Saddle Point
Back to the cover

Part I · Foundations

  1. 0 Mathematical Foundations
  2. 1 Observation, Beliefs, and Decision

Part II · Engines

  1. 2 Competing for Allocation: The Blotto Game
  2. 3 Bargaining, Commitment, and Repeated Cooperation
  3. 4 Signals, Disclosure, and Persuasion
  4. 5 Different Models of One Game
  5. 6 Leadership and Rules: Inspection
  6. 7 Decisions in Time
  7. 8 Many Agents
  8. 9 Networks, Dependence, and Resilience
  9. 10 Aggregating Information

Part III · Systems

  1. 11 Architecture of Decision Support
  2. 12 Simulation and Wargaming with AI Agents

Part IV · Limits

  1. 13 Where the Mathematics Stops

Chapter 1 · Observation, Beliefs, and Decision

Hans S. Witsenhausen

1930 – 2016

The problem on the desk

Do linear dynamics, Gaussian noise and a quadratic objective always justify linear controllers? Witsenhausen tested the missing information-structure assumption: controllers at different stations do not share a single perfect memory. His 1968 counterexample showed why the familiar conclusion can fail.1

A life in moments

  1. 1930

    Born on 6 May.2

  2. 1965

    Massachusetts Institute of Technology · Cambridge

    Began a Hertz fellowship in electrical engineering.3

  3. 1966

    Massachusetts Institute of Technology · Cambridge

    Submitted his doctoral work on minimax control of uncertain systems.4

  4. 1968

    Published the counterexample in stochastic optimum control.1

  5. 1975

    Published conditions for two observers to extract agreeing decisions from dependent data.5

  6. 2016

    Died on 19 November.2

Every line rests on a dated source (numbered below) unless it carries a mark: R for an inference, S for a story as told.

In their own words

The control of uncertain systems is considered as a decision problem.

Minimax Controls of Uncertain Systems, 19667

A story

The assumption that mattered

His counterexample targeted a conjecture that linear control should suffice in a linear–Gaussian quadratic setting. The abstract explicitly identifies the missing qualification: established results assumed one station with perfect memory.6

This is a documented research episode, not a personal anecdote.

Around Witsenhausen

  • doctoral advisor Michael Athans His thesis acknowledgements thank Athans for teaching, encouragement and criticism.8
  • results he sharpened Péter Gács His 1975 paper states that it sharpens and clarifies results of Gács and Körner.9
  • results he sharpened János Körner His 1975 paper states that it sharpens and clarifies results of Gács and Körner.9

Recorded as advisor Michael (Athanassiades) Athans Mathematics Genealogy Project record

The genealogy lists only what the database records; a missing name is not a missing teacher.

The card in the book

Engineer and mathematician, born in Frankfurt am Main and educated at the Université Libre de Bruxelles, in electrical engineering and in mathematical physics, and at the Massachusetts Institute of Technology, where he received his doctorate in electrical engineering in 1966 with a thesis on the minimax control of uncertain systems. He then joined Bell Laboratories. He worked on stochastic control with decentralised information — the intrinsic model of information structures and the counterexample that bears his name — and on information theory, including the common information of dependent random variables.

Main works “A counterexample in stochastic optimum control” (SIAM J. Control 6, 1968); “Separation of estimation and control for discrete time systems” (Proc. IEEE 59, 1971); “On sequences of pairs of dependent random variables” (SIAM J. Appl. Math. 28, 1975).

To read further

Sources (9)
  1. A Counterexample in Stochastic Optimum Control, Hans S. Witsenhausen, 1968; SIAM Journal on Control 6(1), pp. 131–147; abstract
  2. Hans Witsenhausen: obituary notice, New York Times, family notice, 2016; Notice published 23 November 2016
  3. Hans Witsenhausen, Hertz Foundation; 1965 Hertz Fellow; Making History; Education
  4. Minimax Controls of Uncertain Systems, Hans S. Witsenhausen, 1966; Acknowledgements p. iii
  5. On Sequences of Pairs of Dependent Random Variables, Hans S. Witsenhausen, 1975; SIAM Journal on Applied Mathematics 28; abstract, final paragraph
  6. A Counterexample in Stochastic Optimum Control, Hans S. Witsenhausen, 1968; Abstract
  7. Minimax Controls of Uncertain Systems, Hans S. Witsenhausen, 1966; Abstract p. ii
  8. Minimax Controls of Uncertain Systems, Hans S. Witsenhausen, 1966; p. iii
  9. On Sequences of Pairs of Dependent Random Variables, Hans S. Witsenhausen, 1975; Abstract, final paragraph

The facts on this page were gathered for the site from the sources listed, each checked against its locator; the book's card is reproduced unchanged.