Authors:
Héctor J. Sussmann,
Volume: 1, Page 558 Paper number 3301
Abstract:
We present a general axiomatic definition of the concept of a "generalized
differentiation theory" (GDT) and state a version of the hybrid finite-dimensional
Pontryagin Maximum Principle for arbitrary GDTs that have a directional
open mapping property. We illustrate the notion of GDT by means of
two recent examples: the generalized differential quotients and the
path-integral generalized differentials.
Authors:
Zvi Artstein,
Volume: 1, Page 564 Paper number 3302
Abstract:
The paper examines the structure of the variational limits that may
arise in connection with singularly perturbed optimal control problems.
Once the notion of a variational limit is displayed, we analyze the
roles of the fast and slow components of the singularly perturbed system
in the generation of the variational limits. Comparing a general form
of variational limits for singularly perturbed systems to the method
of order reduction, which is largely used --- yet a special case, is
a goal of the paper.
Authors:
Carmeliza L. Navasca,
Arthur J. Krener,
Volume: 1, Page 570 Paper number 3303
Abstract:
We present a new method for the numerical solution of the Hamilton
Jacobi Bellman PDE that arises in an infinite time optimal control
problem. The method can be of higher order to reduce "the curse of
dimensionality". It proceeds in two stages. First the HJB PDE is
solved in a neighborhood of the origin using the power series method
of Al'brecht. From a boundary point of this neighborhood, an extremal
trajectory is computed backward in time using the Pontryagin Maximum
Principle. Then ordinary differential equations are developed for
the higher partial derivatives of the solution along the extremal.
These are solved yielding a power series for the approximate solution
in a neighborhood of the extremal. This is repeated for other extremals
and these approximate solutions are fitted together by transferring
them to a rectangular grid using splines.
Authors:
Ugo Boscain,
Benedetto Piccoli,
Volume: 1, Page 575 Paper number 3304
Abstract:
For a generic single input planar control system we analyze the properties
of abnormal extremals for the minimum time stabilization to the origin.
We prove that abnormal extremals are finite concatenations of bang
arcs and we we study the switching strategy. Moreover, all the singularities
of one parametric families of extremal trajectories near to abnormal
extremals are studied. In particular we prove that all possible sequences
of these singularities can be classified by a set of words recognizable
by an automaton. This permits to prove that all the singularities of
the projection of the extremal locus to the plane, studied in a previous
paper, are in fact realized.
Authors:
Andrea Balluchi,
Antonio Bicchi,
Benedetto Piccoli,
Philippe Soueres,
Volume: 1, Page 581 Paper number 3305
Abstract:
In this paper we consider the properties of stability and robustness
of an optimal control synthesis obtained for the problem of route tracking
by a kinematic vehicle moving forward only with a lower bounded turning
radius. This model, sometimes referred to as ``Dubins' vehicle'', is
relevant to the kinematics of road vehicles as well as aircraft cruising
at constant altitude, or sea vessels.
Authors:
Magnus Egerstedt,
Petter Ögren,
Omid Shakernia,
John Lygeros,
Volume: 1, Page 587 Paper number 3306
Abstract:
We investigate the problem of driving the state of a switched linear
control system between boundary states. We propose tight lower bounds
for the minimum energy control problem. Furthermore, we show that
the fact that the system dynamics change discontinuously on the switching
surface gives rise to phenomena that can be treated as a decidability
problem for hybrid control systems. Applying recent results on controller
synthesis for hybrid systems with linear continuous dynamics, we show
that the problem of computing the minimum number of switchings of a
trajectory between two boundary points is semi-decidable.
Authors:
Weihua Xu,
Jun Wu,
Jian Chu,
Volume: 1, Page 593 Paper number 8002
Abstract:
A l-inf control problem is formulated for digital finite-word-length
(FWL) controllers with synchronous sampling and fixed-point arithmetic.
The l-inf FWL controllers design problem is reduced to the problem
of solving a Quadratic Matrix Inequality (QMI) such that the closed-loop
system is asymptotically stable. The approach can be generalized to
deal with other problems such as H-inf ,H-2 and LQR FWL control problem.
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