On the design of correct and optimal dynamical systems and games

There exist various methods for designing dynamical systems and dynamical games in order to ensure correctness and optimality. In the paper, they are systematically organized as follows. Two variational principles are recalled. Firstly, solutions must be stationary: this leads to necessary conditions and to gradient algorithms. Secondly, solutions, if any, must be optimal or correct; this leads to sufficient conditions and to dynamic-programming algorithms. Methods based on these principles allow to design dynamical systems and games such as control systems, hybrid systems and reactive ones. Time may be discrete or continuous; correctness can be viewed as an abstraction of optimality. The structured presentation of design methods is intended to foster their understanding, integration, cross-fertilization and improvement. (C) 2003 Elsevier B.V. All rights reserved.