Multiple objective H(infinity) control
Abstract
Most control problems of practical interest have several performance and robustness requirements. A large class of these requirements can be stated in terms of closed loop frequency responses. This reduces the control problem to that of finding a controller such that the ${\cal H}\sb\infty$ norms of several closed loop transfer matrices are below specified levels. The first part of this thesis is concerned with the approximate solution of control problems with multiple ${\cal H}\sb\infty$ norm constraints. It is shown that approximate solutions can be obtained by solving optimization problems that are finite dimensional and convex; hence efficient numerical methods are available to compute approximate solutions. Moreover, only standard ${\cal H}\sb\infty$ computations are needed to solve these optimization problems. Under certain assumptions, we also reduce the convex optimization problems to linear matrix inequality problems. Two numerical examples are provided to illustrate the effectiveness of the design techniques developed. The second part of the thesis deals with the existence and computation of exact solutions of multiple objective ${\cal H}\sb\infty$ problems. We show a class of plants for which exact solutions can be computed using a linear matrix inequality program. A related control problem for discrete time systems involving time domain constraints is also considered.
Degree
Ph.D.
Advisors
Rotea, Purdue University.
Subject Area
Aerospace materials|Electrical engineering
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