This thesis presents a Fortran program that numerically solves the steady-state matrix Riccati equation of the quadratic cost optimal control problem. Each step of the program is presented, analytically and computationally. The check points incorporated in the program and the input parameters that can be used to assure a correct solution are identified and discussed. Difficulties encountered when verifying the program, and the suggested solutions, are also presented.

Topics: Aeronautics, Riccati equation, steady-state Riccati equation, Lyapunov equation

http://uf.catalog.fcla.edu/uf.jsp?st=UF000295846&ix=nu&I=0&V=D

Topics: Control theory, Riccati equation.

Thesis (Ph. D.)--Johns Hopkins University, 1887

Topics: Riccati equation, Differential equations

618
618

Oct 4, 2012
10/12

by
Johler, J. Ralph.

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Topics: Radio wave propagation., Riccati equation.

Click here to view the University of Florida catalog record

Topics: Riccati equation, Boundary value problems

University of Illinois Urbana-Champaign

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153

Mar 12, 2013
03/13

by
Trivedi, Kishor Shridharbhai, 1946-; University of Illinois at Urbana-Champaign. Dept. of Computer Science

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iii, 28 p. ; 28 cm

Topics: Functions, Riccati equation, Computer arithmetic, Continued fractions

Includes bibliographical references

Topics: Riccati equation, Continued fractions, Functions, Computer arithmetic

271
271

Jun 9, 2011
06/11

by
Seifert, Avi; Pack-Melton, La Tuni

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Effective delay of turbulent boundary layer separation could be achieved via closed-loop control. Constructing such a system requires that sensor data be processed, real-time, and fed into the controller to determine the output. Current methods for detection of turbulent boundary layer separation are lacking the capability of localized, fast and reliable identification of the boundary layer state. A method is proposed for short-time FFT processing of time series, measured by hot-film sensors,...

Topics: FEEDBACK CONTROL, NONLINEARITY, RICCATI EQUATION, EQUATIONS OF STATE, REGULATORS

The directrix approach, which gives powerful insight to the geometric structure of solutions of the general Riccati equation, is developed. Burgers' Riccati equation is derived, and conclusions are drawn utilizing the directrix approach concerning the boundedness properties of solutions of this equation with certain restrictions on parameter values. Closed form solutions are developed for Burgers' Riccati equation for certain parameter values. A method is produced to obtain the verti' cal...

Topics: Mathematics, Riccati equation, Burgers' equation, nonlinear differential equation, mathematical...

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244

May 23, 2011
05/11

by
NON

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A process for preparing an ultra-thin, adhesiveless, multi-layered, patterned polymer substrate is disclosed. The process may be used to prepare both rigid and flexible cables and circuit boards. A substrate is provided and a polymeric solution comprising a self-bonding, soluble polymer and a solvent is applied to the substrate. Next, the polymer solution is dried to form a polymer coated substrate. The polymer coated substrate is metallized and patterned. At least one additional coating of the...

Topics: SYSTEMS STABILITY, RICCATI EQUATION, ENERGY DISSIPATION, LINEAR SYSTEMS, ROBUSTNESS (MATHEMATICS),...

— The present paper is focused on linear quadratic regulator (LQR) synthesis. It is evident that the solution of the problem leads to finding a solution of symmetric root locus (SRL) problem. It is proven and analytical evidences is also presented that by using SRL synthesis method and further application of LQR method guarantees stability, minimum phase and gain margins of the closed loop system. The presented mathematical relationships are further proven with experimental investigation in...

Topics: linear quadratic regulator, minimum phase system, Riccati equation, stability, state space,...

A comprehensive study of the stochastic realization problem was undertaken both in its algorithmic and structural aspects. A geometric state space theory of linear stochastic systems was obtained, providing a complete characterization of all stochastic realizations. The phenomenon of invariant directions of the matrix Riccati equation was investigated in this framework, clarifying its connections to filtering algorithms as well as to geometric aspects of linear systems theory. Non-Riccati...

Topics: DTIC Archive, Lindquist,Anders, KENTUCKY UNIV LEXINGTON DEPT OF MATHEMATICS, *ALGORITHMS,...

352
352

May 22, 2011
05/11

by
Mulvehill, Alice M

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THOR is a knowledge-based system which incorporates techniques from signal processing, pattern recognition, and artificial intelligence (AI) in order to determine the boundary of small thunderstorms which develop and dissipate over the area encompassed by KSC and the Cape Canaveral Air Force Station. THOR interprets electric field mill data (derived from a network of electric field mills) by using heuristics and algorithms about thunderstorms that have been obtained from several domain...

Topics: CONTROL STABILITY, MANIPULATORS, SIMULATION, CONTROL SYSTEMS DESIGN, CONTROL THEORY, CONTROLLERS,...

Some of the rigorous aspects of invariant imbedding are discussed: existence and uniqueness of solution, asymptotic behavior over space and time, stability, computational stability, applications to classical boundary-value theory, and so on. An important conservation property, obvious on physical grounds, is used in establishing the existence of the solution of a matrix Riccati equation without recourse to the associated linear differential equation, and thus with out any appeal to spectral...

Topics: DTIC Archive, Bellman, R, RAND CORP SANTA MONICA CA, *INVARIANCE, *RICCATI EQUATION,...

The research reported herein has concentrated on the development of design methodologies to meet simultaneously several diverse requirements including transient performance, disturbance rejection, robustness, and reliability. The design methodologies developed herein are based on (1) projective controls, which provide a parametrized family of low-order controllers that guarantee certain performance specifications are met and possess free parameters to be used to meet additional requirements (2)...

Topics: DTIC Archive, Perkins, William R, ILLINOIS UNIV CHAMPAIGN, *RICCATI EQUATION, TRANSIENTS,...

Topics: NASA Technical Reports Server (NTRS), COMPUTER PROGRAMS, FEEDBACK CONTROL, LINEAR SYSTEMS, FLIGHT...

Various algorithms are given for the case of constant coefficients. The algorithms are based on two ideas: first, relate the Re solution with general initial conditions to anchored RE solutions; and second, when the coefficients are constant the anchored solutions have a basic shift-invariance property. These ideas are used to construct an integration free superlinearly convergent iterative solution to the algebraic RE. The algorithm, arranged in square-root form, is thought to be numerically...

Topics: NASA Technical Reports Server (NTRS), ALGORITHMS, RICCATI EQUATION, CONVERGENCE, ITERATION,...

Robust stability conditions obtained through generalization of the notion of energy dissipation in physical systems are discussed in this report. Linear time-invariant (LTI) systems which dissipate energy corresponding to quadratic power functions are characterized in the time-domain and the frequency-domain, in terms of linear matrix inequalities (LMls) and algebraic Riccati equations (ARE's). A novel characterization of strictly dissipative LTI systems is introduced in this report. Sufficient...

Topics: NASA Technical Reports Server (NTRS), SYSTEMS STABILITY, RICCATI EQUATION, ENERGY DISSIPATION,...

Topics: DTIC Archive, Repperger,D W, AEROSPACE MEDICAL RESEARCH LAB WRIGHT-PATTERSON AFB OHIO, *MATRIX...

Topics: DTIC Archive, Repperger,Daniel W, AEROSPACE MEDICAL RESEARCH LAB WRIGHT-PATTERSON AFB OHIO,...

The problem is considered of designing an optimal linear time-invariant dynamic compensator for the regulation of an n-th order linear time-invariant plant with m independent outputs. The initial plant state is characterized by its first and second moments, and the cost is usual quadratic infinite-time penalty on the state and control, averaged over the initial plant and compensator states. The compensator is based on a minimal-order Luenberger observer and consequently has fixed dimension n-m....

Topics: NASA Technical Reports Server (NTRS), LINEAR SYSTEMS, OPTIMAL CONTROL, CANONICAL FORMS,...

This tutorial presentation introduces the two-time-scale concept and applies it to provide approximate solutions to initial-value problems for large-scale linear systems. (Author)

Topics: DTIC Archive, O'Malley,Robert E , Jr, ARIZONA UNIV TUCSON, *BOUNDARY VALUE PROBLEMS,...

The paper is concerned with giving sufficient conditions that in the non-linear boundary-value problem u'(x) + (q(x) + G(x,u(x), lambda))u(x) = 0 with u(0) = 0, u(1) = 0 or u'(1) = 0 there should be no secondary bifurcation, i.e. that, given a branch of solutions (u, lambda) bifurcating from the trivial solution, there should be no further bifurcation on that branch. Sufficient conditions on G are given which include, for example, Kolodner's problem of the motion of a heavy rotating string....

Topics: DTIC Archive, McLeod,J B, WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER, *NONLINEAR...

The state-dependent Riccati equations (SDRE) is the basis of a technique for suboptimal feedback control of a nonlinear quadratic regulator (NQR) problem. It is an extension of the Riccati equation used for feedback control of linear problems, with the addition of nonlinearities in the state dynamics of the system resulting in a state-dependent gain matrix as the solution of the equation. In this paper several variations on the SDRE-based method will be considered for the feedback control...

Topics: NASA Technical Reports Server (NTRS), FEEDBACK CONTROL, NONLINEARITY, RICCATI EQUATION, EQUATIONS...

In this research, the issue of uniform stabilization has been investigated for large classes of conservative systems arising in elasticity. In the case of linear problems, two types of feedback have been considered: (1) dissipative feedback operators acting only on the 'velocity' (2) generally non- dissipative feedback based on Riccati operators and acting on the full pair of position and velocity. In non linear problems, feedback of type (1) have been studied. Numerical implementation for both...

Topics: DTIC Archive, Lasiecka, I, VIRGINIA UNIV CHARLOTTESVILLE SCHOOL OF ENGINEERING AND APPLIED SCIENCE,...

Numerical issues related to the computational solution of the algebraic matrix Riccati equation were studied. The approach used the generalized eigenproblem formulation for the solution of general forms of algebraic Riccati equations arising in both continuous- and discrete-time applications. These general forms result from control and filtering problems for systems in generalized state space form. A Newton-type iterative refinement procedure for the generalized Riccati solution was derived....

Topics: DTIC Archive, Laub,A J, UNIVERSITY OF SOUTHERN CALIFORNIA LOS ANGELES, *ALGORITHMS, *RICCATI...

Viewgraphs on robust control for uncertain structures are presented. Topics covered include: robust linear quadratic regulator (RLQR) formulas; mismatched LQR design; RLQR design; interpretations of RLQR design; disturbance rejection; and performance comparisons: RLQR vs. mismatched LQR.

Topics: NASA Technical Reports Server (NTRS), CONTROL SYSTEMS DESIGN, LINEAR QUADRATIC REGULATOR,...

In this paper we present results related to the smoothing problem and related generalized Riccati equations for the two-point boundary value descriptor system (TP3VDS).

Topics: DTIC Archive, Nikoukhah, Ramine, MASSACHUSETTS INST OF TECH CAMBRIDGE LAB FOR INFORMATION AND...

The solutions of large linear systems with slow and fast modes are well approximated away from endpoints by a slow-mode solution. This corresponds to the use of outer solutions as approximate solutions of singular perturbation problems away from boundary layer regions. This paper gives an algorithm for obtaining the slow-mode solutions, and illustrates how the slow and fast components are obtained for the initial value problem. (Author)

Topics: DTIC Archive, O'Malley,R E , Jr, ARIZONA UNIV TUCSON, *BOUNDARY VALUE PROBLEMS, *PERTURBATIONS,...

During the period covered by the grant, ten papers were written. Titles include Error Bounds for Newton Refinement of Solutions to Algebraic Riccati Equations, Computable Bounds for the Sensitivity of Algebraic Riccati Equations, and Estimating the Distance to the Nearest Uncontrollable Pair through the Algebraic Riccati Equation.

Topics: DTIC Archive, Trefethen, Lloyd N, MASSACHUSETTS INST OF TECH CAMBRIDGE DEPT OF MATHEMATICS,...

Research in this program has concentrated on the generalized eigenvalue problem and its natural extension to the computation of the associated canonical form. Furthermore, there has been an extensive effort to study the matrix equation arising in control engineering such as controllability observability decomposition and the solution of the Riccati equations. In particular, error bounds for the computed eigenvalues and eigenvectors of the generalized eigenvalue problem have been devised. In...

Topics: DTIC Archive, Boley,Daniel L, STANFORD UNIV CA DEPT OF COMPUTER SCIENCE, *EIGENVECTORS,...

In this chapter, we are concerned with the second-order, self-adjoint dynamic equation P(T)X(SUB TRIANGLE UP)(T)(sup triangle down) + q(t)x(t) = 0 on a time scale. Since this equation combines both A and V derivatives in the same equation, we will begin by examining how these two types of derivatives interact. We will then study some basic results concerning this equation, specifically the Lagrange Identity and Abel's Formula. The remainder of the chapter will cover zeros of solutions and...

Topics: DTIC Archive, Messer, Kirsten R, NEBRASKA UNIV LINCOLN DEPT OF MATHEMATICS AND STATISTICS,...

A survey is presented of the current knowledge available for designing and predicting the effectiveness of controllers for dynamic systems which can be modeled by ordinary differential equations. A short discussion of feedback control is followed by a description of deterministic controller design and the concept of system state. The need for more realistic disturbance models led to the use of stochastic process concepts, in particular the Gauss-Markov process. A compensator controlled system,...

Topics: NASA Technical Reports Server (NTRS), CONTROL THEORY, DIFFERENTIAL EQUATIONS, RANDOM PROCESSES,...

This paper introduces methods tailored especially for problems whose solution behave like sub lambda x, ch1, where lambda is complex. The shallow water equations with topography admit such solution. This paper complements the results of Pratt and others on exponential-fitted methods and those of Gautschi, Neta, van der Houwen and others on trigonometrically-fitted methods.

Topics: DTIC Archive, Neta,Beny, NAVAL POSTGRADUATE SCHOOL MONTEREY CA, *EXPONENTIAL FUNCTIONS, *FITTING...

Many space science experiments need an active isolation system to provide them with the requisite microgravity environment. The isolation systems planned for use with the International Space Station have been appropriately modeled using relative position, relative velocity, and acceleration states. In theory, frequency design filters can be applied to these state-space models, in order to develop optimal H, or mixed-norm controllers with desired stability- and performance characteristics. In...

Topics: NASA Technical Reports Server (NTRS), MICROGRAVITY, VIBRATION ISOLATORS, KINEMATICS, AEROSPACE...

212
212

Jul 26, 2010
07/10

by
Ruggles, Stephen L

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A design approach for a support system or test station necessary to functionally operate a very high-speed integrated circuit (VHSIC) microprocessor brassboard is presented. Major subsystems which make up the support are the following: (1) power supply unit; (2) temperature controller unit; (3) input/output module; and (4) mechanical test fixture. Theoretical analyses and experimental techniques were utilized to design and implement the power and temperature requirements for the VHSIC...

Topics: CONTROL STABILITY, LINEAR QUADRATIC REGULATOR, RICCATI EQUATION, SYSTEMS STABILITY, DISTRIBUTED...

An approximation and convergence theory was developed for Galerkin approximations to infinite dimensional operator Riccati differential equations formulated in the space of Hilbert-Schmidt operators on a separable Hilbert space. The Riccati equation was treated as a nonlinear evolution equation with dynamics described by a nonlinear monotone perturbation of a strongly coercive linear operator. A generic approximation result was proven for quasi-autonomous nonlinear evolution system involving...

Topics: NASA Technical Reports Server (NTRS), APPROXIMATION, CONVERGENCE, GALERKIN METHOD, NONLINEAR...

Coherent states for a family of isospectral oscillator Hamiltonians are derived from a suitable choice of annihilation and creation operators. The Fock-Bargmann representation is also obtained.

Topics: NASA Technical Reports Server (NTRS), ANNIHILATION REACTIONS, CONGRUENCES, HAMILTONIAN FUNCTIONS,...

193
193

Jul 25, 2010
07/10

by
Whittenberger, J. Danie

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Measurements of the slow plastic flow behavior of cobalt, iron and nickel B2 crystal structure aluminides were conducted on materials fabricated by metallurical techniques. Due to this processing, the aluminides invariably had small equiaxed grains, ranging in size from about 3 to 60 microns in diameter. Grain size was dependent on the extrusion temperature used for powder consolidation, and it proved to be remarkably stable at elevated temperatures. Mechanical properties of all three...

Topics: APPROXIMATION, FEEDBACK CONTROL, LINEAR QUADRATIC REGULATOR, STATE ESTIMATION, COMPENSATORS,...

The purpose of this paper is to introduce a new spline approximation scheme for retarded functional differential equations. The special feature of this approximation scheme is that it preserves the product space structure of retarded systems and approximates the adjoint semigroup in a strong sense. These facts guarantee the convergence of the solution operators to the differential Riccati equation in a strong sense. Numerical findings indicate a significant improvement in the convergence...

Topics: DTIC Archive, Kappel,F, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER,...

The linear regulator problem for delay equation is discussed. We propose a (theoretical) solution involving Riccati integral equations and them axiomatically discuss a general approximation scheme. The details are given for spline and averaging approximations. (Author)

Topics: DTIC Archive, Kunisch,Karl, BROWN UNIV PROVIDENCE RI LEFSCHETZ CENTER FOR DYNAMICAL SYSTEMS,...

Two significant contributions have been made during this research period in the research 'Robust Control of Systems with Real Parameter Uncertainty and Unmodelled Dynamics' under NASA Research Grant NAG-1-1102. They are: (1) a fast algorithm for computing the optimal H(sub infinity) norm for the four-block, the two block, or the one-block optimal H(sub infinity) optimization problem; and (2) a construction of an optimal H infinity controller without numerical difficulty. In using GD (Glover and...

Topics: NASA Technical Reports Server (NTRS), ALGORITHMS, COMPUTERIZED SIMULATION, CONTROL SYSTEMS DESIGN,...

Square root, least squares estimation algorithms are examined from the viewpoint that square root arrays are arrays expressing relevant problem random variables in terms of basis sets of orthonormal (identity covariance) random variables. With this viewpoint, projection-theorem arguments can be expressed directly in the square root arrays, giving simple, geometric derivations of square root algorithms. A unifying framework is provided for previously proposed square root algorithms (and...

Topics: DTIC Archive, Kailath,Thomas, STANFORD UNIV CALIF INFORMATION SYSTEMS LAB, *LEAST SQUARES METHOD,...

The conventional six-engine reaction control jet relay attitude control law with deadband is shown to be a good linear approximation to a weighted time-fuel optimal control law. Techniques for evaluating the value of the relative weighting between time and fuel for a particular relay control law is studied along with techniques to interrelate other parameters for the two control laws. Vehicle attitude control laws employing control moment gyros are then investigated. Steering laws obtained from...

Topics: NASA Technical Reports Server (NTRS), ATTITUDE CONTROL, ATTITUDE STABILITY, DEGREES OF FREEDOM,...

During this period four papers were written including the titles, Stabilization of infinite dimensional systems and the steady state Riccati equation, Stability of an exponentially stabilize system, and Strong stability of quasi-affine transforms of contraction semigroups. Further information on these papers and the research topics involved are contained in this report. (Author)

Topics: DTIC Archive, Levan,N, CALIFORNIA UNIV LOS ANGELES SCHOOL OF ENGINEERING AND APPLIED SCIENCE,...

222
222

Jun 15, 2011
06/11

by
NON

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This invention relates generally to materials testing, and more particularly, to an ultrasonic apparatus for determining crack opening load in a specimen having a crack. A specimen having a crack is provided with a transmit transducer and a receive transmitter. An ultrasonic signal passing between the two transducers is mechanically rectified by the crack to produce a second harmonic of the input signal. By measuring the peak harmonic amplitude while increasing the tension load on the specimen,...

Topics: DYNAMIC STRUCTURAL ANALYSIS, NUMERICAL ANALYSIS, PROBABILITY THEORY, RICCATI EQUATION, STATISTICAL...

An abstract approximation framework for the solution of operator algebraic Riccati equations is developed. The approach taken is based on a formulation of the Riccati equation as an abstract nonlinear operator equation on the space of Hilbert-Schmidt operators. Hilbert-Schmidt norm convergence of solutions to generic finite dimensional Galerkin approximations to the Riccati equation to the solution of the original infinite dimensional problem is argued. The application of the general theory is...

Topics: NASA Technical Reports Server (NTRS), APPROXIMATION, CONVERGENCE, GALERKIN METHOD, HILBERT SPACE,...

In this paper we discuss the linear regulator problem associated with delay-differential equations. Formulas for the optimal feedback control and optimal trajectory are derived; this naturally leads to a Riccati integral equation in the state space of the delay equation. Finally, the linear regulator problem for the delay equation is approximated by sequences of regulator problems associated with ordinary differential equations in Euclidean space. (Author)

Topics: DTIC Archive, Kunisch,K, BROWN UNIV PROVIDENCE RI LEFSCHETZ CENTER FOR DYNAMICAL SYSTEMS, *CONTROL...

Methods to synthesize controllers for nonlinear systems are developed by exploiting the fact that under mild differentiability conditions, systems of the form: x-dot = f(x) + G(x)u can be represented in quasilinear form, viz: x-dot = A(x)x + B(x)u. Two classes of control methods are investigated. The first is zero-look-ahead control, where the control input depends only on the current values of A(x) and B(x). For this case the control input is computed by continuously solving a matrix Riccati...

Topics: NASA Technical Reports Server (NTRS), CONTROL STABILITY, CONTROL SYSTEMS DESIGN, CONTROL THEORY,...

A near optimal fixed-interval smoother for singularly perturbed systems is derived using the two filter (forward and backward) formulation. This intuitively-pleasing approach simplifies the fast mode boundary layer complications encountered previously, and results in a much simpler implementation than the exact solution. Application of similar singular perturbation techniques as for the (forward) filters, to the backward filter, results in a near optimal smoother with a similar two time-scale...

Topics: DTIC Archive, Altshuler,Dean, ILLINOIS UNIV AT URBANA-CHAMPAIGN COORDINATED SCIENCE LAB,...