On a Lagrange problem and its generalizations
On almost-Riemannian surfaces
An almost-Riemannian structure on a surface is a generalized Riemannian structure whose local orthonormal frames are given by Lie bracket generating pairs of vector fields that can become collinear. The distribution generated locally by orthonormal frames has maximal rank at almost every point of the surface, but in general it has rank 1 on a nonempty set which is generically a smooth curve. In this paper we provide a short introduction to 2-dimensional almost-Riemannian geometry highlighting its...
On asymptotic exit-time control problems lacking coercivity
The research on a class of asymptotic exit-time problems with a vanishing Lagrangian, begun in [M. Motta and C. Sartori, Nonlinear Differ. Equ. Appl. Springer (2014).] for the compact control case, is extended here to the case of unbounded controls and data, including both coercive and non-coercive problems. We give sufficient conditions to have a well-posed notion of generalized control problem and obtain regularity, characterization and approximation results for the value function of the problem....
On bang-bang principles in linear-quadratic control problems for generalized analytic functions
On Bellman spheres for linear controlled objects of second order.
On complexity and motion planning for co-rank one sub-riemannian metrics
In this paper, we study the motion planning problem for generic sub-riemannian metrics of co-rank one. We give explicit expressions for the metric complexity (in the sense of Jean [10, 11]), in terms of the elementary invariants of the problem. We construct asymptotic optimal syntheses. It turns out that among the results we show, the most complicated case is the 3-dimensional. Besides the generic case, we study some non-generic generalizations in the analytic case.
On complexity and motion planning for co-rank one sub-Riemannian metrics
In this paper, we study the motion planning problem for generic sub-Riemannian metrics of co-rank one. We give explicit expressions for the metric complexity (in the sense of Jean [CITE]), in terms of the elementary invariants of the problem. We construct asymptotic optimal syntheses. It turns out that among the results we show, the most complicated case is the 3-dimensional. Besides the generic C∞ case, we study some non-generic generalizations in the analytic case.
On infinite-horizon optimal control problems.
On nonlinear variational inequalities.
On some asymptotic minimum problems
On the Existence of Optimal Solutions for Infinite Horizon Optimal Control Problems: Nonconvex and Multicriteria Problems
In questa Nota si continua la discussione iniziata in [4] dell'esistenza di soluzioni ottimali per problemi di ottimo controllo in . Si definiscono problemi generalizzati, e si ottengono estensioni di risultati già presentati in [4]. Si dimostrano anche varie relazioni tra le soluzioni ottimali dei problemi generalizzati e i problemi originali e non convessi di ottimo controllo. Alla fine si considerano problemi lineari nelle variabili di stato anche nel caso di costi funzionali a valori vettoriali...
On the optimal control of affine nonlinear systems.
On the role of abnormal minimizers in sub-riemannian geometry
On the solution of the variational problem of the arc length in 4-dimensinal affine space.
On transformations of singular quadratic functionals corresponding to equation
Optimal control of an inventory system with ameliorating and deteriorating items.
Optimal control of combined therapy in a single strain HIV-1 model.
Optimal control of nonlinear delay systems with implicit derivative and quadratic performance
The existence of optimal control for nonlinear delay systems having an implicit derivative with quadratic performance criteria is proved. The results are established by an iterative technique and using the Darbo fixed point theorem.
Optimal control problem and maximum principle for fractional order cooperative systems
In this paper, by using the classical control theory, the optimal control problem for fractional order cooperative system governed by Schrödinger operator is considered. The fractional time derivative is considered in a Riemann-Liouville and Caputo senses. The maximum principle for this system is discussed. We first study by using the Lax-Milgram Theorem, the existence and the uniqueness of the solution of the fractional differential system in a Hilbert space. Then we show that the considered optimal...
Optimal control processes associated with a class of discontinuous control systems: Applications to sliding mode dynamics
This paper presents a theoretical approach to optimal control problems (OCPs) governed by a class of control systems with discontinuous right-hand sides. A possible application of the framework developed in this paper is constituted by the conventional sliding mode dynamic processes. The general theory of constrained OCPs is used as an analytic background for designing numerically tractable schemes and computational methods for their solutions. The proposed analytic method guarantees consistency...