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In this work, we propose a trajectory generation method for robotic systems with contact force constraint based on optimal control and reachability analysis. Normally, the dynamics and constraints of the contact-constrained robot are…

We study the verification problem for closed-loop dynamical systems with neural-network controllers (NNCS). This problem is commonly reduced to computing the set of reachable states. When considering dynamical systems and neural networks in…

In this work, we present a numerical optimal control framework for reachable set computation using \emph{normotopes}, a new set representation as a norm ball with a shaping matrix. In reachable set computations, we expect to continuously…

The proliferation of neural networks in safety-critical applications necessitates the development of effective methods to ensure their safety. This letter presents a novel approach for computing the exact backward reachable sets of neural…

Redundancy is a persistent challenge in Capsule Networks (CapsNet),leading to high computational costs and parameter counts. Although previous works have introduced pruning after the initial capsule layer, dynamic routing's fully connected…

In formal safety verification, many proposed algorithms use parametric set representations and convert the computation of the relevant sets into an optimization problem; consequently, the choice of parameterization and objective function…

Autonomous reconfiguration of agent-based systems is a key challenge in the study of programmable matter, distributed robotics, and molecular self-assembly. While substantial prior work has focused on size-preserving transformations, much…

The gradual decommissioning of fossil fuel-driven power plants, that traditionally provide most operational flexibility in power systems, has led to more frequent grid stability issues. To compensate for the lack of flexible resources,…

Reachability analysis of hybrid systems has been used as a safety verification tool to assess offline whether the state of a system is capable of remaining within a designated safe region for a given time horizon. Although it has been…

Deploying autonomous systems in safety critical settings necessitates methods to verify their safety properties. This is challenging because real-world systems may be subject to disturbances that affect their performance, but are unknown a…

Mixed-monotone systems are separable via a decomposition function into increasing and decreasing components, and this decomposition function allows for embedding the system dynamics in a higher-order monotone embedding system. Embedding the…

In this paper we propose an improvement for flowpipe-construction-based reachability analysis techniques for hybrid systems. Such methods apply iterative successor computations to pave the reachable region of the state space by state sets…

Shaping the reachable set of a dynamical system is a fundamental challenge in control design, with direct implications for both performance and safety. This paper considers the problem of selecting the optimal input matrix for a linear…

We present a method of computing backward reachable sets for nonlinear discrete-time control systems possessing continuous symmetries. The starting point is a dynamic game formulation of reachability analysis where control inputs aim to…

The last decade witnessed an explosion in the availability of data for operations research applications. Motivated by this growing availability, we propose a novel schema for utilizing data to design uncertainty sets for robust optimization…

Neural Networks (NNs) can provide major empirical performance improvements for closed-loop systems, but they also introduce challenges in formally analyzing those systems' safety properties. In particular, this work focuses on estimating…

Reachability analysis aims at identifying states reachable by a system within a given time horizon. This task is known to be computationally expensive for linear hybrid systems. Reachability analysis works by iteratively applying continuous…

Recent research in decision theoretic planning has focussed on making the solution of Markov decision processes (MDPs) more feasible. We develop a family of algorithms for structured reachability analysis of MDPs that are suitable when an…

Digital control has become increasingly prevalent in modern systems, making continuous-time plants controlled by discrete-time (digital) controllers ubiquitous and crucial across industries, including aerospace, automotive, and…

In this work, we propose a new framework for reachable set computation through continuous evolution of a set of parameters and offsets which define a parametope, through the intersection of constraints. This results in a dynamical approach…