394 research outputs found
A passivity-based stability criterion for a class of interconnected systems and applications to biochemical reaction networks
This paper presents a stability test for a class of interconnected nonlinear
systems motivated by biochemical reaction networks. One of the main results
determines global asymptotic stability of the network from the diagonal
stability of a "dissipativity matrix" which incorporates information about the
passivity properties of the subsystems, the interconnection structure of the
network, and the signs of the interconnection terms. This stability test
encompasses the "secant criterion" for cyclic networks presented in our
previous paper, and extends it to a general interconnection structure
represented by a graph. A second main result allows one to accommodate state
products. This extension makes the new stability criterion applicable to a
broader class of models, even in the case of cyclic systems. The new stability
test is illustrated on a mitogen activated protein kinase (MAPK) cascade model,
and on a branched interconnection structure motivated by metabolic networks.
Finally, another result addresses the robustness of stability in the presence
of diffusion terms in a compartmental system made out of identical systems.Comment: See http://www.math.rutgers.edu/~sontag/PUBDIR/index.html for related
(p)reprint
Design of Optimal Sparse Feedback Gains via the Alternating Direction Method of Multipliers
We design sparse and block sparse feedback gains that minimize the variance
amplification (i.e., the norm) of distributed systems. Our approach
consists of two steps. First, we identify sparsity patterns of feedback gains
by incorporating sparsity-promoting penalty functions into the optimal control
problem, where the added terms penalize the number of communication links in
the distributed controller. Second, we optimize feedback gains subject to
structural constraints determined by the identified sparsity patterns. In the
first step, the sparsity structure of feedback gains is identified using the
alternating direction method of multipliers, which is a powerful algorithm
well-suited to large optimization problems. This method alternates between
promoting the sparsity of the controller and optimizing the closed-loop
performance, which allows us to exploit the structure of the corresponding
objective functions. In particular, we take advantage of the separability of
the sparsity-promoting penalty functions to decompose the minimization problem
into sub-problems that can be solved analytically. Several examples are
provided to illustrate the effectiveness of the developed approach.Comment: To appear in IEEE Trans. Automat. Contro
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