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Hsub2 Optimal Control with H-Infinity, mu, and Lsub1 Constraints
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING
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H2 optimization with convex constraints is considered. The optimal order-free solution is shown to be unique through convex analysis. H-inf constraints with feedforward terms and singular constraints are also allowed. The optimal fixed-order solution is shown to have the same characteristics as a mixed problem with regular H-inf constraints. Furthermore, these results are shown to hold for controller orders as low as the optimal H2 order. A numerical method is developed based on analytical gradients which results in sub- and super-optimal fixed-order controllers. The problem is extended to include an upper bound on a mu constraint through a modification of the D-K iteration method. Next. multiple H-inf constraints are developed. Fixed-order solutions to the multiple constraint problem are characterized and the numerical method is extended to include multiple constraints. Next, a continuous Ll constraint is added. A numerical approach is proposed based on bounding the Ll-norm by the 11- norm of an Euler approximating system. Finally. H2 optimization with a finite set of H-inf, mu, and Ll constraints is characterized. SISO and MIMO numerical examples demonstrate the application of these methods. Control theory, Mathematical programming, Riccati equation, H2 Optimization, H-inf Optimization, Mu-Synthesis, Ll Optimization, Multiobjective optimal control.
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