222 research outputs found
Dissipative Stabilization of Linear Systems with Time-Varying General Distributed Delays (Complete Version)
New methods are developed for the stabilization of a linear system with
general time-varying distributed delays existing at the system's states, inputs
and outputs. In contrast to most existing literature where the function of
time-varying delay is continuous and bounded, we assume it to be bounded and
measurable. Furthermore, the distributed delay kernels can be any
square-integrable function over a bounded interval, where the kernels are
handled directly by using a decomposition scenario without using
approximations. By constructing a Krasovski\u{i} functional via the application
of a novel integral inequality, sufficient conditions for the existence of a
dissipative state feedback controller are derived in terms of matrix
inequalities without utilizing the existing reciprocally convex combination
lemmas. The proposed synthesis (stability) conditions, which take dissipativity
into account, can be either solved directly by a standard numerical solver of
semidefinite programming if they are convex, or reshaped into linear matrix
inequalities, or solved via a proposed iterative algorithm. To the best of our
knowledge, no existing methods can handle the synthesis problem investigated in
this paper. Finally, numerical examples are presented to demonstrate the
effectiveness of the proposed methodologies.Comment: Accepted by Automatic
Quantum Feedback Networks and Control: A Brief Survey
The purpose of this paper is to provide a brief review of some recent
developments in quantum feedback networks and control. A quantum feedback
network (QFN) is an interconnected system consisting of open quantum systems
linked by free fields and/or direct physical couplings. Basic network
constructs, including series connections as well as feedback loops, are
discussed. The quantum feedback network theory provides a natural framework for
analysis and design. Basic properties such as dissipation, stability, passivity
and gain of open quantum systems are discussed. Control system design is also
discussed, primarily in the context of open linear quantum stochastic systems.
The issue of physical realizability is discussed, and explicit criteria for
stability, positive real lemma, and bounded real lemma are presented. Finally
for linear quantum systems, coherent and LQG control are described.Comment: 29 pages, 11 figures. A new reference has been adde
From Small-Gain Theory to Compositional Construction of Barrier Certificates for Large-Scale Stochastic Systems
This paper is concerned with a compositional approach for the construction of
control barrier certificates for large-scale interconnected stochastic systems
while synthesizing hybrid controllers against high-level logic properties. Our
proposed methodology involves decomposition of interconnected systems into
smaller subsystems and leverages the notion of control sub-barrier certificates
of subsystems, enabling one to construct control barrier certificates of
interconnected systems by employing some -type small-gain conditions. The
main goal is to synthesize hybrid controllers enforcing complex logic
properties including the ones represented by the accepting language of
deterministic finite automata (DFA), while providing probabilistic guarantees
on the satisfaction of given specifications in bounded-time horizons. To do so,
we propose a systematic approach to first decompose high-level specifications
into simple reachability tasks by utilizing automata corresponding to the
complement of specifications. We then construct control sub-barrier
certificates and synthesize local controllers for those simpler tasks and
combine them to obtain a hybrid controller that ensures satisfaction of the
complex specification with some lower-bound on the probability of satisfaction.
To compute control sub-barrier certificates and corresponding local
controllers, we provide two systematic approaches based on sum-of-squares (SOS)
optimization program and counter-example guided inductive synthesis (CEGIS)
framework. We finally apply our proposed techniques to two physical case
studies
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