LAGRANGIAN AND FOURIER ANALYSIS

ABSTRACT

Thus an explicit closed-form control for an uncertain, nonlinear, nonautonomous multi-body system that satisfies trajectory control requirements placed on the nominal system (to within pre-specified error bounds), is obtained. An example of a triple pendulum in which there are uncertainties both in the description of its physical parameters and in the description of the gravity field in which it moves is considered. The example demonstrates the simplicity and efficacy of the approach when there are uncertainties both in the description of a dynamical system and in the given forces to which it is subjected.

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]]>One things that comes to mind is that modeling the FLOPS is a good measure of performance only if the computation has a high arithmetic intensity. That is, the number of floating point operations to memory accesses is high. This is true of Gaussian Elimination. However, in an operation such as a sparse matrix-vector multiply the arithmetic intensity is low (1 fused multiply add per memory access) and the operation becomes bandwidth limited.

]]>One thing that comes to mind is that this is true as long as the computation is arithmetically intense. That is, the number of floating point operations to memory accesses is large. In the case of Gaussian elimination, this is true and so counting FLOPS is a good measure of cost. However, in a operation such as a sparse matrix-vector product (where you have low arithmetic intensity, 1 fused multiply-add per memory access) it is the memory bandwidth that limits performance.

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