Search results for " and Control"
showing 10 items of 385 documents
Periodic controls in step 2 sub-Finsler problems
2019
We consider control-linear left-invariant time-optimal problems on step 2 Carnot groups with strictly convex set of control parameters (in particular, sub-Finsler problems). We describe all linear-in-momenta Casimirs on the dual of the Lie algebra. In the case of rank 3 Lie groups we describe the symplectic foliation on the dual of the Lie algebra. On this basis we show that extremal controls are either constant or periodic. Some related results for other Carnot groups are presented.
Corners in non-equiregular sub-Riemannian manifolds
2014
We prove that in a class of non-equiregular sub-Riemannian manifolds corners are not length minimizing. This extends the results of (G.P. Leonardi and R. Monti, Geom. Funct. Anal. 18 (2008) 552-582). As an application of our main result we complete and simplify the analysis in (R. Monti, Ann. Mat. Pura Appl. (2013)), showing that in a 4-dimensional sub-Riemannian structure suggested by Agrachev and Gauthier all length-minimizing curves are smooth. Mathematics Subject Classification. 53C17, 49K21, 49J15.
Geometric characterizations of the strict Hadamard differentiability of sets
2021
Let $S$ be a closed subset of a Banach space $X$. Assuming that $S$ is epi-Lipschitzian at $\bar{x}$ in the boundary $ \bd S$ of $S$, we show that $S$ is strictly Hadamard differentiable at $\bar{x}$ IFF the Clarke tangent cone $T(S, \bar{x})$ to $S$ at $\bar{x}$ contains a closed hyperplane IFF the Clarke tangent cone $T(\bd S, \bar{x})$ to $\bd S$ at $\bar{x}$ is a closed hyperplane. Moreover when $X$ is of finite dimension, $Y$ is a Banach space and $g: X \mapsto Y$ is a locally Lipschitz mapping around $\bar{x}$, we show that $g$ is strictly Hadamard differentiable at $\bar{x}$ IFF $T(\mathrm{graph}\,g, (\bar{x}, g(\bar{x})))$ is isomorphic to $X$ IFF the set-valued mapping $x\rightrigh…
The approximate subdifferential of composite functions
1993
This paper deals with the approximate subdifferential chain rule in a Banach space. It establishes specific results when the real-valued function is locally Lipschitzian and the mapping is strongly compactly Lipschitzian.
Qualification conditions for multivalued functions in Banach spaces with applications to nonsmooth vector optimization problems
1994
In this paper we introduce qualification conditions for multivalued functions in Banach spaces involving the A-approximate subdifferential, and we show that these conditions guarantee metric regularity of multivalued functions. The results are then applied for deriving Lagrange multipliers of Fritz—John type and Kuhn—Tucker type for infinite non-smooth vector optimization problems.
Integration of multifunctions with closed convex values in arbitrary Banach spaces
2018
Integral properties of multifunctions with closed convex values are studied. In this more general framework not all the tools and the technique used for weakly compact convex valued multifunctions work. We pay particular attention to the "positive multifunctions". Among them an investigation of multifunctions determined by vector-valued functions is presented. Finally, decomposition results are obtained for scalarly and gauge-defined integrals of multifunctions and a full description of McShane integrability in terms of Henstock and Pettis integrability is given.
Noncoincidence of Approximate and Limiting Subdifferentials of Integral Functionals
2011
For a locally Lipschitz integral functional $I_f$ on $L^1(T,\mathbf{R}^n)$ associated with a measurable integrand f, the limiting subdifferential and the approximate subdifferential never coincide at a point $x_0$ where $f(t,\cdot)$ is not subdifferentially regular at $x_0(t)$ for a.e. $t\in T$. The coincidence of both subdifferentials occurs on a dense set of $L^1(T,\mathbf{R}^n)$ if and only if $f(t,\cdot)$ is convex for a.e. $t\in T$. Our results allow us to characterize Aubin's Lipschitz-like property as well as the convexity of multivalued mappings between $L^1$-spaces. New necessary optimality conditions for some Bolza problems are also obtained.
Limited memory bundle algorithm for inequality constrained nondifferentiable optimization
2007
Many practical optimization problems involve nonsmooth (that is, not necessarily differentiable) functions of hundreds or thousands of variables with various constraints. In this paper, we describe a new efficient adaptive limited memory interior point bundle method for large, possible nonconvex, nonsmooth inequality constrained optimization. The method is a hybrid of the nonsmooth variable metric bundle method and the smooth limited memory variable metric method, and the constraint handling is based on the primal-dual feasible direction interior point approach. The preliminary numerical experiments to be presented confirm the effectiveness of the method.
Test problems for large-scale nonsmooth minimization
2007
Many practical optimization problems involve nonsmooth (that is, not necessarily differentiable) functions of hundreds or thousands of variables with various constraints. However, there exist only few large-scale academic test problems for nonsmooth case and there is no established practice for testing solvers for large-scale nonsmooth optimization. For this reason, we now collect the nonsmooth test problems used in our previous numerical experiments and also give some new problems. Namely, we give problems for unconstrained, bound constrained, and inequality constrained nonsmooth minimization.
Mechanical Bistable Structures for Microrobotics and Mesorobotics from Microfabrication to Additive Manufacturing
2018
International audience; The use of mechanical bistable structures in the design of microrobots and mesorobots has many advantages especially for flexible robotic structures. However, depending on the fabrication technology used, the adequacy of theoretical and experimental mechanical behaviors can vary widely. In this paper, we present the manufacturing results of bistable structures made with two extensively used contemporary technologies: MEMS and FDM additive manufacturing. Key issues of these fabrication technologies are discussed in the context of microrobotics and mesorobotics applications.