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We propose an approach to trajectory optimization for piecewise polynomial systems based on the recently proposed graphs of convex sets framework. We instantiate the framework with a convex relaxation of optimal control based on occupation…
Approximate dynamic programming (ADP) faces challenges in dealing with constraints in control problems. Model predictive control (MPC) is, in comparison, well-known for its accommodation of constraints and stability guarantees, although its…
The DPG method with optimal test functions for solving linear quadratic optimal control problems with control constraints is studied. We prove existence of a unique optimal solution of the nonlinear discrete problem and characterize it…
Structural symmetries of linear dynamical systems can be exploited for decoupling the dynamics and reducing the computational complexity of the controller implementation. However, in practical applications, inexact structural symmetries…
We give a new computational method to obtain symmetries of ordinary differential equations. The proposed approach appears as an extension of a recent algorithm to compute variational symmetries of optimal control problems [Comput. Methods…
The problem of finding sparse solutions to underdetermined systems of linear equations arises in several applications (e.g. signal and image processing, compressive sensing, statistical inference). A standard tool for dealing with sparse…
This paper addresses an open problem in the area of linear quadratic optimal control. We consider the regular, infinite-horizon, stability-modulo-a-subspace, indefinite linear quadratic problem under the assumption that the dynamics are…
We study the problem of feedback control for skew-symmetric and skew-Hamiltonian transfer functions using skew-symmetric controllers. This extends work of Helmke, et al., who studied static symmetric feedback control of symmetric and…
We study a signature-driven numerical scheme to solve multi-dimensional linear-quadratic (LQ) stochastic control problems. Using that linear signature functionals are dense in the natural class of admissible controls, we show that our…
In this paper, we develop a unified framework for studying constrained robust optimal control problems with adjustable uncertainty sets. In contrast to standard constrained robust optimal control problems with known uncertainty sets, we…
Here an original idea is suggested to prove the existence of optimal control for some types of non- linear problems. The obtained results can be considered as individual existence theorems (in some sense).
Conservation of symmetries plays a crucial role in both classical and quantum simulations of many-body systems, enabling the tracking of states with specific symmetry properties and leading to substantial reductions in the number of…
The continuous-time analysis of existing iterative algorithms for optimization has a long history. This work proposes a novel continuous-time control-theoretic framework for equality-constrained optimization. The key idea is to design a…
This paper introduces a continuous-time constrained nonlinear control scheme which implements a model predictive control strategy as a continuous-time dynamic system. The approach is based on the idea that the solution of the optimal…
This paper investigates the asymptotic behavior of the solution to a linear-quadratic stochastic optimal control problems. The so-called probability cell problem is introduced the first time. It serves as the probability interpretation of…
Many applications require solving non-linear control problems that are classically not well behaved. This paper develops a simple and efficient chattering algorithm that learns near optimal decision policies through an open-loop feedback…
We consider nonlinear optimal control problems (OCPs) for which all problem data are polynomial. In the first part of the paper, we review how occupation measures can be used to approximate pointwise the optimal value function of a given…
This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of…
Moment optimization techniques have been recently proposed to solve globally various classes of optimal control problems. As those methods return truncated moment sequences of occupation measures, this paper explores a numeric method for…
An emerging and challenging area in mathematical control theory called Ensemble Control encompasses a class of problems that involves the guidance of an uncountably infinite collection of structurally identical dynamical systems, which are…