Journal ArticleDOI
Design of a flight control architecture using a non-convex bundle method
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A non-convex bundle method is presented, its convergence is proved, and it is shown that it is apt to solve the longitudinal flight control problem.Abstract:
We design a feedback control architecture for longitudinal flight of an aircraft. The multi-level architecture includes the flight control loop to govern the short-term dynamics of the aircraft, and the autopilot to control the long-term modes. Using $$H_\infty $$
performance and robustness criteria, the problem is cast as a non-convex and non-smooth optimization program. We present a non-convex bundle method, prove its convergence, and show that it is apt to solve the longitudinal flight control problem.read more
Citations
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Journal ArticleDOI
Convergence of Non-smooth Descent Methods Using the Kurdyka–Łojasiewicz Inequality
TL;DR: This work proves convergence in the sense of subsequences for functions with a strict standard model, and shows that convergence to a single critical point may be guaranteed if the Kurdyka–Łojasiewicz inequality is satisfied.
Book ChapterDOI
Bundle Method for Non-Convex Minimization with Inexact Subgradients and Function Values
TL;DR: In this paper, a bundle method is proposed to minimize locally Lipschitz functions which are both nonconvex and nonsmooth, and for suitable classes of such non-smooth functions, it is proved convergence of the algorithm to approximate critical points.
Journal ArticleDOI
Nonconvex bundle method with application to a delamination problem
TL;DR: This work considers the problem of computing the propagation of the crack front and the stress field along the contact boundary, and proposes a bundle method suited for both types of nonsmoothness, which is proved to have global convergence in the sense of subsequences.
Journal ArticleDOI
A new infeasible proximal bundle algorithm for nonsmooth nonconvex constrained optimization
TL;DR: An infeasible proximal bundle method for nonsmooth nonconvex constrained optimization problems is developed and the global convergence, starting from any point, is proved in the sense that every accumulation point of the iterative sequence is stationary for the improvement function.
Journal ArticleDOI
On Minty variational principle for nonsmooth vector optimization problems with generalized approximate convexity
Pooja Gupta,Shashi Kant Mishra +1 more
TL;DR: In this paper, the authors considered a nonsmooth vector optimization problem involving locally Lipschitz generalized approximate convex functions and found some relations between approximate conveXity and gen...
References
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Book
Aircraft Control and Simulation
Brian L. Stevens,Frank L. Lewis +1 more
TL;DR: Equations of Motion Building the Aircraft Model Basic Analytical and Computational Tools Aircraft Dynamics and Classical Design Techniques Modern Design Techniques Robustness and Multivariable Frequency-Domain Techniques Digital Control Appendices Index.
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Optimization: Algorithms and Consistent Approximations
TL;DR: This paper presents a meta-anatomy of semi-Infinite Optimization, a branch of optimization that combines the efforts of biologists and mathematicians to study the response of the immune system to injury.
Journal ArticleDOI
Nonsmooth $H_infty$ Synthesis
Pierre Apkarian,Dominikus Noll +1 more
TL;DR: This work develops nonsmooth optimization techniques to solve H_inftysynthesis problems under additional structural constraints on the controller that avoids the use of Lyapunov variables and therefore leads to moderate size optimization programs even for very large systems.
Journal ArticleDOI
NP-Hardness of Some Linear Control Design Problems
TL;DR: It is shown that some basic linear control design problems are NP-hard, implying that, unless P=NP, they cannot be solved by polynomial time algorithms.
Nonsmooth H ∞ synthesis
Pierre Apkarian,Dominikus Noll +1 more
TL;DR: In this paper, a nonsmooth optimization technique is proposed to solve H∞ synthesis problems under additional structural constraints on the controller, which avoids the use of Lyapunov variables and therefore leads to moderate size optimization programs even for very large systems.