Related papers: Pontryagin principle for a Mayer problem governed …
We consider the design of external inputs to achieve a control objective on the opinions, represented by scalars, in a social network. The opinion dynamics follow a variant of the discrete-time Friedkin-Johnsen model. We first consider two…
We consider the Lagrange problem of optimal control with unrestricted controls and address the question: under what conditions we can assure optimal controls are bounded? This question is related to the one of Lipschitzian regularity of…
In this paper we study reduction by symmetry for optimality conditions in optimal control problems of left-invariant affine multi-agent control systems, with partial symmetry breaking cost functions. Our approach emphasizes the role of…
We reconsider the variational integration of optimal control problems for mechanical systems based on a direct discretization of the Lagrange-d'Alembert principle. This approach yields discrete dynamical constraints which by construction…
Controllability maximization problem under sparsity constraints is a node selection problem that selects inputs that are effective for control in order to minimize the energy to control for desired state. In this paper we discuss the…
A Hamiltonian algorithm, both theoretical and numerical, to obtain the reduced equations implementing Pontryagine's Maximum Principle for singular linear-quadratic optimal control problems is presented. This algorithm is inspired on the…
In this paper, we investigate the consensus models on the sphere with control signals, where both the first and second order systems are considered. We provide the existence of the optimal control-trajectory pair and derive the first order…
The turnpike phenomenon stipulates that the solution of an optimal control problem in large time, remains essentially close to a steady-state of the dynamics, itself being the optimal solution of an associated static optimal control…
We consider variational discretization of a parabolic optimal control problem governed by space-time measure controls. For the state discretization we use a Petrov-Galerkin method employing piecewise constant states and piecewise linear and…
Since the second half of the 20th century, Pontryagin's Maximum Principle has been widely discussed and used as a method to solve optimal control problems in medicine, robotics, finance, engineering, astronomy. Here, we focus on the proof…
Quantum optimal control is a set of methods for designing time-varying electromagnetic fields to perform operations in quantum technologies. This tutorial paper introduces the basic elements of this theory based on the Pontryagin maximum…
We study a class of mean-field stochastic differential equations driven by a fractional Brownian motion with Hurst parameter $H\in(1/2,1)$ and a related stochastic control problem. We derive a Pontryagin type maximum principle and the…
The paper presents necessary and sufficient conditions for a nonlinear system to be stabilized by a feedback. The conditions are based on the ideas related to the well-known Pontryagin's maximum principle. That allows us to formulate the…
A geometric setup for control theory is presented. The argument is developed through the study of the extremals of action functionals defined on piecewise differentiable curves, in the presence of differentiable non-holonomic constraints.…
We consider control systems governed by nonlinear O.D.E.'s that are affine in the time-derivative du/dt of the control u. The latter is allowed to be an integrable, possibly of unbounded variation function, which gives the system an…
In this paper, we derive sufficient and necessary maximum principles for a stochastic optimal control problem where the system state is given by a controlled stochastic differential equation with default. We prove existence of a unique…
The controlled motion of a rolling ball actuated by internal point masses that move along arbitrarily-shaped rails fixed within the ball is considered. Application of the variational Pontryagin's minimum principle yields the ball's…
Limited bandwidth and limited saturation in actuators are practical concerns in control systems. Mathematically, these limitations manifest as constraints being imposed on the control actions, their rates of change, and more generally, the…
The first motivation of our paper is to explore further the idea that, in risk control problems, it may be profitable to base decisions both on the position of the underlying process Xt and on its supremum Xt := sup 0$\le$s$\le$t Xs.…
In this paper, we solve an open problem and obtain a general maximum principle for a stochastic optimal control problem where the control domain is an arbitrary non-empty set and all the coefficients (especially the diffusion term and the…