Related papers: Analysis of extremum value theorems for function s…
We consider the control problem with \textit{exit time}. Unlike the Bolza and Mayer problems, in this problem the terminal time of the trajectories is not fixed, but it is the first time at which they reach a given closed subset -…
We study the problem of empirical minimization for variance-type functionals over functional classes. Sharp non-asymptotic bounds for the excess variance are derived under mild conditions. In particular, it is shown that under some…
We establish a linear programming formulation for the solution of joint chance constrained optimal control problems over finite time horizons. The joint chance constraint may represent an invariance, reachability or reach-avoid…
Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. Approximation theorems are available in the literature. The originality of our approach relies on…
We study an optimal control problem in which both the objective function and the dynamic constraint contain an uncertain parameter. Since the distribution of this uncertain parameter is not exactly known, the objective function is taken as…
We consider bounded extremum seeking controls for time-varying linear systems with uncertain coefficient matrices and measurement uncertainty. Using a new change of variables, Lyapunov functions, and a comparison principle, we provide…
We consider linear model reduction in both the control and state variables for unconstrained linear-quadratic optimal control problems subject to time-varying parabolic PDEs. The first-order optimality condition for a state-space reduced…
We study the extremes for a class of a symmetric stable random fields with long range dependence. We prove functional extremal theorems both in the space of sup measures and in the space of cadlag functions of several variables. The limits…
This paper contains selected applications of the new tangential extremal principles and related results developed in Part I to calculus rules for infinite intersections of sets and optimality conditions for problems of semi-infinite…
We revisit the optimal control problem with maximum cost with the objective to provide different equivalent reformulations suitable to numerical methods. We propose two reformulations in terms of extended Mayer problems with constraint, and…
We investigate a limit value of an optimal control problem when the horizon converges to infinity. For this aim, we suppose suitable nonexpansive-like assumptions which does not imply that the limit is independent of the initial state as it…
We study in optimal control the important relation between invariance of the problem under a family of transformations, and the existence of preserved quantities along the Pontryagin extremals. Several extensions of Noether theorem are…
We give a one-sentence proof that a continuous real-valued function f on a closed, bounded interval attains a maximum value, by the following device. We define x in [a, b] to be a lookout point if f(t) does not exceed f(x) whenever t lies…
Let $\Delta_m$ be the standard $m$-dimensional simplex of non-negative $m+1$ tuples that sum to unity and let $S$ be a nonempty subset of $\Delta_m$. A real valued function $h$ defined on a convex subset of a real vector space is $S$-almost…
Our object of study is extremal functions which are defined by distance functions of convex bodies. These functions take values in the moduli spaces of algebraic and geometric objects associated with these ${\mathbb Z}$-modules (geometric…
A coordinate-free proof of the Maximum Principle is provided in the specific case of an optimal control problem with fixed time. Our treatment heavily relies on a special notion of variation of curves that consist of a concatenation of…
For an optimal control problem, the concept of a strong local infimum is introduce, for which necessary conditions consisting of some family of "maximum principles" are formulated. If a function delivers a strong local minimum in this…
Affine policies (or control) are widely used as a solution approach in dynamic optimization where computing an optimal adjustable solution is usually intractable. While the worst case performance of affine policies can be significantly bad,…
We establish a variety of results extending the well-known Pontryagin maximum principle of optimal control to discrete-time optimal control problems posed on smooth manifolds. These results are organized around a new theorem on critical and…
Much of statistics relies upon four key elements: a law of large numbers, a calculus to operationalize stochastic convergence, a central limit theorem, and a framework for constructing local approximations. These elements are…