1,023 research outputs found
Robust â„‹2 Performance: Guaranteeing Margins for LQG Regulators
This paper shows that ℋ2 (LQG) performance specifications can be combined with structured uncertainty in the system, yielding robustness analysis conditions of the same nature and computational complexity as the corresponding conditions for ℋ∞ performance. These conditions are convex feasibility tests in terms of Linear Matrix Inequalities, and can be proven to be necessary and sufficient under the same conditions as in the ℋ∞ case.
With these results, the tools of robust control can be viewed as coming full circle to treat the problem where it all began: guaranteeing margins for LQG regulators
Galerkin approximations for the optimal control of nonlinear delay differential equations
Optimal control problems of nonlinear delay differential equations (DDEs) are
considered for which we propose a general Galerkin approximation scheme built
from Koornwinder polynomials. Error estimates for the resulting
Galerkin-Koornwinder approximations to the optimal control and the value
function, are derived for a broad class of cost functionals and nonlinear DDEs.
The approach is illustrated on a delayed logistic equation set not far away
from its Hopf bifurcation point in the parameter space. In this case, we show
that low-dimensional controls for a standard quadratic cost functional can be
efficiently computed from Galerkin-Koornwinder approximations to reduce at a
nearly optimal cost the oscillation amplitude displayed by the DDE's solution.
Optimal controls computed from the Pontryagin's maximum principle (PMP) and the
Hamilton-Jacobi-Bellman equation (HJB) associated with the corresponding ODE
systems, are shown to provide numerical solutions in good agreement. It is
finally argued that the value function computed from the corresponding reduced
HJB equation provides a good approximation of that obtained from the full HJB
equation.Comment: 29 pages. This is a sequel of the arXiv preprint arXiv:1704.0042
Mean-Field Optimal Control
We introduce the concept of {\it mean-field optimal control} which is the
rigorous limit process connecting finite dimensional optimal control problems
with ODE constraints modeling multi-agent interactions to an infinite
dimensional optimal control problem with a constraint given by a PDE of
Vlasov-type, governing the dynamics of the probability distribution of
interacting agents. While in the classical mean-field theory one studies the
behavior of a large number of small individuals {\it freely interacting} with
each other, by simplifying the effect of all the other individuals on any given
individual by a single averaged effect, we address the situation where the
individuals are actually influenced also by an external {\it policy maker}, and
we propagate its effect for the number of individuals going to infinity. On
the one hand, from a modeling point of view, we take into account also that the
policy maker is constrained to act according to optimal strategies promoting
its most parsimonious interaction with the group of individuals. This will be
realized by considering cost functionals including -norm terms penalizing
a broadly distributed control of the group, while promoting its sparsity. On
the other hand, from the analysis point of view, and for the sake of
generality, we consider broader classes of convex control penalizations. In
order to develop this new concept of limit rigorously, we need to carefully
combine the classical concept of mean-field limit, connecting the finite
dimensional system of ODE describing the dynamics of each individual of the
group to the PDE describing the dynamics of the respective probability
distribution, with the well-known concept of -convergence to show that
optimal strategies for the finite dimensional problems converge to optimal
strategies of the infinite dimensional problem.Comment: 31 page
Sparse and switching infinite horizon optimal controls with mixed-norm penalizations
© 2020 EDP Sciences, SMAI. A class of infinite horizon optimal control problems involving mixed quasi-norms of Lp-type cost functionals for the controls is discussed. These functionals enhance sparsity and switching properties of the optimal controls. The existence of optimal controls and their structural properties are analyzed on the basis of first order optimality conditions. A dynamic programming approach is used for numerical realization
The economic basis of periodic enzyme dynamics
Periodic enzyme activities can improve the metabolic performance of cells. As
an adaptation to periodic environments or by driving metabolic cycles that can
shift fluxes and rearrange metabolic processes in time to increase their
efficiency. To study what benefits can ensue from rhythmic gene expression or
posttranslational modification of enzymes, I propose a theory of optimal enzyme
rhythms in periodic or static environments. The theory is based on kinetic
metabolic models with predefined metabolic objectives, scores the effects of
harmonic enzyme oscillations, and determines amplitudes and phase shifts that
maximise cell fitness. In an expansion around optimal steady states, the
optimal enzyme profiles can be computed by solving a quadratic optimality
problem. The formulae show how enzymes can increase their efficiency by
oscillating in phase with their substrates and how cells can benefit from
adapting to external rhythms and from spontaneous, intrinsic enzyme rhythms.
Both types of behaviour may occur different parameter regions of the same
model. Optimal enzyme profiles are not passively adapted to existing substrate
rhythms, but shape them actively to create opportunities for further fitness
advantage: in doing so, they reflect the dynamic effects that enzymes can exert
in the network. The proposed theory combines the dynamics and economics of
metabolic systems and shows how optimal enzyme profiles are shaped by network
structure, dynamics, external rhythms, and metabolic objectives. It covers
static enzyme adaptation as a special case, reveals the conditions for
beneficial metabolic cycles, and predicts optimally combinations of gene
expression and posttranslational modification for creating enzyme rhythms
Robust Hâ‚‚analysis for continuous time systems
Caption title.Includes bibliographical references (p. 35-37).Supported by ARO. DAALO3-92-G-0115 Supported by a grant from Siemens AG and Draper Lab. DL-H-48452Fernando Paganini
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