Related papers: Reachability analysis for piecewise affine systems…
Neural networks (NNs) are now routinely implemented on systems that must operate in uncertain environments, but the tools for formally analyzing how this uncertainty propagates to NN outputs are not yet commonplace. Computing tight bounds…
The control of large-scale cyber-physical systems requires optimal distributed policies relying solely on limited communication with neighboring agents. However, computing stabilizing controllers for nonlinear systems while optimizing…
This paper studies the approximation property of ReLU neural networks (NNs) to piecewise constant functions with unknown interfaces in bounded regions in $\mathbb{R}^d$. Under the assumption that the discontinuity interface $\Gamma$ may be…
An almost periodic piecewise linear system (APPLS) is a type of piecewise linear system where the system cyclically switches between different modes, each with an uncertain but bounded dwell-time. Process regulation, especially disturbance…
This paper aims to synthesize a reachability controller for an unknown dynamical system. We first learn the unknown system using Gaussian processes and the (probabilistic) guarantee on the learned model. Then we use the funnel-based…
Neural networks (NNs) are increasingly applied in safety-critical systems such as autonomous vehicles. However, they are fragile and are often ill-behaved. Consequently, their behaviors should undergo rigorous guarantees before deployment…
While reachability analysis is one of the most promising approaches for formal verification of dynamic systems, a major disadvantage preventing a more widespread application is the requirement to manually tune algorithm parameters such as…
We study the optimal control of multiple-input and multiple-output dynamical systems via the design of neural network-based controllers with stability and output tracking guarantees. While neural network-based nonlinear controllers have…
We propose a scalable reachability-based framework for probabilistic, data-driven safety verification of unknown nonlinear dynamics. We use Koopman theory with a neural network (NN) lifting function to learn an approximate linear…
In this paper, we propose a framework for performing state space exploration of closed loop control systems. Our approach involves approximating sensitivity and a newly introduced notion of inverse sensitivity by a neural network. We show…
We propose a simple safety filter design for stochastic discrete-time systems based on piecewise affine probabilistic control barrier functions, providing an appealing balance between modeling flexibility and computational complexity. Exact…
Model inversion is a fundamental technique in feedforward control. Unstable inverse models present a challenge in that useful feedforward control trajectories cannot be generated by directly propagating them. Stable inversion is a process…
In this paper, a method is presented to synthesize neural network controllers such that the feedback system of plant and controller is dissipative, certifying performance requirements such as L2 gain bounds. The class of plants considered…
We investigate the complexity of the reachability problem for (deep) neural networks: does it compute valid output given some valid input? It was recently claimed that the problem is NP-complete for general neural networks and conjunctive…
We study the following reachability problem for piecewise affine maps: Given two vectors $\mathbf{s}, \mathbf{t} \in \mathbb{Q}^d$ and a piecewise affine map $f \colon \mathbb{Q}^d\rightarrow \mathbb{Q}^d$, does there exist $n\in…
Deep neural networks are known to be fragile to small adversarial perturbations. This issue becomes more critical when a neural network is interconnected with a physical system in a closed loop. In this paper, we show how to combine recent…
In exchange for large quantities of data and processing power, deep neural networks have yielded models that provide state of the art predication capabilities in many fields. However, a lack of strong guarantees on their behaviour have…
In this work we provide a computationally tractable procedure for designing affine control policies, applied to constrained, discrete-time, partially observable, linear systems subject to set bounded disturbances, stochastic noise and…
Under a regularity assumption we prove that reachability in fixed time for nonlinear control systems is robust under control sampling.
In this paper we propose a stochastic model predictive control (MPC) algorithm for linear discrete-time systems affected by possibly unbounded additive disturbances and subject to probabilistic constraints. Constraints are treated in…