On the minimax reachability of target sets and target tubes

D. P. Bertsekas, I. B. Rhodes

Research output: Contribution to journalArticlepeer-review

322 Scopus citations


This paper is concerned with the closed-loop control of discrete-time systems in the presence of uncertainty. The uncertainty may arise as disturbances in the system dynamics, disturbances corrupting the output measurements or incomplete knowledge of the initial state of the system. In all cases, the uncertain quantities are assumed unknown except that they lie in given sets. Attention is first given to the problem of driving the system state at the final time into a prescribed target set under the worst possible combination of disturbances. This is then extended to the problem of keeping the entire state trajectory in a given target "tube". Necessary and sufficient conditions for reachability of a target set and a target tube are given in the case where the system state can be measured exactly, while sufficient conditions for reachability are given for the case when only disturbance corrupted output measurements are available. An algorithm is given for the efficient construction of ellipsoidal approximations to the sets involved, and it is shown that this algorithm leads to linear control laws. The application of the results in this paper to pursuit-evasion games is also discussed.

Original languageEnglish (US)
Pages (from-to)233-247
Number of pages15
Issue number2
StatePublished - Mar 1971
Externally publishedYes

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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