Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Controllability and Observability Imply Exponential Decay of Sensitivity
  in Dynamic Optimization   We study a property of dynamic optimization (DO) problems (as those
encountered in model predictive control and moving horizon estimation) that is
known as exponential decay of sensitivity (EDS). This property indicates that
the sensitivity of the solution at stage $i$ against a data perturbation at
stage $j$ decays exponentially with $|i-j|$. {Building upon our previous
results, we show that EDS holds under uniform boundedness of the Lagrangian
Hessian, a uniform second order sufficiency condition (uSOSC), and a uniform
linear independence constraint qualification (uLICQ). Furthermore, we prove
that uSOSC and uLICQ can be obtained under uniform controllability and
observability. Hence, we have that uniform controllability and observability
imply EDS.} These results provide insights into how perturbations propagate
along the horizon and enable the development of approximation and solution
schemes. We illustrate the developments with numerical examples.

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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga