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Showing 1 to 17 of 17 for “"Functional Differential Equations"”.
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STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE MEMORY
… existence and uniqueness of Ito-type stochastic functional differential equations with infinite memory using fixed point theorem technique. We also address the properties of the solution which are an upper bound for the pth moments of the solution and the Lp-regularity. Then, we provide an …
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Nonlinear neutral functional differential equations in product spaces
Control systems governed by nonlinear neutral functional differential equations are formulated as abstract evolution equations in product spaces. At this point existence and uniqueness of solutions are studied. This formulation is used to develop a general approximation scheme for those systems. …
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Closing the memory gap in stochastic functional differential equations
… we obtain convergence of solutions of stochastic differential systems with memory gap to those with full finite memory. More specifically, solutions of stochastic differential systems with memory gap are processes in which the intrinsic dependence of the state on its history goes only up to a …
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A class of functional differential equations of mixed type
This thesis is concerned with a class of linear functional differential equations of mixed type.
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Solution Representation and Indentification for Singular neutral Functional Differential Equations
The solutions for a class of Neutral Functional Di erential Equations (NFDE) with weakly singular kernels are studied. Using singular expansion techniques, a representation of the solution of the NFDE is obtained by studing an associated Volterra Integral Equation. We study the Collocation Method …
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STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS DRIVEN BY FRACTIONAL BROWNIAN MOTION AND THEIR GENERALIZATIONS
We consider a stochastic functional differential equation with infinite memory driven by a fractional Brownian motion with Hurst parameter $H>1/2$. We prove an existence and uniqueness result of the solution to the stochastic differential equation. We investigate the dependence of the solution on …
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Approximation of the LQR control problem for systems governed by partial functional differential equations
… which can be applied to a class of partial functional differential equations which arise in the modeling of viscoelastic and certain thermo-viscoelastic systems. Examples to which the theory applies include both second- and fourth-order equations with a variety of boundary conditions. The …
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Well-posedness questions and approximation schemes for a general class of functional differential equations
… of well-posedness for a general class of functional differential equations of neutral-type (NFDE) where the difference operator does not have an atom at zero. Equations of this type occur in the modeling of certain aeroelastic control problems and include many singular integro-differential …
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BIFDE: a numerical software package for the hopf bifurcation problem in functional differential equations
… to compute the Hopf bifurcation structure in functional differential equations. The package is modular, and consists of several routines which perform one or more tasks. In conjunction with the routines available in this package, the user is required to provide a few routines which describe …
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Vibrational control: Application to a laser-illuminated reaction and extension to nonlinear functional differential equations
Vibrational Control method is an open-loop control technique which utilizes zero mean parametric excitations to modify the behavior of dynamical systems in a desired manner. It may be used where conventional methods such as feedback or feedforward techniques fail due to restricted sensing and/or …
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On the pathwise large deviations of stochatic differential and functional differential equations with applications to finance
… behaviour of highly nonlinear stochastic differential equations, as well as linear and nonlinear functional differential equations. Both ordinary functional and neutral equations are analysed. In the first chapter, a class of nonlinear stochastic differential equations which satisfy the …
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Modeling, Approximation, and Control for a Class of Nonlinear Systems
… excitation in a RKHS in terms of an evaluation functional is introduced to establish the convergence of finite dimensional approximations of the unknown function in RKHS. Lastly, a numerical validation of this framework is presented, which could have potential applications in terrain mapping …
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Numerical approximation and identification problems for singular neutral equations
… to approximate solutions of singular neutral functional differential equations (SNFDEs). Using solution representations and general well-posedness results for SNFDEs convergence of the method is shown for a large class of initial data including the case of discontinuous initial function. Using …
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Stochastic delay difference and differential equations: applications to financial markets
… behaviour of stochastic difference and functional differential equations of Itˆo type. Numerical methods which both minimise error and preserve asymptotic features of the underlying continuous equation are studied. The equations have a form which makes them suitable to model financial …
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Stability and robustness of adaptive controllers for underactuated Lagrangian systems and robotic networks
… analysis based on input-output maps of functional differential equations shows that the adaptive control system's behavior matches closely that of a nonadaptive reference system. The tracking-synchronization objective is achieved despite the effects of communication delays and unknown …
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Modeling and Approximation of Nonlinear Dynamics of Flapping Flight
… a set of coupled nonlinear ordinary or partial differential equations. For this class of systems, the models derived from morphology of the skeleton are usually very high dimensional, nonlinear, and complex. This is particularly true if joint and link flexibility are included in the model. In …
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Design and development of thin optical components for nonimaging applications = Diseño y desarrollo de componentes ópticos delgados para aplicaciones anidólicas
… two steps: a mathematical analysis of the functional differential equations and the SMS design method. All presented 2D V-groove reflectors show very good performances. The V-groove design procedure has been extended into three dimensions in Chapter 6. This chapter explains design of …