Related papers: Optimal Control of Underactuated Mechanical System…
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.…
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…
Geometric optimal control utilizes tools from differential geometry to analyze the structure of a problem to determine the control and state trajectories to reach a desired outcome while minimizing some cost function. For a controlled…
Controlling large-scale particle or robot systems is challenging because of their high dimensionality. We use a centralized stochastic approach that allows for optimal control at the cost of a central element instead of a decentralized…
We review some recent results on the theory of Lagrangian systems on Lie algebroids. In particular we consider the symplectic and variational formalism and we study reduction. Finally we also consider optimal control systems on Lie…
After reviewing the Lagrangian-Hamiltonian unified formalism (i.e, the Skinner-Rusk formalism) for higher-order (non-autonomous) dynamical systems, we state a unified geometrical version of the Variational Principles which allows us to…
Hybrid dynamical systems are systems which undergo both continuous and discrete transitions. The Bolza problem from optimal control theory was applied to these systems and a hybrid version of Pontryagin's maximum principle was presented.…
In this paper we study, from a variational and geometrical point of view, second-order variational problems on Lie groupoids and the construction of variational integrators for optimal control problems. First, we develop variational…
A time optimal attitude control problem is studied for the dynamics of a rigid body. The objective is to minimize the time to rotate the rigid body to a desired attitude and angular velocity while subject to constraints on the control…
This note proposes a general control approach, called vector-field guided constraint-following control, to solve the dynamics control problem of geometric path-following for a class of uncertain mechanical systems. More specifically, it…
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…
Model-based controllers can offer strong guarantees on stability and convergence by relying on physically accurate dynamic models. However, these are rarely available for high-dimensional mechanical systems such as deformable objects or…
Controlled Lagrangian and matching techniques are developed for the stabilization of relative equilibria and equilibria of discrete mechanical systems with symmetry as well as broken symmetry. Interesting new phenomena arise in the…
The optimal control of problems that are constrained by partial differential equations with uncertainties and with uncertain controls is addressed. The Lagrangian that defines the problem is postulated in terms of stochastic functions, with…
In this paper, we consider a generalization of variational calculus which allows us to consider in the same framework different cases of mechanical systems, for instance, Lagrangian mechanics, Hamiltonian mechanics, systems subjected to…
We discuss a mathematical framework for analysis of optimal control problems on infinite-dimensional manifolds. Such problems arise in study of optimization for partial differential equations with some symmetry. It is shown that some…
In this paper we will discuss some new developments in the design of numerical methods for optimal control problems of Lagrangian systems on Lie groups. We will construct these geometric integrators using discrete variational calculus on…
In this paper, we study representation formulas for finite-horizon optimal control problems with or without state constraints, unifying two different viewpoints: the Lagrangian and dynamic programming (DP) frameworks. In a recent work [1],…
This paper studies the stochastic optimal control problem for systems with unknown dynamics. First, an open-loop deterministic trajectory optimization problem is solved without knowing the explicit form of the dynamical system. Next, a…
In this paper, we present a framework for solving continuous optimal control problems when the true system dynamics are approximated through an imperfect model. We derive a control strategy by applying Pontryagin's Minimum Principle to the…