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In this paper we propose novel optimization-based methods for verifying reach-avoid (or, eventuality) properties of continuous-time systems modelled by ordinary differential equations. Given a system, an initial set, a safe set and a target…
Pontryagin's Maximum Principle is an outstanding result for solving optimal control problems by means of optimizing a specific function on some particular variables, the so called controls. However, this is not always enough for solving all…
This paper settles the existence question for a rather general class of convex optimal design problems with a volume constraint. In low dimensions, we prove the existence of an optimal configuration for general convex minimization problems…
We investigate optimal control problems with $L^0$ constraints, which restrict the measure of the support of the controls. We prove necessary optimality conditions of Pontryagin maximum principle type. Here, a special control perturbation…
In this paper, we consider optimal control problems derived by stochastic systems with delay, where control domains are non-convex and the diffusion coefficients depend on control variables. By an estimate of the integral of…
This article deals with the Lipschitz regularity of the ''approximate`` minimizers for the Bolza type control functional of the form \[J_t(y,u):=\int_t^T\Lambda(s,y(s), u(s))\,ds+g(y(T))\] among the pairs $(y,u)$ satisfying a prescribed…
This paper presents an inverse optimal control methodology and its application to training a predictive model of human motor control from a manipulation task. It introduces a convex formulation for learning both objective function and…
Within this chapter, we discuss control in the coefficients of an obstacle problem. Utilizing tools from H-convergence, we show existence of optimal solutions. First order necessary optimality conditions are obtained after deriving…
This paper proves universality of the distribution of the smallest and largest gaps between eigenvalues of generalized Wigner matrices, under some smoothness assumption for the density of the entries. The proof relies on the Erd{\H…
We obtain the variational equations for backward stochastic differential equations in recursive stochastic optimal control problems, and then get the maximum principle which is novel. The control domain need not be convex, and the generator…
We consider cost minimising control problems, in which the dynamical system is constrained by higher order differential equations of Euler-Lagrange type. Following ideas from a previous paper by the first and the third author, we prove that…
A controlled sweeping process with prox-regular set, $W^{1,2}$-controls, and separable endpoints constraints is considered in this paper. Existence of optimal solutions is established and local optimality conditions are derived via strong…
We generalize a Maximum Principle for optimal control problems involving sweeping systems previously derived in ``Necessary conditions for optimal control problems with sweeping systems and end point constraints'', by de Pinho, Ferreira and…
Necessary optimality conditions in the form of the maximum principle for control problems with infinite time horizon are considered. Both finite and infinite values of objective functional are allowed since the concept of overtaking or…
Using the Grosshans Principle, we develop a method for proving lower bounds for the maximal degree of a system of generators of an invariant ring. This method also gives lower bounds for the maximal degree of a set of invariants that define…
Large-scale networked systems typically operate under resource constraints, and it is also difficult to exactly obtain the network structure between nodes. To address these issues, this paper investigates a sparse optimal control for…
We consider an optimal control problem $\cQ$ governed by an elliptic quasivariational inequality with unilateral constraints. The existence of optimal pairs of the problem is a well known result, see \cite{SS}, for instance. We associate to…
In this paper, we develop an optimal control framework for dynamical systems when only an approximate model of the underlying plant is available. We consider a setting in which the control strategy is synthesized using a model-based optimal…
In this paper we propose a finite-dimensional and deterministic approach to the study of invariant sets of certain nonautonomous differential inclusions naturally arising in the context of random and control dynamical systems, as well as in…
In this paper we study a problem of looking for an optimal solution of a system of the differential equations with a control and an optimized function. The system of differential equations is changed for two systems with the upper and lower…