Authors:
B. Ross Barmish,
Pavel S. Shcherbakov,
Volume: 1, Page 1031 Paper number 1967
Abstract:
For a large class of robustness problems with uncertain parameter vector
q confined to a box Q, there are many papers providing results along
the following lines: The desired performance specification is robustly
specified for all q in Q if and only if it is satisfied at each vertex
q_i of Q. Since the number of vertices of G explodes combinatorically
with the dimension of q, the computation associated with the implementation
of such results is often intractable. The main point of this paper
is to introduce a new approach to such problems. To this end, the definition
of approximate feasibility is introduced, and the theory which follows
from this definition is vertex-free.
Authors:
Boris T. Polyak,
R. Tempo,
Volume: 1, Page 1037 Paper number 1212
Abstract:
In this paper, we study robust design of uncertain systems in a probabilistic
setting by means of Linear Quadratic Regulators. We consider systems
affected by random bounded nonlinear uncertainty so that classical
optimization methods based on Linear Matrix Inequalities cannot be
used without conservatism. The approach followed here is a blend of
randomization techniques for the uncertainty together with convex optimization
for the controller parameters. In particular, we propose an iterative
algorithm for designing a controller which is based upon subgradient
iterations. At each step of the sequence, we first generate a random
sample and then we make a subgradient step for a convex constraint
defined by the LQR problem. The main result of the paper is to prove
that this iterative algorithm provides a controller which quadratically
stabilizes the uncertain system with probability one in a finite number
of steps. In addition, at a fixed step, we compute a lower bound of
the probability that a quadratically stabilizing controller is found.
Authors:
J. William Helton,
Marshall A. Whittlesey,
Volume: 1, Page 1043 Paper number 1720
Abstract:
Optimization of sup norm type performance functions over the space
of H-infinity functions is central to the subject of H-infinity design.
Problems with a large amount of plant uncertainty are often highly
non-convex and therefore may have many solutions. In this article,
even for highly non-convex problems, we give a test one can perform,
once a local optimum f has been computed, to see if it is a global
optimum. The uniqueness phenomena we discovered uses H-infinity properties
(stability properties) heavily and are considerably stronger than what
occurs in other types of general optimization. One of the least
intuitive properties of SISO control is that a (local) optimum for
a carefully set up H-infinity problem even with large amounts of plant
uncertainty is unique. Such problems can be quite non -convex so the
fact is surprising. While the result is false in general for MIMO
control, in this note we are describing MIMO situations where uniqueness
holds. The setting in this paper is simultaneous (Pareto) optimization
of several competing performances and we obtain uniqueness results
for its solutions.
Authors:
Satoru Tanaka,
Katsuhisa Furuta,
Volume: 1, Page 1049 Paper number 9906
Abstract:
This paper is concerned with a mixed H-infinity/deadbeat suboptimal
control problem for SISO continuous servo systems. By considering the
deadbeat tracking, time domain performance may improve. Simultaneously,
to improve frequency domain performance of the closed loop system,
H-infinity norm constraint is introduced. This problem gives the deadbeat
tracking control with H-infinity norm constraint and has been studied
by Nobuyama et al. and Tsumura et al. individually. However, there
is a structural difference between their designs. This paper proposes
a new controller design of the mixed H-infinity/deadbeat suboptimal
control problem. The controller is more general since the structure
of the controller covers those of the previous two designs.
Authors:
Thordur Runolfsson,
Volume: 1, Page 1055 Paper number 1912
Abstract:
In this paper we study systems that are subject to sudden structural
changes due to either changes in the operational mode of the system
or due to failure. We consider linear dynamical that depend on a modal
variable which is either modeled as a finite state Markov chain or
generated by an automaton that is subject to an external disturbance.
In the Markov chain case the objective of the control is to minimize
a risk sensitive cost functional. The risk sensitive cost functional
measures the risk sensitivity of the system to transitions caused by
the random modal variable. In the case when a disturbed automaton describes
the modal variable, the objective of the control is to make the system
as robust to changes in the external disturbance as possible. Optimality
conditions for both problems are derived and it is shown that the disturbance
rejection problem is closely related to a certain risk sensitive control
problem for the hybrid system.
Authors:
Giuseppe Franzé,
Pietro Maria Muraca,
Volume: 1, Page 1061 Paper number 1084
Abstract:
This paper presents a method for determining the maximum allowable
perturbation, for m.i.m.o. linear-invariant uncertain system, such
that the closed-loop poles are assigned in a specifie disk by static
output feedback; the uncertainty being norm-2 bounded. A sufficient
condition for d-stabilizability is derived. Hence, in order to solve
the related optimization problem a genetic-like algorithm is performed.
An illustrative example shows the effectiveness of the proposed procedure.
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