In the Hamadryas baboon, males are substantially larger than females. A troop of baboons is subdivided into a number of ‘one-male groups’, consisting of one adult male and one or more females with their young. The male prevents any of ‘his’ females from moving too far from him. Kummer (1971) performed the following experiment. Two males, A and B, previously unknown to each other, were placed in a large enclosure. Male A was free to move about the enclosure, but male B was shut in a small cage, from which he could observe A but not interfere. A female, unknown to both males, was then placed in the enclosure. Within 20 minutes male A had persuaded the female to accept his ownership. Male B was then released into the open enclosure. Instead of challenging male A , B avoided any contact, accepting A’s ownership.

Evolution and the Theory of Games

This paper is a brief historical review of linear singular systems, followed by a survey of results on their solution and properties. The frequency domain and time domain approaches are discussed together to sketch an overall picture of the current status of the theory.

A survey of linear singular systems

https://hal.inria.fr/inria-00131031/document

Technical Communique: Robust sampled-data stabilization of linear systems: an input delay approach

Survey Constructive nonlinear control: a historical perspective

In this paper the disturbance attenuation and rejection problem is investigated for a class of MIMO nonlinear systems in the disturbance-observer-based control (DOBC) framework. The unknown external disturbances are supposed to be generated by an exogenous system, where some classic assumptions on disturbances can be removed. Two kinds of nonlinear dynamics in the plants are considered, respectively, which correspond to the known and unknown functions. Design schemes are presented for both the full-order and reduced-order disturbance observers via LMI-based algorithms. For the plants with known nonlinearity, it is shown that the full-order observer can be constructed by augmenting the estimation of disturbances into the full-state estimation, and the reduced-order ones can be designed by using of the separation principle. For the uncertain nonlinearity, the problem can be reduced to a robust observer design problem. By integrating the disturbance observers with conventional control laws, the disturbances can be rejected and the desired dynamic performances can be guaranteed. If the disturbance also has perturbations, it is shown that the proposed approaches are infeasible and further research is required in the future. Finally, simulations for a flight control system is given to demonstrate the effectiveness of the results. Copyright © 2005 John Wiley & Sons, Ltd.

Disturbance attenuation and rejection for systems with nonlinearity via DOBC approach

H-Optimal Control and Related Minimax Design Problems

H∞-Optimal Control and Related

We investigate properties of existence, unicity, representation, of the (causal) solutions of implicit linear systems (or “generalized systems”) when the underlying matrix pencil is singular. We relate the geometric and the algebraic approaches. The main conclusion is that if the underlying matrix pencil is “column singular” (i.e., has a nonempty set of column minimal indices) the causal solutions, when they exist, can exactly be represented as the output of a classical two-player dynamical system, where the second player accounts for the nonunicity. Properties of the equivalent system are related to those of the singular matrix pencils made with the given matrices.

On Singular Implicit Linear Dynamical Systems

Several versions of Danskin’s theorem, which deals with the derivative (or subdifferential) of the upper envelope J̄(u) = supv J(u, v) of a family of functions, are given. Some versions do not require compacity of the set over which the maximizing variable v ranges. It is then shown that the theorem of Von-Neumann Sion can be seen as a simple consequence of a convex-concave version of Danskin’s theorem.

On a theorem of Danskin with an application to a theorem of Von Neumann-Sion

On Lasker's card game- On a class of zero-sum discrete games with delayed information- A survey of recent results in differential games- Contingent Isaacs equations of a differential game- A PDE framework for games of pursuit-evasion type- Time-optimal pursuit inside a circle- A feedback guidance for pre-launch maneuvering in medium range air combat with missiles- Guidance law synthesis based on a planar pursuit-evasion game solution- Piecewise deterministic differential games- Newton-type methods for stochastic games- Nash-cournot equilibria in the buropean gas market: A case where open-loop and feedback solutions coincide- Time-dependent cooperation in games- A cooperative differential game in predator-prey systems- Repeated bargaining under uncertainty- The theory of teams: A selective annotated bibliography

Pierre Bernhard

Papers

H-Optimal Control and Related Minimax Design Problems

H∞-Optimal Control and Related

On Singular Implicit Linear Dynamical Systems

On a theorem of Danskin with an application to a theorem of Von Neumann-Sion

Differential Games and Applications