Related papers: Piecewise semi-ellipsoidal control invariant sets
We introduce several algebraic structures related to handlebody-knots, including $G$-families of biquandles, partially multiplicative biquandles and group decomposable biquandles. These structures can be used to color the semiarcs in…
We study properties and applications of various circuit imbalance measures associated with linear spaces. These measures describe possible ratios between nonzero entries of support-minimal nonzero vectors of the space. The fractional…
The intrinsic nature of a problem usually suggests a first suitable method to deal with it. Unfortunately, the apparent ease of application of these initial approaches may make their possible flaws seem to be inherent to the problem and…
Piecewise constant control approximation provides a practical framework for designing numerical schemes of continuous-time control problems. We analyze the accuracy of such approximations for extended mean field control (MFC) problems,…
Computing the autotopism group of a partial Latin rectangle can be performed in a variety of ways. This pilot study has two aims: (a) to compare these methods experimentally, and (b) to identify the design goals one should have in mind for…
This paper deals with the computation of polytopic invariant sets for polynomial dynamical systems. An invariant set of a dynamical system is a subset of the state space such that if the state of the system belongs to the set at a given…
The paper deals with finite element approximations of elliptic Dirichlet boundary control problems posed on two-dimensional polygonal domains. Error estimates are derived for the approximation of the control and the state variables. Special…
It is well-known that the convex and concave envelope of a multilinear polynomial over a box are polyhedral functions. Exponential-sized extended and projected formulations for these envelopes are also known. We consider the convexification…
Sufficiently accurate finite state models, also called symbolic models or discrete abstractions, allow one to apply fully automated methods, originally developed for purely discrete systems, to formally reason about continuous and hybrid…
Various control schemes rely on a solution of a convex optimization problem involving a particular robust quadratic constraint, which can be reformulated as a linear matrix inequality using the well-known $\mathcal{S}$-lemma. However, the…
The variation distance closure of an exponential family with a convex set of canonical parameters is described, assuming no regularity conditions. The tools are the concepts of convex core of a measure and extension of an exponential…
Sequential Convex Programming (SCP) has recently gained significant popularity as an effective method for solving optimal control problems and has been successfully applied in several different domains. However, the theoretical analysis of…
We develop an indirect-adaptive model predictive control algorithm for uncertain linear systems subject to constraints. The system is modeled as a polytopic linear parameter varying system where the convex combination vector is constant but…
We study a control system resembling a singularly perturbed system whose variables are decomposed into groups that change their values with rates of different orders of magnitude. We establish that the slow trajectories of this system are…
We devise and analyze a reliable and efficient a posteriori error estimator for a semilinear control-constrained optimal control problem in two and three dimensional Lipschitz, but not necessarily convex, polytopal domains. We consider a…
The smooth piecewise-linear models cover a wide range of applications nowadays. Basically, there are two classes of them: models are transitional or hyperbolic according to their behaviour at the phase-transition zones. This study explored…
Learning-based control methods for industrial processes leverage the repetitive nature of the underlying process to learn optimal inputs for the system. While many works focus on linear systems, real-world problems involve nonlinear…
A polyhedral convex set optimization problem is given by a set-valued objective mapping from the $n$-dimensional to the $q$-dimensional Euclidean space whose graph is a convex polyhedron. This problem can be seen as the most elementary…
We consider the problem of projecting a convex set onto a subspace, or equivalently formulated, the problem of computing a set obtained by applying a linear mapping to a convex feasible set. This includes the problem of approximating convex…
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…