Abstract
In the first section of this chapter we deal with the problem of feedback impulse control in the class of generalized inputs that may involve delta functions and discontinuous trajectories in the state space. Such feedback controls are not physically realizable. The second section thus treats the problem of feedback control under double constraints: both hard bounds and integral bounds. Such solutions are then used for approximating impulse controls by bounded “ordinary” functions.
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Notes
- 1.
In this book we give a concise description of impulse controls that are confined only to δ-functions, but not their derivatives. A general theory of impulse control that also involves derivatives of δ-functions is beyond the scope of this book and is presented in [152, 154]. Such theory leads to the description of “fast” or “ultra fast” control solutions achieved on a quantum level and in “nano”-time.
- 2.
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Kurzhanski, A.B., Varaiya, P. (2014). Impulse Controls and Double Constraints. In: Dynamics and Control of Trajectory Tubes. Systems & Control: Foundations & Applications, vol 85. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-10277-1_6
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DOI: https://doi.org/10.1007/978-3-319-10277-1_6
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