statement is in such a form so that the Maximum Principle of Pontryagin can be applied to obtain the necessary conditions and it is used to derive the so-called “on-off≓ principle. The results prove that under total energy and peak amplitude constraints, the optimal signal, as a function of time, must alternate between its peak-power and its zero-power levels. A set of matrix differential equations—with split boundary conditions—is also derived; the numerical solution of this set of equations can yield the explicit time-dependence of the optimal waveform.