Related papers: Bernstein approximation of optimal control problem…
In this work, we present composite Bernstein polynomials as a direct collocation method for approximating optimal control problems. An analysis of the convergence properties of composite Bernstein polynomials is provided, and beneficial…
A fundamental problem in numerical analysis and approximation theory is approximating smooth functions by polynomials. A much harder version under recent consideration is to enforce bounds constraints on the approximating polynomial. In…
The Bernstein polynomial basis sees significant use owing to its unique properties, particularly in the field of optimal control. However, the basis is known to have a slow rate of convergence to the function it approximates. With this in…
In this paper, we propose a Transformer-based framework for approximating solutions to infinite-dimensional optimization problems: calculus of variations problems and optimal control problems. Our approach leverages offline training on data…
Efficient trajectory generation is crucial for autonomous systems; however, current numerical methods often struggle to handle periodic behaviors effectively, particularly when the onboard sensors require equidistant temporal sampling. This…
The Koopman operator approach provides a powerful linear description of nonlinear dynamical systems in terms of the evolution of observables. While the operator is typically infinite-dimensional, it is crucial to develop finite-dimensional…
This work considers the infinite-time discounted optimal control problem for continuous time input-affine polynomial dynamical systems subject to polynomial state and box input constraints. We propose a sequence of sum-of-squares (SOS)…
A novel inner approximation algorithm is proposed for dynamic optimization problems to ensure strict satisfaction of path constraints. Distinct from traditional methods relying on interval analysis, the proposed algorithm leverages the…
Optimal control under uncertainty is a prevailing challenge for many reasons. One of the critical difficulties lies in producing tractable solutions for the underlying stochastic optimization problem. We show how advanced approximate…
In this paper, we present a new iterative approximate method of solving boundary value problems. The idea is to compute approximate polynomial solutions in the Bernstein form using least squares approximation combined with some properties…
In this paper, we examine linear programming (LP) relaxations based on Bernstein polynomials for polynomial optimization problems (POPs). We present a progression of increasingly more precise LP relaxations based on expressing the given…
This paper focuses on finding approximate solutions to stochastic optimal control problems with control domains being not necessarily convex, where the state trajectory is subject to controlled stochastic differential equations. The…
This article presents a constrained policy optimization approach for the optimal control of systems under nonstationary uncertainties. We introduce an assumption that we call Markov embeddability that allows us to cast the stochastic…
In this article, a formulation of a point-collocation method in which the unknown function is approximated using global expansion in tensor product Bernstein polynomial basis is presented. Bernstein polynomials used in this study are…
We propose a novel reformulation of the stochastic optimal control problem as an approximate inference problem, demonstrating, that such a interpretation leads to new practical methods for the original problem. In particular we characterise…
We consider a class of stochastic optimal control problems with partial observation, and study their approximation by discrete-time control problems. We establish a convergence result by using weak convergence technique of Kushner and…
We define the notion of Bernstein measures and Bernstein approximations over general convex polytopes. This generalizes well-known Bernstein polynomials which are used to prove the Weierstrass approximation theorem on one dimensional…
This papers shows the convergence of optimal control problems where the constraint function is discretised by a particle method. In particular, we investigate the viscous Burgers equation in the whole space $\mathbb R$ by using…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…
We consider the Chance Constrained Model Predictive Control problem for polynomial systems subject to disturbances. In this problem, we aim at finding optimal control input for given disturbed dynamical system to minimize a given cost…