Related papers: Optimal Control using Composite Bernstein Approxim…
Bernstein polynomial approximation to a continuous function has a slower rate of convergence as compared to other approximation methods. "The fact seems to have precluded any numerical application of Bernstein polynomials from having been…
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…
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…
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 use of autonomous vehicles for target localization in modern applications has emphasized their superior efficiency, improved safety, and cost advantages over human-operated methods. For localization tasks, autonomous vehicles can be…
This paper presents a method for optimal motion planning of continuum robots by employing Bernstein surfaces to approximate the system's dynamics and impose complex constraints, including collision avoidance. The main contribution is the…
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…
A special class of optimal control problems with complementarity constraints on the control functions is studied. It is shown that such problems possess optimal solutions whenever the underlying control space is a first-order Sobolev space.…
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…
In the context of optimal control, we consider the inverse problem of Lagrangian identification given system dynamics and optimal trajectories. Many of its theoretical and practical aspects are still open. Potential applications are very…
Orthogonal collocation methods are direct approaches for solving optimal control problems (OCP). A high solution accuracy is achieved with few optimization variables, making it more favorable for embedded and real-time NMPC applications.…
This paper details a methodology to transcribe an optimal control problem into a nonlinear program for generation of the trajectories that optimize a given functional by approximating only the highest order derivatives of a given system's…
In this work, we will investigate the question of optimal control for bilinear systems with constrained endpoint. The optimal control will be characterized through a set of unconstrained minimization problems that approximate the former.…
This paper deals with the merging problem of segments of a composite B\'ezier curve, with the endpoints continuity constraints. We present a novel method which is based on the idea of using constrained dual Bernstein polynomial basis (P.…
Nonsmooth composite optimization problems under uncertainty are prevalent in various scientific and engineering applications. We consider risk-neutral composite optimal control problems, where the objective function is the sum of a…
This paper proposes an algorithmic technique for a class of optimal control problems where it is easy to compute a pointwise minimizer of the Hamiltonian associated with every applied control. The algorithm operates in the space of relaxed…
This paper presents a method and an open-source implementation, Bernstein/B\'ezier Optimal Trajectories (BeBOT), for the generation of trajectories for autonomous system operations. The proposed method is based on infinite dimensional…
We consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. We analyze a lifting and decomposition approach into a mixed-integer optimal control problem without…
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…
A local convergence rate is established for an orthogonal collocation method based on Gauss quadrature applied to an unconstrained optimal control problem. If the continuous problem has a sufficiently smooth solution and the Hamiltonian…