On the controllability of delay-differential systems.
Controllability type applicable to optimal control problems for systems described by delay differential equations
Weiss, L.↗
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Fully unsteady subsonic and supersonic potential aerodynamics for complex aircraft configurations for flutter applications
A general theory for study, oscillatory or fully unsteady potential compressible aerodynamics around complex configurations is presented. Using the finite-element method to discretize the space problem, one obtains a set of differential-delay equations in time relating the potential to its normal derivative which is expressed in terms of the generalized coordinates of the structure. For oscillatory flow, the motion consists of sinusoidal oscillations around a steady, subsonic or supersonic flow. For fully unsteady flow, the motion is assumed to consist of constant subsonic or supersonic speed for time t or = 0 and of small perturbations around the steady state for time t 0.
Tseng, K.↗
Spline approximations for nonlinear hereditary control systems
A sline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized.
Daniel, P. L.↗
Parameter identification for an abstract Cauchy problem by quasilinearization
A parameter identification problem is considered in the context of a linear abstract Cauchy problem with a parameter-dependent evolution operator. Conditions are investigated under which the gradient of the state with respect to a parameter possesses smoothness properties which lead to local convergence of an estimation algorithm based on quasi-linearization. Numerical results are presented concerning estimation of unknown parameters in delay-differential equations.
Brewer, Dennis W.↗
Gradient methods for identification of distributed parameter systems
Parameter-dependence properties are developed in the context of a linear abstract Cauchy problem governed by a parameter-dependent operator. Of particular interest are problems in which the parameter induces an unbounded perturbation of the evolution operator. Conditions are stated under which the derivative of the state with respect to the parameter possesses certain smoothness properties. These properties lead to local convergence results for a gradient-based estimation algorithm based on quasi-linearization. Numerical results concerning a delay-differential equation indicate the effect of a forcing function on parameter sensitivity.
Brewer, Dennis W.↗
Parameter identification for an abstract Cauchy problem by quasilinearization
A parameter identification problem is considered in the context of a linear abstract Cauchy problem with a parameter-dependent evolution operator. Conditions are investigated under which the gradient of the state with respect to a parameter possesses smoothness properties which lead to local convergence of an estimation algorithm based on quasi-linearization. Numerical results are presented concerning estimation of unknown parameters in delay-differential equations.
Brewer, Dennis W.↗
Estimation of delays and other parameters in nonlinear functional differential equations
A spline-based approximation scheme for nonlinear nonautonomous delay differential equations is discussed. Convergence results (using dissipative type estimates on the underlying nonlinear operators) are given in the context of parameter estimation problems which include estimation of multiple delays and initial data as well as the usual coefficient-type parameters. A brief summary of some of the related numerical findings is also given.
Banks, H. T.↗
Uniqueness and successive approximations for functional differential equations.
Uniqueness theorem and successive approximations for delay functional differential equations, noting scalar problems
Proctor, T. G.↗
Estimation of time- and state-dependent delays and other parameters in functional differential equations
A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.
Murphy, K. A.↗
Estimation of time- and state-dependent delays and other parameters in functional differential equations
A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.
Murphy, K. A.↗
Earth Filter Mathematica Toolbox V4 User’s Guide: Simplifying, Visualizing and Quick Modeling of All Fission Products from 60 Nuclear Sources
The Earth Filter Mathematica toolbox is a set of user-friendly routines that accurately calculate the ingrowth and decay of any of the 908 fission products for an infinite combination of sources over a large dynamic range and large time scales. This toolbox was developed by Dr. W. P. Brug at Los Alamos National Laboratory and eliminates the need for the user to define and solve differential equations by automatically scanning the ENDF-349 dataset and creating a complete set of differential equations (including delayed neutron branches to both the ground and metastable states) for every fission product. Additionally, this code allows the user to choose the data source for half-lives from several key references (i.e., TORI, IAEA, ENDF or NUDAT.) The complete set of ENDF-349 independent and cumulative fission yields for all 60 isotopic targets and 4 different neutron spectrums are included. This allows nearly any nuclear fission source to be accurately modeled as a linear combination of endpoint sources. The Earth Filter Toolbox has no limit as to the length of split list, and split lists of 5 or more endpoint sources can be quite common.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
A maximum principle for optimal control problems with functional differential systems
Maximum principle for optimal control problems with delay-differential system equations
Banks, H. T.↗
A maximum principle for optimal control problems with functional differential systems.
Maximum principle in integral form for optimal control problems with delay differential system equations, using vector matrix notation
Banks, H. T.↗
A new approach to approximating the linear quadratic optimal control law for hereditary systems with control delays
A factorization approach is presented for deriving approximations to the optimal feedback gain for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the feedback kernels.
Milman, M. H.↗
A numerical algorithm for optimal feedback gains in high dimensional LQR problems
A hybrid method for computing the feedback gains in linear quadratic regulator problems is proposed. The method, which combines the use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated so as to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantage of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed and numerical evidence of the efficacy of our ideas presented.
Banks, H. T.↗
A numerical algorithm for optimal feedback gains in high dimensional linear quadratic regulator problems
A hybrid method for computing the feedback gains in linear quadratic regulator problem is proposed. The method, which combines use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite-dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantages of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed, and numerical evidence of the efficacy of these ideas is presented.
Banks, H. T.↗
Variational problems involving functional differential equations.
Variational or optimal control for delayed systems, involving integrated maximum principle for problems with nonlinear functional differential systems
Banks, H. T.↗
Approximating the linear quadratic optimal control law for hereditary systems with delays in the control
The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary systems. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.
Milman, Mark H.↗