Related papers: Approximating Reachable Sets for Neural Network ba…
Adaptive methods are popular within the control literature due to the flexibility and forgiveness they offer in the area of modelling. Neural network adaptive control is favorable specifically for the powerful nature of the machine learning…
Safe navigation in cluttered environments is an important challenge for autonomous systems. Robots navigating through obstacle ridden scenarios need to be able to navigate safely in the presence of obstacles, goals, and ego objects of…
In real world applications, uncertain parameters are the rule rather than the exception. We present a reachability algorithm for linear systems with uncertain parameters and inputs using set propagation of polynomial zonotopes. In contrast…
To address the computational challenges of Model Predictive Control (MPC), recent research has studied using imitation learning to approximate MPC with a computationally efficient Deep Neural Network (DNN). However, this introduces a common…
In this paper, we present a geometric framework for the reachability analysis of attitude control systems. We model the attitude dynamics on the product manifold $\mathrm{SO}(3) \times \mathbb{R}^3$ and introduce a novel parametrized family…
Applying neural networks as controllers in dynamical systems has shown great promises. However, it is critical yet challenging to verify the safety of such control systems with neural-network controllers in the loop. Previous methods for…
Neural networks (NN) have been successfully applied to approximate various types of complex control laws, resulting in low-complexity NN-based controllers that are fast to evaluate. However, when approximating control laws using NN,…
We present a real-time-capable set-based framework for closed-loop predictive control of autonomous systems using tools from computational geometry, dynamic programming, and convex optimization. The control architecture relies on the…
Extracting physical laws from observation data is a central challenge in many diverse areas of science and engineering. We propose Optimal Control Neural Networks (OCN) to learn the laws of vector fields in dynamical systems, with no…
Deep convolutional neural networks have been widely employed as an effective technique to handle complex and practical problems. However, one of the fundamental problems is the lack of formal methods to analyze their behavior. To address…
As neural networks (NNs) become more prevalent in safety-critical applications such as control of vehicles, there is a growing need to certify that systems with NN components are safe. This paper presents a set of backward reachability…
Traditional learning approaches proposed for controlling quadrotors or helicopters have focused on improving performance for specific trajectories by iteratively improving upon a nominal controller, for example learning from demonstrations,…
Approximating the set of reachable states of a dynamical system is an algorithmic yet mathematically rigorous way to reason about its safety. Although progress has been made in the development of efficient algorithms for affine dynamical…
Reachable sets of nonlinear control systems can in general only be approximated numerically, and these approximations are typically very expensive to compute. In this paper, we explore a strategy for choosing the temporal and spatial…
Fast feedback control and safety guarantees are essential in modern robotics. We present an approach that achieves both by combining novel robust model predictive control (MPC) with function approximation via (deep) neural networks (NNs).…
We consider the design of fast and reliable neural network (NN)-based approximations of traditional stabilizing controllers for linear systems with polytopic uncertainty, including control laws with variable structure and those based on a…
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…
This work proposes a robust data-driven predictive control approach for unknown nonlinear systems in the presence of bounded process and measurement noise. Data-driven reachable sets are employed for the controller design instead of using…
In this paper, we propose a Transformer-based framework for approximating solutions to infinite-dimensional optimization problems: calculus of variations problems and optimal control problems. Our approach leverages offline training on data…
The Neural Network (NN), as a black-box function approximator, has been considered in many control and robotics applications. However, difficulties in verifying the overall system safety in the presence of uncertainties hinder the…