Related papers: A hybrid optimal control problem constrained with …
The purpose of this paper is to model mathematically mechanical aspects of cardiac tissues. The latter constitute an elastic domain whose total volume remains constant. The time deformation of the heart tissue is modeled with the…
This paper joins some concepts from Mechanics, Partial Differential Equations and Control Theory in order to solve bi-time optimization problems related to stress tensor in plastic deformations. The main goal is to analyze some optimal…
A class of optimal control problems of hybrid nature governed by semilinear parabolic equations is considered. These problems involve the optimization of switching times at which the dynamics, the integral cost, and the bounds on the…
We consider an optimal control problem where the state equations are a coupled hyperbolic-elliptic system. This system arises in elastodynamics with piezoelectric effects -- the elastic stress tensor is a function of elastic displacement…
Models involving hybrid systems are versatile in their application but difficult to optimize efficiently due to their combinatorial nature. This work presents a method to cope with hybrid optimal control problems which, in contrast to…
This article discusses an optimal control problem for a phase field model of two immiscible incompressible fluid flow, incorporating surface tension effects. The optimal control problem is defined with a $L^2$-cost functional and subject to…
Hybrid dynamical systems are systems which posses both continuous and discrete transitions. Assuming that the discrete transitions (resets) occur a finite number of times, the optimal control problem can be solved by gluing together the…
The hybrid optimal control problem with reach time to a target set is addressed and the continuity and uniqueness of the associated value function is proved. Hybrid systems involves interaction of different types of dynamics: continuous and…
We consider an optimal control problem constrained by a parabolic partial differential equation (PDE) with Robin boundary conditions. We use a well-posed space-time variational formulation in Lebesgue--Bochner spaces with minimal…
The paper is concerned with an optimal control problem governed by the equations of elasto plasticity with linear kinematic hardening and the inertia term at small strain. The objective is to optimize the displacement field and plastic…
In this paper we study the problem of designing periodic orbits for a special class of hybrid systems, namely mechanical systems with underactuated continuous dynamics and impulse events. We approach the problem by means of optimal control.…
In this paper, we describe a constrained Lagrangian and Hamiltonian formalism for the optimal control of nonholonomic mechanical systems. In particular, we aim to minimize a cost functional, given initial and final conditions where the…
This work addresses an optimal control problem constrained by a degenerate kinetic equation of parabolic-hyperbolic type. Using a hypocoercivity framework we establish the well-posedness of the problem and demonstrate that the optimal…
A new framework for formulating reachability problems with competing inputs, nonlinear dynamics and state constraints as optimal control problems is developed. Such reach-avoid problems arise in, among others, the study of safety problems…
The paper is concerned with an optimal control problem governed by a state equation in form of a generalized abstract operator differential equation involving a maximal monotone operator. The state equation is uniquely solvable, but the…
Hybrid dynamical systems are systems which undergo both continuous and discrete transitions. The Bolza problem from optimal control theory is applied to these systems and a hybrid version of Pontryagin's maximum principle is presented. This…
We study a stochastic optimal control problem with the state constrained to a smooth, compact domain. The control influences both the drift and a possibly degenerate, control-dependent dispersion matrix, leading to a fully nonlinear,…
Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…
Most modern control systems are switched, meaning they have continuous as well as discrete decision variables. Switched systems often have constraints called dwell-time constraints (e.g., cycling constraints in a heat pump) on the switching…
In this paper we combine two main topics in mechanics and optimal control theory: contact Hamiltonian systems and Pontryagin Maximum Principle. As an important result, among others, we develop a contact Pontryagin Maximum Principle that…