Trajectory Tubes State-Constrained Feedback Control

Part of the Systems & Control: Foundations & Applications book series (SCFA, volume 85)


This chapter begins with the theory of trajectory tubes which are necessary elements of realistic mathematical models for controlled processes and their evolutionary dynamics. We then deal with the evolution in time of state-constrained forward and backward reachability tubes also known as “viability tubes.” The backward tubes are then used to design feedback controls under state constraints that may also appear in the form of obstacles to be avoided by system trajectories.


Trajectory tubes Viable solutions Funnel equations Feedback control Obstacle problems 


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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Faculty of Computational Mathematics and CyberneticsMoscow State (Lomonosov) UniversityMoscowRussia
  2. 2.Electrical Engineering and Computer SciencesUniversity of California, BerkeleyBerkeleyUSA

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