We consider the boundary control problem to stabilize the power of a signal and a pump propagating down a Raman amplifier. This is essentially an initial-boundary value problem (IBVP) of a hyperbolic system with Lotka-Volterra type nonlinearities. We treat the system as a control problem with states in the function space and use Lyapunov-based analysis to demonstrate asymptotic stability in the C_0 and the L_2-sense. The stability conditions are derived for closed-loop systems with a proportional controller and a dynamic controller, and confirmed by simulations in MATLAB.

We consider the boundary control problem to stabilize the power of a signal and a pump propagating down a Raman amplifier. This is essentially an initial-boundary value problem (IBVP) of a hyperbolic system with Lotka-Volterra type nonlinearities. We treat the system as a control problem with states in the function space and use Lyapunov-based analysis to demonstrate asymptotic stability in the C_0 and the L_2-sense. The stability conditions are derived for closed-loop systems with a proportional controller and a dynamic controller, and confirmed by simulations in MATLAB.

Today’s advances in communication systems and VLSI circuits increases the performance requirements and complexity of circuits. The performance of RF and mixed-signal circuits is normally limited by the nonlinear behavior of the transistors used in the design. This makes simulation of nonlinear circuits more important. Volterra series is a method used for simulation of mildly nonlinear circuits. Using Volterra series the response of the nonlinear circuit is converted into a sum of multiple linear circuit responses. Thus, using Volterra series, simulation of nonlinear circuits in frequency-domain analysis becomes possible. However, Volterra series is not able to simulate strongly nonlinear circuits such as saturated Power Amplifiers. In this thesis, a new time-varying Volterra analysis is presented. The time-varying Volterra analysis is the generalization of conventional Volterra analysis where instead of using a DC expansion point a time-varying waveform has been used. Employing a time-varying expansion waveform for Volterra analysis, time-varying Volterra achieves better accuracy than conventional Volterra. The time-varying expansion waveforms are derived using a fast pre-analysis of the circuit. Using numerical examples, it has been shown that the time-varying Volterra is capable of simulating nonlinear circuits with better accuracy than conventional Volterra analysis. The time-varying Volterra analysis in both time and frequency domains are discussed in this thesis. The time-varying Volterra analysis has been used to simulate a saturated Class-F Power Amplifier in frequency-domain. The simulation results show good agreement with ELDO® steady-state and Harmonic Balance simulation results. The proposed method manages to simulate nonlinear circuits, such as saturated Power Amplifier, mixers and nonlinear microwave circuits, with good accuracy. Also, this method can be used to simulate circuit with large number of nonlinear elements without the convergence issues of Harmonic Balance.

Today’s advances in communication systems and VLSI circuits increases the performance requirements and complexity of circuits. The performance of RF and mixed-signal circuits is normally limited by the nonlinear behavior of the transistors used in the design. This makes simulation of nonlinear circuits more important. Volterra series is a method used for simulation of mildly nonlinear circuits. Using Volterra series the response of the nonlinear circuit is converted into a sum of multiple linear circuit responses. Thus, using Volterra series, simulation of nonlinear circuits in frequency-domain analysis becomes possible. However, Volterra series is not able to simulate strongly nonlinear circuits such as saturated Power Amplifiers. In this thesis, a new time-varying Volterra analysis is presented. The time-varying Volterra analysis is the generalization of conventional Volterra analysis where instead of using a DC expansion point a time-varying waveform has been used. Employing a time-varying expansion waveform for Volterra analysis, time-varying Volterra achieves better accuracy than conventional Volterra. The time-varying expansion waveforms are derived using a fast pre-analysis of the circuit. Using numerical examples, it has been shown that the time-varying Volterra is capable of simulating nonlinear circuits with better accuracy than conventional Volterra analysis. The time-varying Volterra analysis in both time and frequency domains are discussed in this thesis. The time-varying Volterra analysis has been used to simulate a saturated Class-F Power Amplifier in frequency-domain. The simulation results show good agreement with ELDO® steady-state and Harmonic Balance simulation results. The proposed method manages to simulate nonlinear circuits, such as saturated Power Amplifier, mixers and nonlinear microwave circuits, with good accuracy. Also, this method can be used to simulate circuit with large number of nonlinear elements without the convergence issues of Harmonic Balance.

This research was done to study the effect of sea severity on the vertical ship responses like heave and pitch. Model testing of a 175m moored container ship with zero heading speed was done for different sea states varying from very rough to very high seas. Transfer functions were extracted using Volterra model which constitutes both linear and quadratic part. The experimental linear transfer functions were calculated using Volterra linear model and were compared with linear transfer function from the hydrodynamic theory. Experimental second order transfer functions were also extracted using Volterra quadratic model and their behavior was studied for different sea states. After the extraction of linear and second order transfer functions total responses were reconstructed and compared with the measured responses. This also helped to investigate the contribution of second order part to the total vertical ship responses. In the last stage of the research a new semi- empirical method was developed called as ‘UNIOM’ for the prediction of the responses. Laboratory input waves and theoretical LTFs were used for the simulation of ship response and these were compared with measured responses.

The objective of the thesis is to treat the Schrodinger equation in parallel with a standard treatment of the heat equation. In the books of the Rubensteins and Kress, the heat equation initial value problem is converted into a Volterra integral equation of the second kind, and then the Picard algorithm is used to find the exact solution of the integral equation. Similarly, the Schrodinger equation boundary initial value problem can be turned into a Volterra integral equation. We follow the books of the Rubinsteins and Kress to show for the Schrodinger equation similar results to those for the heat equation. The thesis proves that the Schrodinger equation with a source function does indeed have a unique solution. The Poisson integral formula with the Schrodinger kernel is shown to hold in the Abel summable sense. The Green functions are introduced in order to obtain a representation for any function which satisfies the Schrodinger initial-boundary value problem. The Picard method of successive approximations is to be used to construct an approximate solution which should approach the exact Green function as n goes to infinity. To prove convergence, Volterra kernels are introduced in arbitrary Banach spaces, and the Volterra and General Volterra theorems are proved and used in order to show that the Neumann series for the L^1 kernel, the L^infinity kernel, the Hilbert-Schmidt kernel, the unitary kernel, and the WKB kernel converge to the exact Green function. In the WKB case, the solution of the Schrodinger equation is given in terms of classical paths; that is, the multiple scattering expansions are used to construct from, the action S, the quantum Green function. Then the interior Dirichlet problem is converted into a Volterra integral problem, and it is shown that Volterra integral equation with the quantum surface kernel can be solved by the method of successive approximations.

Thesis--Groningen. / At head of title: Rijksuniversiteit te Groningen. Includes bibliographical references (p. 132-142).

No description available.

Thesis (Ph.D.)--Memorial University of Newfoundland, 1999. / Bibliography: leaves 173-181.

Thesis (M. Eng.)--Carleton University, 1995. / Includes bibliographical references. Also available in electronic format on the Internet.