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Optimization problems involving linear systems with retardations in the controls are studied in a systematic way. Some physical motivation for the problems is discussed. The topics covered are: controllability, existence and uniqueness of the optimal control, sufficient conditions, techniques of synthesis, and dynamic programming. A number of solved examples are presented.
Sufficient conditions for linear time optimal control system on compact real intervals in Euclidean n space
Increasing numbers of distributed generators in the electric power distribution networks require developing a control strategy to optimize solutions in real time. Linearized optimal distribution flow development has seen growth and acceptance in the distribution systems literature for efficiently modeling the \glspl{opf} for distribution systems. This paper examines the implementation and integration procedure for linearized optimal distribution flow federate to \gls{oedisi} platform. Specifically, we discuss i) the usage of the \gls{oedisi} platform, ii) obtaining a tractable solution using developed \gls{opf} federate, and iii) validation of solutions and bench-marking the \gls{oedisi} platform with developed \gls{opf} federate using OpenDSS. In brief, we demonstrate how a general linearized optimal distribution flow federate can be developed and integrated with a co-simulation environment to mimic real-world examples. The efficacy of the proposed method is demonstrated using the IEEE 123-bus test system under different scenarios to obtain a tractable solution and compare its results.
EOPS empirically optimizes linear array of radiating elements. Program directly addresses problem of minimizing maximum side-lobe level of fixed length, linear arrays of radiating elements under realistic "on-the-vehicle" conditions. Used for both electromagnetic and acoustic arrays.
Trajectory optimization and linearized pitch computer program for Scout launch vehicle
Linear parameter optimization with quadratic cost in application to ballistic missile guidance coefficient
The maintenance of accurate primary mirror figure in the face of environmental disturbances is the key to the achievement of diffraction-limited performance in a large space telescope. In order to develop the concepts of optical mirror figure control, an experimental program was initiated. A major component in this experiment will be an XDS Sigma 5.7 digital computer which will realize the control algorithm. A software package is described which realizes linear optimal, simplified linear, and iterative optimal control algorithms. The software, in addition, provides for interactive communication between the operator and the computer, and interaction between the computer and the experimental hardware elements. A brief description of a small hybrid computer system is also presented.
Function space approach to linear stochastic optimal control systems
A computational algorithm is presented for the extraction of an optimal single linear feature from several Gaussian pattern classes. The algorithm minimizes the increase in the probability of misclassification in the transformed (feature) space. Numerical results on the application of this procedure to the remotely sensed data from the Purdue Cl flight line as well as LANDSAT data are presented. It was found that classification using the optimal single linear feature yielded a value for the probability of misclassification on the order of 30% less than that obtained by using the best single untransformed feature. Also, the optimal single linear feature gave performance results comparable to those obtained by using the two features which maximized the average divergence.
Linear optimal stationary control system with state dependent white noise disturbances described by differential equation
For optimization problems with linear equality constraints, we prove that the (1,1) block of the inverse KKT matrix remains unchanged when projected onto the nullspace of the constraint matrix. In this work, we develop reduced compact representations of the limited-memory inverse BFGS Hessian to compute search directions efficiently when the constraint Jacobian is sparse. Orthogonal projections are implemented by a sparse QR factorization or a preconditioned LSQR iteration. In numerical experiments two proposed trust-region algorithms improve in computation times, often significantly, compared to previous implementations of related algorithms and compared to IPOPT.
Linear time optimal control problem and calculus of variations
A computer program is described which solves the linear stochastic optimal control and estimation (LSOCE) problem by using a time-domain formulation. The LSOCE problem is defined as that of designing controls for a linear time-invariant system which is disturbed by white noise in such a way as to minimize a performance index which is quadratic in state and control variables. The LSOCE problem and solution are outlined; brief descriptions are given of the solution algorithms, and complete descriptions of each subroutine, including usage information and digital listings, are provided. A test case is included, as well as information on the IBM 7090-7094 DCS time and storage requirements.
An explicit parametrization of a subclass of linear constant gain feedback maps that never destabilize an originally open-loop stable system is presented. These results are used to obtain several new structural stability results for multiinput linear-quadratic feedback optimal designs.
Strong sufficient conditions are derived for the robustness of optimal linear-quadratic (LQ) regulators to large parameter perturbations. In particular, it is shown that under certain conditions LQ designs remain stable in the presence of actuator channel failures. The general results can be specialized to provide insight into the gain margin, gain reduction, and phase margin properties of optimal LQ regulators.
Optimal linear mean square filtering for piecewise linear correlation functions
The Fast Linearized Coronagraph Optimizer (FALCO) is an open-source toolbox of routines for coronagraphic focal plane wavefront correction. The goal of FALCO is to provide a free, modular framework for the simulation or testbed operation of several common types of coronagraphs. FALCO includes routines for pair-wise probing estimation of the complex electric field and Electric Field Conjugation (EFC) control, and we ask the community to contribute other wavefront correction algorithms. FALCO utilizes and builds upon PROPER, an established optical propagation library. The key innovation in FALCO is the rapid computation of the linearized response matrix for each deformable mirror (DM), which facilitates re-linearization after each control step for faster DM-integrated coronagraph design and wavefront correction experiments. FALCO is freely available as source code in MATLAB at github.com/ajeldorado/falco-matlab and will be available later this year in Python 3 at github.com/ajeldorado/falco-python.
We have developed the Fast Linearized Coronagraph Optimizer (FALCO), a new software toolbox for high-contrast, coronagraphic wavefront sensing and control. FALCO rapidly calculates the linearized deformable mirror (DM) response matrices, also called control Jacobians, and can be used for the design, simulation, or testbed operation of several types of coronagraphs. In this paper, we demonstrate that the optical propagation used in FALCO is accurate and matches PROPER. In addition, we demonstrate the drastic reduction in runtime when using FALCO for DM Jacobian calculations instead of the conventional method used, for example with a model of the Wide-Field Infrared Survey Telescope (WFIRST) Coronagraph Instrument (CGI). We then compare the relative accuracy between optical models in FALCO and PROPER.