Colonius, Fritz.
Optimal Periodic Control [electronic resource] / by Fritz Colonius. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1988. - VI, 177 p. online resource. - Lecture Notes in Mathematics, 1313 0075-8434 ; . - Lecture Notes in Mathematics, 1313 .
Optimization theory -- Retarded functional differential equations -- Strong local minima -- Weak local minima -- Local relaxed minima -- Tests for local properness -- A scenario for local properness -- Optimal periodic control of ordinary differential equations.
This research monograph deals with optimal periodic control problems for systems governed by ordinary and functional differential equations of retarded type. Particular attention is given to the problem of local properness, i.e. whether system performance can be improved by introducing periodic motions. Using either Ekeland's Variational Principle or optimization theory in Banach spaces, necessary optimality conditions are proved. In particular, complete proofs of second-order conditions are included and the result is used for various versions of the optimal periodic control problem. Furthermore a scenario for local properness (related to Hopf bifurcation) is drawn up, giving hints as to where to look for optimal periodic solutions. The book provides mathematically rigorous proofs for results which are potentially of importance in chemical engineering and aerospace engineering.
9783540391708
10.1007/BFb0077931 doi
Mathematics.
Systems theory.
Mathematical optimization.
Mathematics.
Systems Theory, Control.
Calculus of Variations and Optimal Control; Optimization.
Q295 QA402.3-402.37
519
Optimal Periodic Control [electronic resource] / by Fritz Colonius. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1988. - VI, 177 p. online resource. - Lecture Notes in Mathematics, 1313 0075-8434 ; . - Lecture Notes in Mathematics, 1313 .
Optimization theory -- Retarded functional differential equations -- Strong local minima -- Weak local minima -- Local relaxed minima -- Tests for local properness -- A scenario for local properness -- Optimal periodic control of ordinary differential equations.
This research monograph deals with optimal periodic control problems for systems governed by ordinary and functional differential equations of retarded type. Particular attention is given to the problem of local properness, i.e. whether system performance can be improved by introducing periodic motions. Using either Ekeland's Variational Principle or optimization theory in Banach spaces, necessary optimality conditions are proved. In particular, complete proofs of second-order conditions are included and the result is used for various versions of the optimal periodic control problem. Furthermore a scenario for local properness (related to Hopf bifurcation) is drawn up, giving hints as to where to look for optimal periodic solutions. The book provides mathematically rigorous proofs for results which are potentially of importance in chemical engineering and aerospace engineering.
9783540391708
10.1007/BFb0077931 doi
Mathematics.
Systems theory.
Mathematical optimization.
Mathematics.
Systems Theory, Control.
Calculus of Variations and Optimal Control; Optimization.
Q295 QA402.3-402.37
519