Related papers: Backward Reachability using Integral Quadratic Con…
In this paper we propose a convex programming based method to address a long-standing problem of inner-approximating backward reachable sets of state-constrained polynomial systems subject to time-varying uncertainties. The backward…
The paper presents a novel approach to synthesize robust controllers for nonlinear systems along perturbed trajectories. The approach linearizes the system with respect to a reference trajectory. In contrast to existing methods rooted in…
The theory of integral quadratic constraints (IQCs) allows verification of stability and gain-bound properties of systems containing nonlinear or uncertain elements. Gain bounds often imply exponential stability, but it can be challenging…
The goal of this paper is to assess the robustness of an uncertain linear time-varying (LTV) system on a finite time horizon. The uncertain system is modeled as a connection of a known LTV system and a perturbation. The input/output…
In this work, we propose a tube-based MPC scheme for state- and input-constrained linear systems subject to dynamic uncertainties characterized by dynamic integral quadratic constraints (IQCs). In particular, we extend the framework of…
Determining the reachable set for a given nonlinear control system is crucial for system control and planning. However, computing such a set is impossible if the system's dynamics are not fully known. This paper is motivated by a scenario…
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…
Scaled relative graphs (SRGs) enable graphical analysis and design of nonlinear systems. In this paper, we present a systematic approach for computing both soft and hard SRGs of nonlinear systems using dynamic integral quadratic constraints…
Iterative imperative programs can be considered as infinite-state systems computing over possibly unbounded domains. Studying reachability in these systems is challenging as it requires to deal with an infinite number of states with…
This paper proposes a framework to assess the stability of an ordinary differential equation which is coupled to a 1D-partial differential equation (PDE). The stability theorem is based on a new result on Integral Quadratic Constraints…
A central notion in systems theory is dissipativity, which has been introduced by Jan Willems with the explicit goal of arriving at a fundamental understanding of the stability properties of feedback interconnections. In robust control, the…
Conditions for input-output stability of barrier-based model predictive control of linear systems with linear and convex nonlinear (hard or soft) constraints are established through the construction of integral quadratic constraints (IQCs).…
In this work, we perform safety analysis of linear dynamical systems with uncertainties. Instead of computing a conservative overapproximation of the reachable set, our approach involves computing a statistical approximate reachable set. As…
We present a method for synthesizing controllers to steer trajectories from an initial set to a target set on a finite time horizon. The proposed control synthesis problem is decomposed into two steps. The first step under-approximates the…
We derive computationally tractable formulations of the robust counterparts of convex quadratic and conic quadratic constraints that are concave in matrix-valued uncertain parameters. We do this for a broad range of uncertainty sets. In…
In this paper, we propose a novel approach for computing robust backward reachable sets from noisy data for unknown constrained linear systems subject to bounded disturbances. In particular, we develop an algorithm for obtaining zonotopic…
We present a robust synthesis algorithm for uncertain linear time-varying (LTV) systems on finite horizons. The uncertain system is described as an interconnection of a known LTV system and a perturbation. The input-output behavior of the…
Quadratic constraints (QCs) are widely used to characterize nonlinearities and uncertainties, but generic analytical characterizations can be conservative on bounded domains. This paper develops a framework for constructing verified…
Forward reachability analysis is the predominant approach for verifying reach-avoid properties in neural feedback systems (dynamical systems controlled by neural networks). This dominance stems from the limited scalability of existing…
We propose a control design method for linear time-invariant systems that iteratively learns to satisfy unknown polyhedral state constraints. At each iteration of a repetitive task, the method constructs an estimate of the unknown…