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A homotopy algorithm for solving coupled riccati equations
Author(s) -
Mariton M.,
Bertrand P.
Publication year - 1985
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.4660060404
Subject(s) - mathematics , riccati equation , linear quadratic regulator , weighting , optimal control , set (abstract data type) , homotopy , nash equilibrium , solution set , algebraic riccati equation , class (philosophy) , linear quadratic gaussian control , homotopy analysis method , mathematical optimization , computer science , mathematical analysis , differential equation , pure mathematics , medicine , programming language , radiology , artificial intelligence
Many applications of optimization theory require the solution of a set of coupled Riccati equations. In multi‐person‐games problems, the players' decision for the Nash equilibrium depend on Riccati equations coupled through their quadratic terms. Another example is provided by linear‐quadratic control. When the system is subject to sudden and random changes in parameter values, the optimal feedback is computed from the solution of Riccati equations coupled through their weighting terms. After recalling the principle of homotopy methods, it is shown how it generates a new and efficient algorithm for this class of problem. An illustrative example is given.