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Results for “Semidefinite optimization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS2006

Spacecraft inertia estimation via constrained least squares

This paper presents a new formulation for spacecraft inertia estimation from test data. Specifically, the inertia estimation problem is formulated as a constrained least squares minimization problem with explicit bounds on the inertia matrix incorporated as LMIs [linear matrix inequalities). The resulting minimization problem is a semidefinite optimization that can be solved efficiently with guaranteed convergence to the global optimum by readily available algorithms. This method is applied to data collected from a robotic testbed consisting of a freely rotating body. The results show that the constrained least squares approach produces more accurate estimates of the inertia matrix than standard unconstrained least squares estimation methods.

inertia estimation↗

NASA NTRS2007

Estimating the Inertia Matrix of a Spacecraft

A paper presents a method of utilizing some flight data, aboard a spacecraft that includes reaction wheels for attitude control, to estimate the inertia matrix of the spacecraft. The required data are digitized samples of (1) the spacecraft attitude in an inertial reference frame as measured, for example, by use of a star tracker and (2) speeds of rotation of the reaction wheels, the moments of inertia of which are deemed to be known. Starting from the classical equations for conservation of angular momentum of a rigid body, the inertia-matrix-estimation problem is formulated as a constrained least-squares minimization problem with explicit bounds on the inertia matrix incorporated as linear matrix inequalities. The explicit bounds reflect physical bounds on the inertia matrix and reduce the volume of data that must be processed to obtain a solution. The resulting minimization problem is a semidefinite optimization problem that can be solved efficiently, with guaranteed convergence to the global optimum, by use of readily available algorithms. In a test case involving a model attitude platform rotating on an air bearing, it is shown that, relative to a prior method, the present method produces better estimates from few data.

Acikmese, Behcet↗

NASA NTRS2017

Interval Predictor Models for Data with Measurement Uncertainty

An interval predictor model (IPM) is a computational model that predicts the range of an output variable given input-output data. This paper proposes strategies for constructing IPMs based on semidefinite programming and sum of squares (SOS). The models are optimal in the sense that they yield an interval valued function of minimal spread containing all the observations. Two different scenarios are considered. The first one is applicable to situations where the data is measured precisely whereas the second one is applicable to data subject to known biases and measurement error. In the latter case, the IPMs are designed to fully contain regions in the input-output space where the data is expected to fall. Moreover, we propose a strategy for reducing the computational cost associated with generating IPMs as well as means to simulate them. Numerical examples illustrate the usage and performance of the proposed formulations.

Lacerda, Marcio J.↗

NASA NTRS1990

Robust control of systems with real parameter uncertainty and unmodelled dynamics

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 Doyle) or DGKF (Doyle, Glover, Khargonekar, and Francis) approach to solve the standard H infinity norm which required bisection search. In this research period, we developed a very fast iterative algorithm for this computation. Our algorithm was developed based on hyperbolic interpolations which is much faster than any existing algorithm. The lower bound of the parameter, gamma, in the H infinity Riccati equation for solution existence is shown to be the square root of the supremum over all frequencies of the maximum eigenvalue of a given transfer matrix which can be computed easily. The lower band of gamma such that the H infinity Riccati equation has positive semidefinite solution can be also obtained by hyperbolic interpolation search. Another significant result in this research period is the elimination of the numerical difficulties arising in the construction of an optimal H infinity controller by directly applying the Glover and Doyle's state-space formulas. With the fast iterative algorithm for the computation of the optimal H infinity norm and the reliable construction of an optimal H infinity controller, we are ready to apply these tools in the design of robust controllers for the systems with unmodelled uncertainties. These tools will be also very useful when we consider systems with structured uncertainties.

Chang, Bor-Chin↗

NASA NTRS1992

The structure of the gamma-domain for H-infinity Riccati solutions

The authors investigated some properties of the solutions to H-infinity Riccati equations which play a key role in the state approach to H-infinity optimization problem. The structure of the gamma-domain for the Riccati solutions has been described. There are two kinds of lower bounds for the solutions to exist and to be positive semidefinite respectively. A quadratically convergent algorithm for computing the lower bound is discussed.

Li, X. P.↗