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A variational framework, initially developed for high-order mesh optimisation, is being extended for r-adaptation. The method is based on the minimisation of a functional of the mesh deformation. To achieve adaptation, elements of the…
Many robotics tasks, such as path planning or trajectory optimization, are formulated as optimal control problems (OCPs). The key to obtaining high performance lies in the design of the OCP's objective function. In practice, the objective…
Optimal control of stochastic nonlinear dynamical systems is a major challenge in the domain of robot learning. Given the intractability of the global control problem, state-of-the-art algorithms focus on approximate sequential optimization…
We propose a variable smoothing algorithm for solving nonconvexly constrained nonsmooth optimization problems. The target problem has two issues that need to be addressed: (i) the nonconvex constraint and (ii) the nonsmooth term. To handle…
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…
In this chapter, we are concerned with inverse optimal control problems, i.e., optimization models which are used to identify parameters in optimal control problems from given measurements. Here, we focus on linear-quadratic optimal control…
The goal of this paper is to address finite-horizon minimum variance and covariance steering problems for discrete-time stochastic (Gaussian) linear systems. On the one hand, the minimum variance problem seeks for a control policy that will…
Optimization is an important module of modern machine learning applications. Tremendous efforts have been made to accelerate optimization algorithms. A common formulation is achieving a lower loss at a given time. This enables a…
In this article, we discuss gradient robust discretizations for the simulation of non-linear incompressible Navier-Stokes problem and the optimal control of such flow. We consider several formulations of the flow problem that are equivalent…
In [1] we consider an optimal control problem subject to a semilinear elliptic PDE together with its variational discretization, where we provide a condition which allows to decide whether a solution of the necessary first order conditions…
We consider a stochastic control problem for a class of nonlinear kernels. More precisely, our problem of interest consists in the optimisation, over a set of possibly non-dominated probability measures, of solutions of backward stochastic…
Optimization in machine learning typically deals with the minimization of empirical objectives defined by training data. However, the ultimate goal of learning is to minimize the error on future data (test error), for which the training…
We derive a-priori error estimates for the finite-element approximation of a distributed optimal control problem governed by the steady one-dimensional Burgers equation with pointwise box constraints on the control. Here the approximation…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
This paper proposes a framework for adaptively learning a feedback linearization-based tracking controller for an unknown system using discrete-time model-free policy-gradient parameter update rules. The primary advantage of the scheme over…
Controller tuning and parameter optimization are crucial in system design to improve closed-loop system performance. Bayesian optimization has been established as an efficient model-free controller tuning and adaptation method. However,…
We consider a nonlinear ordinary differential equation and want to control its behavior so that it reaches a target by minimizing a cost function. Our approach is to use hybrid systems to solve this problem: the complex dynamic is replaced…
We present a methodology for obtaining explicit solutions to infinite time horizon optimal stopping problems involving general, one-dimensional, It\^o diffusions, payoff functions that need not be smooth and state-dependent discounting.…
In this paper, a stochastic control problem under model uncertainty with general penalty term is studied. Two types of penalties are considered. The first one is of type f-divergence penalty treated in the general framework of a continuous…
The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that…