Optimality Zone Algorithms for Hybrid Systems Computation and Control: From Exponential to Linear Complexity
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Bibliographic record
Abstract
Necessary conditions were obtained by Shaikh and Caines (2002, 2003 and 2004) for hybrid optimal control problems (HOCPs) which resulted in a general hybrid maximum principle (HMP); further, a class of efficient, provably convergent hybrid maximum principle (HMP) algorithms were obtained based upon the HMP. The notion of optimality zones (OZs) (2004) was introduced as a theoretical framework enabling the computation of optimal schedules for HOCPs (i.e., discrete state sequences with the associated switching times and states). This paper presents the algorithm HMPZ which fully integrates the prior computation of the OZs into the HMP algorithms. Adding (i) the computational investment in the construction of the OZs for a given HOCP, and (ii) the complexity of the computation of the optimal schedule, optimal switching time and state sequence, and the optimal continuous control input, yields a complexity estimate for the algorithm (HMPZ) which is linear (i.e., O(L)) in the number of switching times L; this is to be compared with the geometric (i.e. O(|Q| <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</sup> )) growth of a direct combinatoric search over the set of schedules, where Q denotes the discrete state set of the hybrid system
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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