Linear discrete-time Pareto-Nash-Stackelberg control problem and principles for its solving

Abstract

A direct-straightforward method for solving linear discrete-time optimal control problem is applied to solve control problem of a linear discrete-time system as a mixture of multi-criteria Stackelberg and Nash games. For simplicity, the exposure starts with the simplest case of linear discrete-time optimal control problem and, by sequential considering of more general cases, investigation finalizes with the highlighted Pareto-Nash-Stackelberg and set valued control problems. Different principles of solving are compared and their equivalence is proved. Mathematics Subject Classification 2010: 49K21, 49N05, 93C05, 93C55, 90C05, 90C29, 91A10, 91A20, 91A44, 91A50.

Keywords

• Linear discrete-time control problem
• non-cooperative game
• multi-criteria strategic game
• Pareto-Nash-Stackelberg control