22,458 research outputs found
A State-Space Approach to Parametrization of Stabilizing Controllers for Nonlinear Systems
A state-space approach to Youla-parametrization of stabilizing controllers for linear and nonlinear systems is suggested. The stabilizing controllers (or a class of stabilizing controllers for nonlinear systems) are characterized as (linear/nonlinear) fractional transformations of stable parameters. The main idea behind this approach is to decompose the output feedback stabilization problem into state feedback and state estimation problems. The parametrized output feedback controllers have separation structures. A separation principle follows from the construction. This machinery allows the parametrization of stabilizing controllers to be conducted directly in state space without using coprime-factorization
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
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Hydrogen Peroxide Wound Irrigation in Orthopaedic Surgery.
As the burden of deep hardware infections continues to rise in orthopaedics, there is increasing interest in strategies for more effective debridement of colonized tissues and biofilm. Hydrogen peroxide has been used medically for almost a century, but its applications in orthopaedic surgery have yet to be fully determined. The basic science and clinical research on the antiseptic efficacy of hydrogen peroxide have demonstrated its efficacy against bacteria, and it has demonstrated potential synergy with other irrigation solutions such as chlorhexidine and povidone-iodine. While hydrogen peroxide is effective in infection reduction, there are concerns with wound healing, cytotoxicity, and embolic phenomena, and we recommend against hydrogen peroxide usage in the treatment of partial knee replacements, hemiarthroplasties, or native joints. Additionally, due to the potential for oxygen gas formation, hydrogen peroxide should not be used in cases of dural compromise, when pressurizing medullary canals, or when irrigating smaller closed spaces to avoid the possibility of air embolism. Finally, we present our protocol for irrigation and debridement and exchange of modular components in total joint arthroplasty, incorporating hydrogen peroxide in combination with povidone-iodine and chlorhexidine
Adaptive ℋ∞-control for nonlinear systems: a dissipation theoretical approach
The adaptive ℋ∞-control problem for parameter-dependent nonlinear systems with full information feedback is considered. The techniques from dissipation theory as well as the vector and parameter projection methods are used to derive the adaptive ℋ∞-control laws. Both of the projection techniques are rigorously treated. The adaptive robust stabilization for nonlinear systems with ℒ2-gain hounded uncertainties is investigated
Anti-dark and Mexican-hat solitons in the Sasa-Satsuma equation on the continuous wave background
In this letter, via the Darboux transformation method we construct new
analytic soliton solutions for the Sasa-Satsuma equation which describes the
femtosecond pulses propagation in a monomode fiber. We reveal that two
different types of femtosecond solitons, i.e., the anti-dark (AD) and
Mexican-hat (MH) solitons, can form on a continuous wave (CW) background, and
numerically study their stability under small initial perturbations. Different
from the common bright and dark solitons, the AD and MH solitons can exhibit
both the resonant and elastic interactions, as well as various
partially/completely inelastic interactions which are composed of such two
fundamental interactions. In addition, we find that the energy exchange between
some interacting soliton and the CW background may lead to one AD soliton
changing into an MH one, or one MH soliton into an AD one.Comment: 12 pages, 6 figure
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
Stabilization of Linear Systems with Structured Perturbations
The problem of stabilization of linear systems with bounded structured uncertainties are considered in this paper. Two notions of stability, denoted quadratic stability (Q-stability) and μ-stability, are considered, and corresponding notions of stabilizability and detectability are defined. In both cases, the output feedback stabilization problem is reduced via a separation argument to two simpler problems: full information (FI) and full control (FC). The set of all stabilizing controllers can be parametrized as a linear fractional transformation (LFT) on a free stable parameter. For Q-stability, stabilizability and detectability can in turn be characterized by Linear Matrix Inequalities (LMIs), and the FI and FC Q-stabilization problems can be solved using the corresponding LMIs. In the standard one-dimensional case the results in this paper reduce to well-known results on controller parametrization using state-space methods, although the development here relies more heavily on elegant LFT machinery and avoids the need for coprime factorizations
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