Control vector iteration; Duality in optimal control with first order differential equations; Dynamic programming and Newton's method in unconstrained optimal control; Dynamic programming: Continuous-time optimal control, Dynamic programming: Optimal control applications, Hamilton–Jacobi–Bellman equation; MINLP: Applications in the interaction of design and control; Multi-objective optimization: Interaction of design and control; Optimal control of a flexible arm; Optimization strategies for dynamic systems; Robust control; Robust control: Schur stability of polytopes of polynomials; Semi-infinite programming and control problems; Sequential quadratic programming: Interior point methods for distributed optimal control problems; Suboptimal control INFINITE HORIZON CONTROL AND DYNAMIC GAMES

• A system evolving over an infinite horizon is characterized by a state x∈ X⊆ R ^m ₀. Some agents also called the players i = 1,..., p can influence the state's evolution through the choice of an appropriate control in an admissible class. The control value at a given time n for player i is denoted u _i (n)∈ U _i ⊆ R _{m i} .

• The state evolution of such a dynamical system may be described either as a difference equation, if discrete time is used, or a differential equation in a continuous time framework. For definiteness we fix our attention here on a stationary difference equation and merely remark that similar comments apply for the case when other types of dynamical systems are considered.

  

  for n = 0, 1,..., where f: R ^m0×...× R ^mp R ^m ₀ is a given state transition function.

• We assume that the agents can observe the state of the system and remember the history of the system evolution up to the current time n, that is, the sequence

  

  where u(n) denotes the controls chosen by all players at...