Related papers: Computing Probabilistic Controlled Invariant Sets

This paper deals with the computation of the largest robust control invariant sets (RCISs) of constrained nonlinear systems. The proposed approach is based on casting the search for the invariant set as a graph theoretical problem.…

We consider the safety evaluation of discrete time, stochastic systems over a finite horizon. Therefore, we discuss and link probabilistic invariance with reachability as well as reach-avoid problems. We show how to efficiently compute…

We study data-driven computation of probabilistic controlled invariant sets (PCIS) for safety-critical reinforcement learning under unknown dynamics. Assuming a linear MDP model, we use regularized least squares and self-normalized…

Identifying controlled safety invariant sets (CSISs) is essential for safety-critical systems. This paper addresses the problem of computing CSISs for black-box discrete-time systems, where the dynamics are unknown and only limited…

In this paper, we revisit the computation of controlled invariant sets for linear discrete-time systems through a trajectory-based viewpoint. We begin by introducing the notion of convex feasible points, which provides a new…

We introduce a numerically stable reformulation of controllability scoring based on a scaled controllability Gramian, which remains reliably computable even for unstable systems. The resulting optimization problems define dynamics-aware…

In this paper, we consider the computation of controlled invariant sets (CIS) of discrete-time nonlinear control affine systems. We propose an iterative refinement procedure based on polytopic inclusion functions, which is able to…

The problem of optimal motion planing and control is fundamental in robotics. However, this problem is intractable for continuous-time stochastic systems in general and the solution is difficult to approximate if non-instantaneous nonlinear…

We compute probabilistic controlled invariant sets for nonlinear systems using Gaussian process state space models, which are data-driven models that account for unmodeled and unknown nonlinear dynamics. We propose a semidefinite…

In this paper, we study the necessary and sufficient conditions for ensuring the well-posedness of the stochastic singular systems. Moreover, we investigate the stochastic singular linear-quadratic control problems, considering both finite…

We propose a Model Predictive Control (MPC) with a single-step prediction horizon to approximate the solution of infinite horizon optimal control problems with the expected sum of convex stage costs for constrained linear uncertain systems.…

This paper considers discrete-time linear systems with bounded additive disturbances, and studies the convergence properties of the backward reachable sets of robust controlled invariant sets (RCIS). Under a simple condition, we prove that…

In this paper we address the problem of designing receding horizon control algorithms for linear discrete-time systems with parametric uncertainty. We do not consider presence of stochastic forcing or process noise in the system. It is…

We consider controllable linear discrete-time systems with bounded perturbations and present two methods to compute robust controlled invariant sets. The first method tolerates an arbitrarily small constraint violation to compute an…

In this paper, we present Robust Model Predictive Control (MPC) problems with adjustable uncertainty sets. In contrast to standard Robust MPC problems with known uncertainty sets, we treat the uncertainty sets in our problems as additional…

This work presents a data-driven method for approximation of the maximum positively invariant (MPI) set and the maximum controlled invariant (MCI) set for nonlinear dynamical systems. The method only requires the knowledge of a finite…

We characterize the maximum controlled invariant (MCI) set for discrete- as well as continuous-time nonlinear dynamical systems as the solution of an infinite-dimensional linear programming problem. For systems with polynomial dynamics and…

This paper is concerned with the problem of Model Predictive Control and Rolling Horizon Control of discrete-time systems subject to possibly unbounded random noise inputs, while satisfying hard bounds on the control inputs. We use a…

In this paper we develop a novel, discrete-time optimal control framework for mechanical systems with uncertain model parameters. We consider finite-horizon problems where the performance index depends on the statistical moments of the…

Existing results on finite-time model predictive control (MPC) often rely on terminal equality constraint, switching inside one-step region, or terminal cost with short control horizon, leading to limited initial feasibility. This paper…