Related papers: A discrete-time Pontryagin maximum principle on ma…
We address Newton-type problems of minimal resistance from an optimal control perspective. It is proven that for Newton-type problems the Pontryagin maximum principle is a necessary and sufficient condition. Solutions are then computed for…
We study a trajectory-planning problem whose solution path evolves by means of a Lie group action and passes near a designated set of target positions at particular times. This is a higher-order variational problem in optimal control,…
In this paper we investigate a variational discretization for the class of mechanical systems in presence of symmetries described by the action of a Lie group which reduces the phase space to a (non-trivial) principal bundle. By introducing…
Optimal Control Theory is a powerful mathematical tool, which has known a rapid development since the 1950s, mainly for engineering applications. More recently, it has become a widely used method to improve process performance in quantum…
We derive the Pontryagin maximum principle and $Q$-functions for the relaxed control of noisy rough differential equations. Our main tool is the development of a novel differentiation procedure along `spike variation' perturbations of the…
In this paper, we study a class of finite-time control problems for discrete-time positive linear systems with time-varying state parameters. Although several interesting control problems appearing in population biology, economics, and…
In this work, we investigate the optimal control problem for continuous-time Markov decision processes with the random impact of the environment. We provide conditions to show the existence of optimal controls under finite-horizon criteria.…
In this paper we present a Learning Model Predictive Control (LMPC) strategy for linear and nonlinear time optimal control problems. Our work builds on existing LMPC methodologies and it guarantees finite time convergence properties for the…
This paper develops a primal-dual dynamical system where the coefficients are designed in closed-loop way for solving a convex optimization problem with linear equality constraints. We first introduce a ``second-order primal" +…
In this paper, we consider a class of continuous-time, continuous-space stochastic optimal control problems. Building upon recent advances in Markov chain approximation methods and sampling-based algorithms for deterministic path planning,…
We discuss the use of Dirac structures to obtain a better understanding of the geometry of a class of optimal control problems and their reduction by symmetries. In particular we will show how to extend the reduction of Dirac structures…
This paper studies the optimal control problem for discrete-time nonlinear systems and an approximate dynamic programming-based Model Predictive Control (MPC) scheme is proposed for minimizing a quadratic performance measure. In the…
We obtain the dynamic programming equations and optimality conditions akin to Pontryagin's extremum principle for certain mathematical models of hybrid control systems.
Based on stochastic curvilinear integrals in the Cairoli-Walsh sense and in the It\^{o}-Udri\c{s}te sense, we develop an original theory regarding the multitime stochastic differential systems. The first group of the original results refer…
This paper concerns a class of infinite horizon optimal control problems with state constraints. By extending the needle variation method to the infinite horizon case we obtain a complete set of necessary optimality conditions for a strong…
We apply an extension of the Pontryagin Maximum Principle to derive time-optimal controls of two-level quantum systems by means of piecewise constant pulses. Global optimal solutions are obtained for state-to-state transfer in the cases…
We analyze a novel class of rough stochastic control problems that allows for a convenient approach to solving pathwise stochastic control problems with both non-anticipative and anticipative controls. We first establish the well-posedness…
An interesting family of geometric integrators for Lagrangian systems can be defined using discretizations of the Hamilton's principle of critical action. This family of geometric integrators is called variational integrators. In this…
We derive the explicit solution of the problem of time-optimal control by a common magnetic fields for two independent spin-$\frac{1}{2}$ particles. Our approach is based on the Pontryagin Maximum Principle and a novel symmetry reduction…
At the core of optimal control theory is the Pontryagin maximum principle - the celebrated first order necessary optimality condition - whose solutions are called extremals and which are obtained through a function called Hamiltonian, akin…