168 research outputs found
H∞ Tracking Control for a Class of Nonlinear Systems
Develops the theory for tracking control using the nonlinear H∞ control design methodology for a class of nonlinear input affine systems. The authors use a two-step process of first designing the feedforward part of the controller to design for perfect trajectory following and then design the feedback part of the controller using nonlinear H∞ regulator theory. Results for infinite-time and finite-time horizons are presente
On the order of singular optimal control problems
In singular optimal control problems, the functional form of the optimal control function is usually determined by solving the algebraic equation which results by successively differentiating the switching function until the control appears explicitly. This process defines the order of the singular problem. Order-related results are developed for singular linear-quadratic problems and for a bilinear example which gives new insights into the relationship between singular problem order and singular are order.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45218/1/10957_2004_Article_BF00934035.pd
Geometric Approach to Pontryagin's Maximum Principle
Since the second half of the 20th century, Pontryagin's Maximum Principle has
been widely discussed and used as a method to solve optimal control problems in
medicine, robotics, finance, engineering, astronomy. Here, we focus on the
proof and on the understanding of this Principle, using as much geometric ideas
and geometric tools as possible. This approach provides a better and clearer
understanding of the Principle and, in particular, of the role of the abnormal
extremals. These extremals are interesting because they do not depend on the
cost function, but only on the control system. Moreover, they were discarded as
solutions until the nineties, when examples of strict abnormal optimal curves
were found. In order to give a detailed exposition of the proof, the paper is
mostly self\textendash{}contained, which forces us to consider different areas
in mathematics such as algebra, analysis, geometry.Comment: Final version. Minors changes have been made. 56 page
Controllability on infinite-dimensional manifolds
Following the unified approach of A. Kriegl and P.W. Michor (1997) for a
treatment of global analysis on a class of locally convex spaces known as
convenient, we give a generalization of Rashevsky-Chow's theorem for control
systems in regular connected manifolds modelled on convenient
(infinite-dimensional) locally convex spaces which are not necessarily
normable.Comment: 19 pages, 1 figur
Second-order necessary conditions in optimal control: Accessory-problem results without normality conditions
An optimal control problem, which includes restrictions on the controls and equality/inequality constraints on the terminal states, is formulated. Second-order necessary conditions of the accessory-problem type are obtained in the absence of normality conditions. It is shown that the necessary conditions generalize and simplify prior results due to Hestenes (Ref. 5) and Warga (Refs. 6 and 7).Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45219/1/10957_2004_Article_BF00934437.pd
- …