Chaos May Be an Optimal Plan

An interpretation of some chaotic systems as the result of optimal decisions is presented. First, a generalized discrete-time two-person game is introduced that may be solved by use of dynamic programming. Then, a specific game of this type is formulated whose optimal solution transforms an originally linear discrete-time system into a well-known discrete-time chaotic system. Finally, a particular continuous-time optimal control problem is formulated, whose optimal feedback solution transforms an originally linear continuous-time system into a well-known continuous-time chaotic system.