810 research outputs found
Survey of Gain-Scheduling Analysis & Design
The gain-scheduling approach is perhaps one of the most popular nonlinear control design approaches which has
been widely and successfully applied in fields ranging from aerospace to process control. Despite the wide
application of gain-scheduling controllers and a diverse academic literature relating to gain-scheduling extending
back nearly thirty years, there is a notable lack of a formal review of the literature. Moreover, whilst much of
the classical gain-scheduling theory originates from the 1960s, there has recently been a considerable increase in
interest in gain-scheduling in the literature with many new results obtained. An extended review of the gainscheduling
literature therefore seems both timely and appropriate. The scope of this paper includes the main
theoretical results and design procedures relating to continuous gain-scheduling (in the sense of decomposition
of nonlinear design into linear sub-problems) control with the aim of providing both a critical overview and a
useful entry point into the relevant literature
Robust distributed linear programming
This paper presents a robust, distributed algorithm to solve general linear
programs. The algorithm design builds on the characterization of the solutions
of the linear program as saddle points of a modified Lagrangian function. We
show that the resulting continuous-time saddle-point algorithm is provably
correct but, in general, not distributed because of a global parameter
associated with the nonsmooth exact penalty function employed to encode the
inequality constraints of the linear program. This motivates the design of a
discontinuous saddle-point dynamics that, while enjoying the same convergence
guarantees, is fully distributed and scalable with the dimension of the
solution vector. We also characterize the robustness against disturbances and
link failures of the proposed dynamics. Specifically, we show that it is
integral-input-to-state stable but not input-to-state stable. The latter fact
is a consequence of a more general result, that we also establish, which states
that no algorithmic solution for linear programming is input-to-state stable
when uncertainty in the problem data affects the dynamics as a disturbance. Our
results allow us to establish the resilience of the proposed distributed
dynamics to disturbances of finite variation and recurrently disconnected
communication among the agents. Simulations in an optimal control application
illustrate the results
A globally convergent matricial algorithm for multivariate spectral estimation
In this paper, we first describe a matricial Newton-type algorithm designed
to solve the multivariable spectrum approximation problem. We then prove its
global convergence. Finally, we apply this approximation procedure to
multivariate spectral estimation, and test its effectiveness through
simulation. Simulation shows that, in the case of short observation records,
this method may provide a valid alternative to standard multivariable
identification techniques such as MATLAB's PEM and MATLAB's N4SID
Waves of maximal height for a class of nonlocal equations with homogeneous symbols
We discuss the existence and regularity of periodic traveling-wave solutions
of a class of nonlocal equations with homogeneous symbol of order , where
. Based on the properties of the nonlocal convolution operator, we apply
analytic bifurcation theory and show that a highest, peaked, periodic
traveling-wave solution is reached as the limiting case at the end of the main
bifurcation curve. The regularity of the highest wave is proved to be exactly
Lipschitz. As an application of our analysis, we reformulate the steady reduced
Ostrovsky equation in a nonlocal form in terms of a Fourier multiplier operator
with symbol . Thereby we recover its unique highest
-periodic, peaked traveling-wave solution, having the property of being
exactly Lipschitz at the crest.Comment: 25 page
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
Caputo fractional differential equation with state dependent delay and practical stability
Practical stability properties of Caputo fractional delay differential equations is studied and, in particular, the case with state dependent delays is considered. These type of delays is a generalization of several types of delays such as constant delays, time variable delays, or distributed delays. In connection with the
presence of a delay in a fractional differential equation and the application of the fractional generalization of the Razumikhin method, we give a brief overview of the
most popular fractional order derivatives of Lyapunov functions among Caputo fractional delay differential equations. Three types of derivatives for Lyapunov functions, the Caputo fractional derivative, the Dini fractional derivative, and the Caputo fractional Dini derivative, are applied to obtain several sufficient conditions for practical stability. An appropriate Razumikhin condition is applied. These derivatives allow the application of non-quadratic Lyapunov function for studying stability properties. We illustrate our theory on several nonlinear Caputo fractional differential equations with different types of delayspublishe
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