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## Status report #4 on nonlinear and adaptive control

Fonte: Massachusetts Institute of Technology, Laboratory for Information and Decision Systems
Publicador: Massachusetts Institute of Technology, Laboratory for Information and Decision Systems

Formato: 19 p.; 1863473 bytes; application/pdf

ENG

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prepared by Michael Athans, Gunter Stein, Lena Valavani ; submitted to NASA, Langley Research Center, Ames Research Center.; Includes bibliographical references.; Supported by NASA. NAG 2-297 MIT OSP no.95178

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## Status report #5 on nonlinear and adaptive control

Fonte: Massachusetts Institute of Technology, Laboratory for Information and Decision Systems
Publicador: Massachusetts Institute of Technology, Laboratory for Information and Decision Systems

Formato: 17 leaves; 1621968 bytes; application/pdf

ENG

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35.57%

prepared by Michael Athans, Gunter Stein, Lena Valavani ; submitted to NASA, Langley Research Center, Ames Research Center.; Includes bibliographical references.; Supported by a grant from NASA. NAG 2-297 MIT OSP no.95178

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## Visual Estimation and Control of Robot Manipulating Systems

Fonte: La Sapienza Universidade de Roma
Publicador: La Sapienza Universidade de Roma

Tipo: Tese de Doutorado

EN

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#Robotics#Visual Control#Settori Disciplinari MIUR::Ingegneria industriale e dell'informazione::AUTOMATICA

With this sentence from his Metaphysica, Aristotle perfectly introduces us to the
importance of eyesight for humans, as well as for any advanced living being. Since, to
a large extent, robotics is concerned with the emulation of human skills in an artificial
context, a natural requirement is to cope with vision for a full interaction with the world. In this
respect, this Thesis explores the problem of exploiting visual information to control the motion
of robotic systems equipped with onboard cameras. We build our proposals upon the Visual
Servoing paradigm, which bridges Computer Vision (image processing, scene interpretation,
feature extraction, etc.) with topics proper to the Control Theory field. Indeed, within Visual
Servoing, a camera is modeled as a nonlinear function of the scene, i.e., of 3D states subject to
rigid body kinematics. Therefore, visual pose control reduces to a problem of output regulation,
or task realization if we conform to the robotic nomenclature. Once this view is adopted, any
task realization algorithm can be used to fulfill a visual task, and, more in general, the problem
can be tackled with the tools of Control Theory.
In order to fully exploit this formulation, however, a suitable task-oriented modeling of robot
manipulators is required. Therefore...

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## Eventum Mechanics of Quantum Trajectories: Continual Measurements, Quantum Predictions and Feedback Control

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 23/02/2007

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Quantum mechanical systems exhibit an inherently probabilistic nature upon
measurement which excludes in principle the singular direct observability
continual case. Quantum theory of time continuous measurements and quantum
prediction theory, developed by the author on the basis of an
independent-increment model for quantum noise and nondemolition causality
principle in the 80's, solves this problem allowing continual quantum
predictions and reducing many quantum information problems like problems of
quantum feedback control to the classical stochastic ones. Using explicit
indirect observation models for diffusive and counting measurements we derive
quantum filtering (prediction) equations to describe the stochastic evolution
of the open quantum system under the continuous partial observation. Working in
parallel with classical indeterministic control theory, we show the Markov
Bellman equations for optimal feedback control of the a posteriori stochastic
quantum states conditioned upon these two kinds of measurements. The resulting
filtering and Bellman equation for the diffusive observation is then applied to
the explicitly solvable quantum linear-quadratic-Gaussian (LQG) problem which
emphasizes many similarities and differences with the corresponding classical
nonlinear filtering and control problems and demonstrates microduality between
quantum filtering and classical control.; Comment: 39 pages. Review paper

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## Pull-Based Distributed Event-triggered Consensus for Multi-agent Systems with Directed Topologies

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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#Mathematics - Optimization and Control#Computer Science - Systems and Control#Nonlinear Sciences - Adaptation and Self-Organizing Systems

This paper mainly investigates consensus problem with pull-based
event-triggered feedback control. For each agent, the diffusion coupling
feedbacks are based on the states of its in-neighbors at its latest triggering
time and the next triggering time of this agent is determined by its
in-neighbors' information as well. The general directed topologies, including
irreducible and reducible cases, are investigated. The scenario of distributed
continuous monitoring is considered firstly, namely each agent can observe its
in-neighbors' continuous states. It is proved that if the network topology has
a spanning tree, then the event-triggered coupling strategy can realize
consensus for the multi-agent system. Then the results are extended to
discontinuous monitoring, i.e., self-triggered control, where each agent
computes its next triggering time in advance without having to observe the
system's states continuously. The effectiveness of the theoretical results are
illustrated by a numerical example finally.; Comment: arXiv admin note: text overlap with arXiv:1407.1377

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## Approximate Consensus Multi-Agent Control Under Stochastic Environment with Application to Load Balancing

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 14/06/2013

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The paper is devoted to the approximate consensus problem for networks of
nonlinear agents with switching topology, noisy and delayed measurements. In
contrast to the existing stochastic approximation-based control algorithms
(protocols), a local voting protocol with nonvanishing step size is proposed.
Nonvanishing (e.g., constant) step size protocols give the opportunity to
achieve better convergence rate (by choosing proper step sizes) in coping with
time-varying loads and agent states. The price to pay is replacement of the
mean square convergence with an approximate one. To analyze dynamics of the
closed loop system, the so-called method of averaged models is used. It allows
to reduce analysis complexity of the closed loop system. In this paper the
upper bounds for mean square distance between the initial system and its
approximate averaged model are proposed. The proposed upper bounds are used to
obtain conditions for approximate consensus achievement.
The method is applied to the load balancing problem in stochastic dynamic
networks with incomplete information about the current states of agents and
with changing set of communication links. The load balancing problem is
formulated as consensus problem in noisy model with switched topology. The
conditions to achieve the optimal level of load balancing (in the sense that if
no new task arrives...

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## Distributed Event-triggered Consensus for Multi-agent Systems with Directed Topologies

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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In this paper, we study consensus problem in multi-agent system with directed
topology by event-triggered feedback control. That is, at each agent, the
diffusion coupling feedbacks are based on the information from its latest
observations to its in-neighbours. We derive distributed criteria to determine
the next observation time of each agent that are triggered by its
in-neighbours' information and its own states respectively. We prove that if
the network topology is irreducible, then under the event-triggered coupling
principles, the multi-agent system reach consensus. Then, we extend these
results to the case of reducible topology with spanning tree. In addition,
these results are also extended to the case of self-triggered control, in terms
that the next triggering time of each agent is computed based on the current
states, i.e., without observing the system's states continuously. The
effectiveness of the theoretical results are illustrated by numerical examples.

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## Pinning networks of coupled dynamical systems with Markovian switching couplings and event-triggered diffusions

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 02/02/2015

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In this paper, stability of linearly coupled dynamical systems with feedback
pinning algorithm is studied. Here, both the coupling matrix and the set of
pinned-nodes vary with time, induced by a continuous-time Markov chain with
finite states. Event-triggered rules are employed on both diffusion coupling
and feedback pinning terms, which can efficiently reduce the computation load,
as well as communication load in some cases and be realized by the latest
observations of the state information of its local neighborhood and the target
trajectory. The next observation is triggered by certain criterion (event)
based on these state information as well. Two scenarios are considered: the
continuous monitoring, that each node observes the state information of its
neighborhood and target (if pinned) in an instantaneous way, to determine the
next triggering event time, and the discrete monitoring, that each node needs
only to observe the state information at the last event time and predict the
next triggering-event time. In both cases, we present several event-triggering
rules and prove that if the conditions that the coupled system with persistent
coupling and control can be stabilized are satisfied, then these event-trigger
strategies can stabilize the system...

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## Morphogenesis by coupled regulatory networks: Reliable control of positional information and proportion regulation

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 25/08/2009

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#Quantitative Biology - Molecular Networks#Condensed Matter - Disordered Systems and Neural Networks#Nonlinear Sciences - Cellular Automata and Lattice Gases#Quantitative Biology - Cell Behavior#Quantitative Biology - Tissues and Organs

Based on a non-equilibrium mechanism for spatial pattern formation we study
how position information can be controlled by locally coupled discrete
dynamical networks, similar to gene regulation networks of cells in a
developing multicellular organism. As an example we study the developmental
problems of domain formation and proportion regulation in the presence of
noise, as well as in the presence of cell flow. We find that networks that
solve this task exhibit a hierarchical structure of information processing and
are of similar complexity as developmental circuits of living cells. Proportion
regulation is scalable with system size and leads to sharp, precisely localized
boundaries of gene expression domains, even for large numbers of cells. A
detailed analysis of noise-induced dynamics, using a mean-field approximation,
shows that noise in gene expression states stabilizes (rather than disrupts)
the spatial pattern in the presence of cell movements, both for stationary as
well as growing systems. Finally, we discuss how this mechanism could be
realized in the highly dynamic environment of growing tissues in multi-cellular
organisms.; Comment: Journal of Theoretical Biology, in press

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## Event-triggered Consensus for Multi-agent Systems with Asymmetric and Reducible Topologies

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 05/07/2014

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This paper studies the consensus problem of multi-agent systems with
asymmetric and reducible topologies. Centralized event-triggered rules are
provided so as to reduce the frequency of system's updating. The diffusion
coupling feedbacks of each agent are based on the latest observations from its
in-neighbors and the system's next observation time is triggered by a criterion
based on all agents' information. The scenario of continuous monitoring is
first considered, namely all agents' instantaneous states can be observed. It
is proved that if the network topology has a spanning tree, then the
centralized event-triggered coupling strategy can realize consensus for the
multi-agent system. Then the results are extended to discontinuous monitoring,
where the system computes its next triggering time in advance without having to
observe all agents' states continuously. Examples with numerical simulation are
provided to show the effectiveness of the theoretical results.

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## Distributed Estimation with Information-Seeking Control in Agent Network

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We introduce a distributed, cooperative framework and method for Bayesian
estimation and control in decentralized agent networks. Our framework combines
joint estimation of time-varying global and local states with
information-seeking control optimizing the behavior of the agents. It is suited
to nonlinear and non-Gaussian problems and, in particular, to location-aware
networks. For cooperative estimation, a combination of belief propagation
message passing and consensus is used. For cooperative control, the negative
posterior joint entropy of all states is maximized via a gradient ascent. The
estimation layer provides the control layer with probabilistic information in
the form of sample representations of probability distributions. Simulation
results demonstrate intelligent behavior of the agents and excellent estimation
performance for a simultaneous self-localization and target tracking problem.
In a cooperative localization scenario with only one anchor, mobile agents can
localize themselves after a short time with an accuracy that is higher than the
accuracy of the performed distance measurements.; Comment: 17 pages, 10 figures

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## Controlling Chimeras

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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35.73%

#Nonlinear Sciences - Adaptation and Self-Organizing Systems#Mathematics - Dynamical Systems#Nonlinear Sciences - Pattern Formation and Solitons

Coupled phase oscillators model a variety of dynamical phenomena in nature
and technological applications. Non-local coupling gives rise to chimera states
which are characterized by a distinct part of phase-synchronized oscillators
while the remaining ones move incoherently. Here, we apply the idea of control
to chimera states: using gradient dynamics to exploit drift of a chimera, it
will attain any desired target position. Through control, chimera states become
functionally relevant; for example, the controlled position of localized
synchrony may encode information and perform computations. Since functional
aspects are crucial in (neuro-)biology and technology, the localized
synchronization of a chimera state becomes accessible to develop novel
applications. Based on gradient dynamics, our control strategy applies to any
suitable observable and can be generalized to arbitrary dimensions. Thus, the
applicability of chimera control goes beyond chimera states in non-locally
coupled systems.

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## The impulse cutoff an entropy functional measure on trajectories of Markov diffusion process integrating in information path functional

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

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#Nonlinear Sciences - Adaptation and Self-Organizing Systems#Computer Science - Information Theory#Mathematics - Optimization and Control#Mathematics - Probability#58J65, 60J65, 93B52, 93E02, 93E15, 93E30#H.1.1

Integrating discrete information extracted from random process solves the
impulse cutoff entropy functional (EF) measure on trajectories Markov diffusion
process, integrated in information path functional (IPF). Process additive
functional defines EF reducing it to a regular integral functional. Compared to
Shannon entropy measure of random state, cutting process on separated states
decreases quantity information concealed in the states correlation holding
hidden process information. Infinite dimensional process cutoffs integrate
finite information in IPF whose information approaches EF restricting maximal
information of the Markov process. Delta impulse and discrete impulse deliver
equivalent information at each cutoff. Constructed finite restriction limits
impulses discrete actions cutting the regular integral on EF increments between
the cutoffs. Finite impulse step-up action transfers EF increment to following
impulse whose step-down action cuts off information and step-up action starts
imaginary-virtual impulse carrying entropy increment to next real cut.
Step-down cut generates maximal information while step-up action delivers
minimal information from impulse cut to next impulse step-down action. Virtual
impulse transfers conjugated entropy increments during microprocess ending with
adjoining increment within actual step-down action at cutoff. Extracting
maximum of minimal impulse information and transferring minimal entropy between
impulses implement maxmin-minimax principle of converting process entropy to
information. Macroprocess extremal integrates imaginary entropy of microprocess
and cutoff information of real impulses in IPF information physical process. EF
cut measures Feller kernel information. Estimation extracting information
confirms nonadditivity of EF measured process fractions.; Comment: 44 pages

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## Unstable Price Dynamics as a Result of Information Absorption in Speculative Markets

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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#Quantitative Finance - Trading and Market Microstructure#Nonlinear Sciences - Adaptation and Self-Organizing Systems#Physics - Physics and Society

In speculative markets, risk-free profit opportunities are eliminated by
traders exploiting them. Markets are therefore often described as
"informationally efficient", rapidly removing predictable price changes, and
leaving only residual unpredictable fluctuations. This classical view of
markets absorbing information and otherwise operating close to an equilibrium
is challenged by extreme price fluctuations, in particular since they occur far
more frequently than can be accounted for by external news. Here we show that
speculative markets which absorb mainly self-generated information can exhibit
both: evolution towards efficient equilibrium states as well as their
subsequent destabilization. This peculiar dynamics, a generic instability
arising from an adaptive control which annihilates predictable information, is
realized in a minimal agent-based market model where the impacts of agents'
strategies adapt according to their trading success. This adaptation implements
a learning rule for the market as a whole minimizing predictable price changes.
The model reproduces stylized statistical properties of price changes in
quantitative detail, including heavy tailed log return distributions and
volatility clusters. Our results demonstrate that the perpetual occurrence of
market instabilities can be a direct consequence of the very mechanisms that
lead to market efficiency.; Comment: Paper and supplement are combined in a single file. Changes in this
Version: Added an introductory paragraph. Expanded discussion on the
differences between the presented model and minority games. Added two
supplementary figures

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## The information path functional approach for solution of a controllable stochastic problem

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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#Computer Science - Systems and Control#Computer Science - Information Theory#Mathematics - Dynamical Systems#Nonlinear Sciences - Adaptation and Self-Organizing Systems#93B52, 93E03, 93E15, 93E30#H.1.1

We study a stochastic control system, described by Ito controllable equation,
and evaluate the solutions by an entropy functional (EF), defined by the
equation functions of controllable drift and diffusion. Considering a control
problem for this functional, we solve the EF control variation problem (VP),
which leads to both a dynamic approximation of the process entropy functional
by an information path functional (IPF) and information dynamic model (IDM) of
the stochastic process. The IPF variation equations allow finding the optimal
control functions, applied to both stochastic system and the IDM for joint
solution of the identification and optimal control problems, combined with
state consolidation. In this optimal dual strategy, the IPF optimum predicts
each current control action not only in terms of total functional path goal,
but also by setting for each following control action the renovated values of
this functional controllable drift and diffusion, identified during the optimal
movement, which concurrently correct this goal. The VP information invariants
allow optimal encoding of the identified dynamic model operator and control.
The introduced method of cutting off the process by applying an impulse control
estimates the cutoff information...

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## Novel coupling scheme to control dynamics of coupled discrete systems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

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We present a new coupling scheme to control spatio-temporal patterns and
chimeras on 1-d and 2-d lattices and random networks of discrete dynamical
systems. The scheme involves coupling with an external lattice or network of
damped systems. When the system network and external network are set in a
feedback loop, the system network can be controlled to a homogeneous steady
state or synchronized periodic state with suppression of the chaotic dynamics
of the individual units. The control scheme has the advantage that its design
does not require any prior information about the system dynamics or its
parameters and works effectively for a range of parameters of the control
network. We analyze the stability of the controlled steady state or amplitude
death state of lattices using the theory of circulant matrices and
Routh-Hurwitz's criterion for discrete systems and this helps to isolate
regions of effective control in the relevant parameter planes. The conditions
thus obtained are found to agree well with those obtained from direct numerical
simulations in the specific context of lattices with logistic map and Henon map
as on-site system dynamics. We show how chimera states developed in an
experimentally realizable 2-d lattice can be controlled using this scheme. We
propose this mechanism can provide a phenomenological model for the control of
spatio-temporal patterns in coupled neurons due to non-synaptic coupling with
the extra cellular medium. We extend the control scheme to regulate dynamics on
random networks and adapt the master stability function method to analyze the
stability of the controlled state for various topologies and coupling
strengths.; Comment: 22 pages...

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## Reduced-Complexity Nonlinear *H* ∞ Control of Discrete-Time Systems

Fonte: Institute of Electrical and Electronics Engineers (IEEE Inc)
Publicador: Institute of Electrical and Electronics Engineers (IEEE Inc)

Tipo: Artigo de Revista Científica

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#Keywords: Computational complexity#Control system synthesis#Discrete time control systems#Feedback control#Nonlinear control systems#Observability#State estimation#State feedback#Infinite-dimensional dynamical systems#Information states#Nonlinear estimati Infinite-dimensional dynamical systems

In this note, we describe a reduced-complexity solution to the nonlinear H∞ control problem. This reduction applies to systems where some of the states are perfectly known, and is an intermediate problem between full state feedback and the standard meas

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## Gap metrics, representations, and nonlinear robust stability

Fonte: SIAM Publications
Publicador: SIAM Publications

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

45.8%

#Keywords: Feedback#Graph theory#Hydrogen#Mathematical operators#Nonlinear systems#Optimization#Problem solving#System stability#Controller synthesis#Gap metric#Graph representations

Various alternative definitions for the nonlinear H2-, L 2-, and v-gap metrics are studied. The concept of β-conjugacy and multiplicative homogeneity are introduced to relate the metrics to each other and to compare the stability margins of nonlinear fee

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## Nonlinear H-∞ Control: Practicality of Implementing the Cheap Sensor Case

Fonte: Institute of Electrical and Electronics Engineers (IEEE Inc)
Publicador: Institute of Electrical and Electronics Engineers (IEEE Inc)

Tipo: Conference paper

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#Keywords: Closed loop control systems#Computational complexity#Control equipment#State feedback#Theorem proving#Information states#Nonlinear control systems Information states#Nonlinear H8 control#Reduced order observers#Reduction of computational complexity

In [5] we introduced a recipe for nonlinear H∞ controllers which takes advantage of extra perfect measurements and stated a theorem to the effect that this controller yielded the best possible "H∞" performance. Pure state feedback is an extreme situat

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## l ∞ -Bounded Robustness for Nonlinear Systems: Analysis and Synthesis

Fonte: Institute of Electrical and Electronics Engineers (IEEE Inc)
Publicador: Institute of Electrical and Electronics Engineers (IEEE Inc)

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

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#Keywords: Approximation theory#Closed loop control systems#Control equipment#Dynamic programming#Nonlinear control systems#Optimal control systems#Spurious signal noise#Dissipative systems#Robustness (control systems) Controller synthesis#Dissipative systems#Dynamic programming

The purpose of this paper is to describe systematic analysis and design tools for robust control problems with l∞ criteria. We first generalize the Hill-Moylan-Willems framework for dissipative systems to accommodate l∞ criteria, and then derive state

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