Academic Journal
Applications of Induced Tensor Norms to Guidance Navigation and Control
| Τίτλος: | Applications of Induced Tensor Norms to Guidance Navigation and Control |
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| Συγγραφείς: | Kulik, Jackson, Orton-Urbina, Cedric, Ruth, Maximilian, Savransky, Dmitry |
| Πηγή: | Journal of Guidance, Control, and Dynamics. 48:2180-2198 |
| Publication Status: | Preprint |
| Στοιχεία εκδότη: | American Institute of Aeronautics and Astronautics (AIAA), 2025. |
| Έτος έκδοσης: | 2025 |
| Θεματικοί όροι: | FOS: Mathematics, Dynamical Systems (math.DS), Mathematics - Dynamical Systems |
| Περιγραφή: | Linear methods are ubiquitous for control and estimation problems. In this work, we present a number of tensor operator norms as a means to approximately bound the error associated with linear methods and determine the situations in which that maximum error is encountered. An emphasis is placed on induced norms that can be computed in terms of matrix or tensor eigenvalues associated with coefficient tensors from higher-order Taylor series. These operator norms can be used to understand the performance and range of applicability of an algorithm exploiting linear approximations in different sets of coordinates. We examine uses of tensor operator norms in the context of linear and higher-order rendezvous guidance and to present a unified treatment of nonlinearity indices for dynamic systems. Tensor norm computations can offer insights into these problems in one to two orders of magnitude less time than similarly accurate sampling methods while providing more general understanding of the error performance of linear or higher-order approximations. |
| Τύπος εγγράφου: | Article |
| Γλώσσα: | English |
| ISSN: | 1533-3884 0731-5090 |
| DOI: | 10.2514/1.g009054 |
| DOI: | 10.48550/arxiv.2408.15362 |
| Σύνδεσμος πρόσβασης: | http://arxiv.org/abs/2408.15362 |
| Rights: | CC BY URL: https://www.aiaa.org/userlicenses/1.0/#CompEndUserLicense |
| Αριθμός Καταχώρησης: | edsair.doi.dedup.....835f9085999ad22b7b14227b11b09c7c |
| Βάση Δεδομένων: | OpenAIRE |
| ISSN: | 15333884 07315090 |
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| DOI: | 10.2514/1.g009054 |