Minimax Pareto Optimal Solutions with Application to Linear-Quadratic Problems
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A particular Pareto optimal solution, related to a class of minimax problems and therefore called the minimax Pareto optimal solution, is defined, analysed and applied to the study of cooperative solutions in problems described by linear dynamic systems and by vector-valued quadratic criteria. Four related topics are considered: (a) solution of the deterministic linear regulator problem with a vector-valued criterion, (b) convex approximation of the solution of the Riccati matrix differential equation, (c) solution of the stochastic linear regulator problem with a vector-valued criterion, and (d) the multiple-plant cooperative control problem.
KeywordsDeterministic Problem Convex Approximation Taylor Series Approximation Matrix Differential Equation Matrix Riccati Equation
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