Abstract
In this chapter, important mathematical preliminaries, required in future chapters are presented, including stability definitions, some neural networks models, the extended Kalman filter learning algorithm and optimal control introduction.
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Notes
- 1.
A function l(z) is positive semidefinite (or nonnegative definite) function if for all vectors z, \(l(z)\ge 0\). In other words, there are vectors z for which \(l(z) = 0\), and for all others z, \(l(z)\ge 0\) [9].
- 2.
A real symmetric matrix R is positive definite if \(z^{\top } R z > 0\) for all \(z \ne 0\) [9].
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Garcia-Hernandez, R., Lopez-Franco, M., Sanchez, E.N., Alanis, A.Y., Ruz-Hernandez, J.A. (2017). Foundations. In: Decentralized Neural Control: Application to Robotics. Studies in Systems, Decision and Control, vol 96. Springer, Cham. https://doi.org/10.1007/978-3-319-53312-4_2
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DOI: https://doi.org/10.1007/978-3-319-53312-4_2
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