9,469 research outputs found
Attenuation of Persistent L∞-Bounded Disturbances for Nonlinear Systems
A version of nonlinear generalization of the L1-control problem, which deals with the attenuation of persistent bounded disturbances in L∞-sense, is investigated in this paper. The methods used in this paper are motivated by [23]. The main idea in the L1-performance analysis and synthesis is to construct a certain invariant subset of the state-space such that achieving disturbance rejection is equivalent to restricting the state-dynamics to this set. The concepts from viability theory, nonsmooth analysis, and set-valued analysis play important roles. In addition, the relation between the L1-control of a continuous-time system and the l1-control of its Euler approximated discrete-time systems is established
Saturated locally optimal designs under differentiable optimality criteria
We develop general theory for finding locally optimal designs in a class of
single-covariate models under any differentiable optimality criterion. Yang and
Stufken [Ann. Statist. 40 (2012) 1665-1681] and Dette and Schorning [Ann.
Statist. 41 (2013) 1260-1267] gave complete class results for optimal designs
under such models. Based on their results, saturated optimal designs exist;
however, how to find such designs has not been addressed. We develop tools to
find saturated optimal designs, and also prove their uniqueness under mild
conditions.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1263 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
H∞ Control of Nonlinear Systems: A Class of Controllers
The standard state space solutions to the H∞ control problem for linear time invariant systems are generalized to nonlinear time-invariant systems. A class of nonlinear H∞-controllers are parameterized as nonlinear fractional transformations on contractive, stable free nonlinear parameters. As in the linear case, the H∞ control problem is solved by its reduction to four simpler special state space problems, together with a separation argument. Another byproduct of this approach is that the sufficient conditions for H∞ control problem to be solved are also derived with this machinery. The solvability for nonlinear H∞-control problem requires positive definite solutions to two parallel decoupled Hamilton-Jacobi inequalities and these two solutions satisfy an additional coupling condition. An illustrative example, which deals with a passive plant, is given at the end
ℋ∞ control of nonlinear systems via output feedback: controller parameterization
The standard state space solutions to the ℋ∞ control problem for linear time invariant systems are generalized to nonlinear time-invariant systems. A class of local nonlinear (output feedback) ℋ∞ controllers are parameterized as nonlinear fractional transformations on contractive, stable nonlinear parameters. As in the linear case, the ℋ∞ control problem is solved by its reduction to state feedback and output estimation problems, together with a separation argument. Sufficient conditions for ℋ∞-control problem to be locally solved are also derived with this machinery
H∞ control of nonlinear systems: a convex characterization
The nonlinear H∞-control problem is considered with an emphasis on developing machinery with promising computational properties. The solutions to H∞-control problems for a class of nonlinear systems are characterized in terms of nonlinear matrix inequalities which result in convex problems. The computational implications for the characterization are discussed
Statistical Mechanical Treatments of Protein Amyloid Formation
Protein aggregation is an important field of investigation because it is
closely related to the problem of neurodegenerative diseases, to the
development of biomaterials, and to the growth of cellular structures such as
cyto-skeleton. Self-aggregation of protein amyloids, for example, is a
complicated process involving many species and levels of structures. This
complexity, however, can be dealt with using statistical mechanical tools, such
as free energies, partition functions, and transfer matrices. In this article,
we review general strategies for studying protein aggregation using statistical
mechanical approaches and show that canonical and grand canonical ensembles can
be used in such approaches. The grand canonical approach is particularly
convenient since competing pathways of assembly and dis-assembly can be
considered simultaneously. Another advantage of using statistical mechanics is
that numerically exact solutions can be obtained for all of the thermodynamic
properties of fibrils, such as the amount of fibrils formed, as a function of
initial protein concentration. Furthermore, statistical mechanics models can be
used to fit experimental data when they are available for comparison.Comment: Accepted to IJM
A Statistical Mechanical Approach to Protein Aggregation
We develop a theory of aggregation using statistical mechanical methods. An
example of a complicated aggregation system with several levels of structures
is peptide/protein self-assembly. The problem of protein aggregation is
important for the understanding and treatment of neurodegenerative diseases and
also for the development of bio-macromolecules as new materials. We write the
effective Hamiltonian in terms of interaction energies between protein
monomers, protein and solvent, as well as between protein filaments. The grand
partition function can be expressed in terms of a Zimm-Bragg-like transfer
matrix, which is calculated exactly and all thermodynamic properties can be
obtained. We start with two-state and three-state descriptions of protein
monomers using Potts models that can be generalized to include q-states, for
which the exactly solvable feature of the model remains. We focus on n X N
lattice systems, corresponding to the ordered structures observed in some real
fibrils. We have obtained results on nucleation processes and phase diagrams,
in which a protein property such as the sheet content of aggregates is
expressed as a function of the number of proteins on the lattice and
inter-protein or interfacial interaction energies. We have applied our methods
to A{\beta}(1-40) and Curli fibrils and obtained results in good agreement with
experiments.Comment: 13 pages, 8 figures, accepted to J. Chem. Phy
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