A time optimal control study of a second- order linear system with delay
Time optimal control study of second-order linear system with delay
Kashiwagi, Y.↗
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Results for “linear system”
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Minimal time control of linear systems with control amplitude and rate saturations
Time optimal control of linear systems with constraints on control amplitude and rate
Luh, J. Y. S.↗
Optimal stationary control of linear systems with control-dependent noise
Optimal stochastic control investigated for linear systems with driving noise intensity proportional to control input
Kleinman, D. L.↗
Bayes and minimax controllers for a linear system with stochastic jump parameters
Optimal zero-memory regulator for linear system with stochastic jump parameters, considering Bayes and minimax controllers
Pierce, B. D.↗
Controllability of nearly nonnegative linear systems using positive controls
A general result for the controllability of linear systems using positive controls was given by Saperstone and Yorke (1971). These results are applied to systems with nearly nonnegative matrices and a theorem is developed which delineates the geometry of the reachable set.
Perry, T. S.↗
Direct computation of optimal control of forced linear system
It is known that the optimal control of a forced linear system may be reduced to that of tracking the system without forces. The solution of the tracking problem is available via the costate variables method. This procedure is computationally expensive for large order systems. It requires solution of matrix Riccati equation and two final value problems. An alternate approach is outlined for the direct computation of the optimal control. Instead of Riccati equation, a matrix Volterra integral must be solved. For this purpose two computational schemes are described, and an illustrative example is given. The results compare favorably with the classical solution. This alternative approach may be especially useful for the control of large space structure where large order models are required.
Utku, S.↗
Recursive inversion of externally defined linear systems by FIR filters
The approximate inversion of an internally unknown linear system, given by its impulse response sequence, by an inverse system having a finite impulse response, is considered. The recursive least-squares procedure is shown to have an exact initialization, based on the triangular Toeplitz structure of the matrix involved. The proposed approach also suggests solutions to the problem of system identification and compensation.
Bach, Ralph E., Jr.↗
Novel Solver Algorithms for Nearly Singular Linear Systems Arising in Combustion Modelling
Direct Numerical Simulations of realistic combustion devices are extremely challenging due to the wide separation of scales in the simulation, for example an internal combustion (IC) engine chamber, and the flame thickness of a high-pressure flame. The PeleLMeX solver uses adaptive mesh refinement (AMR) to evolve multi-species reacting flows in the low Mach number limit at the Exascale and relies on an embedded boundary (EB) approach to represent complex geometries. In that framework, the EB geometries often give rise to very small cut-cells along the boundary, which translate into extreme ill-conditioning of the pressure-projection, with eigenvalues that span 15-16 orders of magnitude. In this talk, we focus on the case of a typical IC piston bowl geometry for which we present on a novel approach towards solving these nearly singular linear systems with ILU-based, C-AMG smoothers on massively parallel architectures. In particular, we use scaling and equilibration algorithms to handle the non-normality of the upper triangular factors. This enables us to approximate the highly sequential triangular solve algorithm, embedded in the AMG smoothing-solve phase, with Jacobi iterations. This approximation can be written as a convergent Neumann series whose terms are composed of highly parallel sparse matrix vector multiplications. The result is an algorithm that substantially decreases setup and solve time, compared to state-of-the-art, for these challenging linear systems.
combustion modelling↗
Analysis of a Linear System for Variable-Thrust Control in the Terminal Phase of Rendezvous
A linear system for applying thrust to a ferry vehicle in the 3 terminal phase of rendezvous with a satellite is analyzed. This system requires that the ferry thrust vector per unit mass be variable and equal to a suitable linear combination of the measured position and velocity vectors of the ferry relative to the satellite. The variations of the ferry position, speed, acceleration, and mass ratio are examined for several combinations of the initial conditions and two basic control parameters analogous to the undamped natural frequency and the fraction of critical damping. Upon making a desirable selection of one control parameter and requiring minimum fuel expenditure for given terminal-phase initial conditions, a simplified analysis in one dimension practically fixes the choice of the remaining control parameter. The system can be implemented by an automatic controller or by a pilot.
Hord, Richard A.↗
Estimability And Regulability Of Linear Systems
Report presents two new properties of systems characterized by linear state space models (e.g., dynamical systems and associated control systems): estimability and regulability. Provides criteria for reductions of errors and cost functions in control systems. Useful in design of optimal controllers and estimators.
Baram, Yoram↗
Response of linear systems to magnitude limited random excitation.
Magnitude limited random excitation effect on linear system response, using single degrees of freedom model representing idealized mechanical structure
Hu, P. Y.↗
A new method of recursive estimation in discrete linear systems
Gain of optimal filter and predictor, using recursive estimation in discrete linear systems
Kashyap, R. L.↗
Identification of a linear system from sampled noisy data, part C Final project report
Step input linear system modeling from nonlinear system sampled noisy data based on method of perturbation or quasilinearization of automatic control system data
Luckinbill, D. L.↗
Weighted least squares stationary approximations to linear systems.
Investigation of the problem of replacing a certain time-varying linear system by a stationary one. Several quadratic criteria are proposed to aid in determining suitable candidate systems. One criterion for choosing the matrix B (in the stationary system) is initial-condition dependent, and another bounds the 'worst case' homogeneous system performance. Both of these criteria produce weighted least square fits.
Bierman, G. J.↗
Iterative solution of linear systems
Recent advances in the field of iterative methods for solving large linear systems are reviewed. The main focus is on developments in the area of conjugate gradient-type algorithms and Krylov subspace methods for nonHermitian matrices.
Freund, Roland W.↗
An automatic multigrid method for the solution of sparse linear systems
An automatic version of the multigrid method for the solution of linear systems arising from the discretization of elliptic PDE's is presented. This version is based on the structure of the algebraic system solely, and does not use the original partial differential operator. Numerical experiments show that for the Poisson equation the rate of convergence of our method is equal to that of classical multigrid methods. Moreover, the method is robust in the sense that its high rate of convergence is conserved for other classes of problems: non-symmetric, hyperbolic (even with closed characteristics) and problems on non-uniform grids. No double discretization or special treatment of sub-domains (e.g. boundaries) is needed. When supplemented with a vector extrapolation method, high rates of convergence are achieved also for anisotropic and discontinuous problems and also for indefinite Helmholtz equations. A new double discretization strategy is proposed for finite and spectral element schemes and is found better than known strategies.
Shapira, Yair↗
A spectral analysis of the domain decomposed Monte Carlo method for linear systems
The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear oper- ator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approxi- mation and the mean chord approximation are applied to estimate the leakage frac- tion of random walks from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem in numerical experiments to test the models for symmetric operators with spectral qualities similar to light water reactor problems. We find, in general, the derived approximations show good agreement with random walk lengths and leakage fractions computed by the numerical experiments.
97 MATHEMATICS AND COMPUTING↗
A spectral analysis of the domain decomposed Monte Carlo method for linear systems
The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear operator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approximation and the mean chord approximation are applied to estimate the leakage fraction of stochastic histories from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem to test the models for symmetric operators. In general, the derived approximations show good agreement with measured computational results. (authors)
97 MATHEMATICS AND COMPUTING↗