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Inverse optimal control problem emerges in different practical applications, where the goal is to design a cost function in order to approximate given optimal strategies of an expert. Typical application is in robotics for generation of…
A recent set of techniques in the robotics community, known as certifiably correct methods, frames robotics problems as polynomial optimization problems (POPs) and applies convex, semidefinite programming (SDP) relaxations to either find or…
We study deterministic optimal control problems for differential games with finite horizon. We propose new approximations of the strategies in feedback form, and show error estimates and a convergence result of the value in some weak sense…
We address the problem of joint optical flow and camera motion estimation in rigid scenes by incorporating geometric constraints into an unsupervised deep learning framework. Unlike existing approaches which rely on brightness constancy and…
A geometric derivation of numerical integrators for optimal control problems is proposed. It is based in the classical technique of generating functions adapted to the special features of optimal control problems.
Trajectory optimization is a fundamental problem in robotics. While optimization of continuous control trajectories is well developed, many applications require both discrete and continuous, i.e., hybrid, controls. Finding an optimal…
The main theme of this thesis is the development of computational methods for classes of infinite-dimensional optimization problems arising in optimal control and information theory. The first part of the thesis is concerned with the…
This paper addresses the time-optimal control problem for a class of control systems which includes controlled mechanical systems with possible dissipation terms. The Lie algebras associated with such mechanical systems enjoy certain…
Retractions maps are used to define a discretization of the tangent bundle of the configuration manifold as two copies of the configuration manifold where the dynamics take place. Such discretization maps can be conveniently lifted to the…
In this paper, we propose a method for constructing a neural network viscosity in order to reduce the non-physical oscillations generated by high-order Discontiuous Galerkin (DG) methods. To this end, the problem is reformulated as an…
This paper presents a novel deep learning framework for solving multiple optimal stopping problems in high dimensions. While deep learning has recently shown promise for single stopping problems, the multiple exercise case involves complex…
Distributed model predictive control (DMPC) is a flexible and scalable feedback control method applicable to a wide range of systems. While the stability analysis of DMPC is quite well understood, there exist only limited implementation…
A family of optimal control problems for a single and two coupled spinning particles in the Euler-Lagrange formalism is discussed. A characteristic of such problems is that the equations controlling the system are implicit and a reduction…
Multi-robot cooperative control has gained extensive research interest due to its wide applications in civil, security, and military domains. This paper proposes a cooperative control algorithm for multi-robot systems with general linear…
The paper deals with the optimal control problem described by second order evolution differential inclusions; to this end first we use an auxiliary problem with second order discrete and discrete-approximate inclusions. Then applying…
In this paper, motivated by the study of optimal control problems for infinite dimensional systems with endpoint state constraints, we introduce the notion of finite codimensional (exact/approximate) controllability. Some equivalent…
Continuous-depth neural networks, such as Neural ODEs, have refashioned the understanding of residual neural networks in terms of non-linear vector-valued optimal control problems. The common solution is to use the adjoint sensitivity…
In this paper error analysis for finite element discretizations of Dirichlet boundary control problems is developed. For the first time, optimal discretization error estimates are established in the case of three dimensional polyhedral and…
With the development of state-of-art deep reinforcement learning, we can efficiently tackle continuous control problems. But the deep reinforcement learning method for continuous control is based on historical data, which would make…
This paper presents an algorithm to solve non-convex optimal control problems, where non-convexity can arise from nonlinear dynamics, and non-convex state and control constraints. This paper assumes that the state and control constraints…