arXiv subjects

Nathan van de Wouw

Publications and source records attributed to Nathan van de Wouw.

61 records · Page 4Linked to original sources

arXiv2022

From Low to High Order Motion Planners: Safe Robot Navigation using Motion Prediction and Reference Governor

Safe navigation around obstacles is a fundamental challenge for highly dynamic robots. The state-of-the-art approach for adapting simple reference path planners to complex robot dynamics using trajectory optimization and tracking control is brittle and requires significant replanning cycles. In this paper, we introduce a novel feedback motion planning framework that extends the applicability of low-order (e.g. position-/velocity-controlled) reference motion planners to high-order (e.g., acceleration-/jerk-controlled) robot models using motion prediction and reference governors. We use predicted robot motion range for safety assessment and establish a bidirectional interface between high-level planning and low-level control via a reference governor. We describe the generic fundamental building blocks of our feedback motion planning framework and give specific example constructions for motion control, prediction, and reference planning. We prove the correctness of our planning framework and demonstrate its performance in numerical simulations. We conclude that accurate motion prediction is crucial for closing the gap between high-level planning and low-level control.

cs.RO↗

arXiv2021

Real-time Fault Estimation for a Class of Discrete-Time Linear Parameter-Varying Systems

Estimating and detecting faults is crucial in ensuring safe and efficient automated systems. In the presence of disturbances, noise or varying system dynamics, such estimation is even more challenging. To address this challenge, this article proposes a novel filter to estimate multiple fault signals for a class of discrete-time linear parameter-varying (LPV) systems. The design of such a filter is formulated as an optimization problem and is solved recursively, while the system dynamics may vary over time. Conditions for existence and detectability of the fault are introduced and the problem is formulated and solved using the quadratic programming framework. We further propose an approximate scheme that can be arbitrarily precise while it enjoys an analytical solution, which supports real-time implementation. The method is illustrated and validated on an automated vehicle's lateral dynamics, which is a practically relevant example for LPV systems. The results show that the estimation filter can decouple unknown disturbances and known or measurable parameter variations in the dynamics while estimating the unknown fault.

math.OC↗

arXiv2021

Finite Horizon Privacy of Stochastic Dynamical Systems: A Synthesis Framework for Dependent Gaussian Mechanisms

We address the problem of synthesizing distorting mechanisms that maximize privacy of stochastic dynamical systems. Information about the system state is obtained through sensor measurements. This data is transmitted to a remote station through an unsecured/public communication network. We aim to keep part of the system state private (a private output); however, because the network is unsecured, adversaries might access sensor data and input signals, which can be used to estimate private outputs. To prevent an accurate estimation, we pass sensor data and input signals through a distorting (privacy-preserving) mechanism before transmission, and send the distorted data to the trusted user. These mechanisms consist of a coordinate transformation and additive dependent Gaussian vectors. We formulate the synthesis of the distorting mechanisms as a convex program, where we minimize the mutual information (our privacy metric) between an arbitrarily large sequence of private outputs and the disclosed distorted data for desired distortion levels -- how different actual and distorted data are allowed to be.

cs.CR↗

arXiv2020

Improving mechanical ventilation for patient care through repetitive control

Mechanical ventilators sustain life of patients that are unable to breathe (sufficiently) on their own. The aim of this paper is to improve pressure tracking performance of mechanical ventilators for a wide variety of sedated patients. This is achieved by utilizing the repetitive nature of sedated ventilation through repetitive control. A systematic design procedure of a repetitive controller for mechanical ventilation is presented. Thereafter, the controller is implemented in an experimental setup showing superior tracking performance for a variety of patients.

eess.SY↗

arXiv2014

Distance function design and Lyapunov techniques for the stability of hybrid trajectories

The comparison between time-varying hybrid trajectories is crucial for tracking, observer design and synchronisation problems for hybrid systems with state-triggered jumps. In this paper, a systematic way of designing an appropriate distance function is proposed that can be used for this purpose. The so-called "peaking phenomenon", which occurs when using the Euclidean distance to compare two hybrid trajectories, is circumvented by taking the hybrid nature of the system explicitly into account in the design of the distance function. Based on the proposed distance function, we define the stability of a trajectory of a hybrid system with state-triggered jumps and present sufficient Lyapunov-type conditions for stability of a hybrid trajectory. A constructive design method for the distance function is presented for hybrid systems with affine flow and jump maps and a jump set that is a hyperplane. For this case, the mentioned Lyapunov-type stability conditions can be verified using linear matrix conditions. Finally, for this class of systems, we present a tracking controller that asymptotically stabilises a given hybrid reference trajectory, and we illustrate our results with examples.

math.DS↗

arXiv2014

Sensitivity analysis of hybrid systems with state jumps with application to trajectory tracking

This paper addresses the sensitivity analysis for hybrid systems with discontinuous (jumping) state trajectories. We consider state-triggered jumps in the state evolution, potentially accompanied by mode switching in the control vector field as well. For a given trajectory with state jumps, we show how to construct an approximation of a nearby perturbed trajectory corresponding to a small variation of the initial condition and input. A major complication in the construction of such an approximation is that, in general, the jump times corresponding to a nearby perturbed trajectory are not equal to those of the nominal one. The main contribution of this work is the development of a notion of error to clarify in which sense the approximate trajectory is, at each instant of time, a firstorder approximation of the perturbed trajectory. This notion of error naturally finds application in the (local) tracking problem of a time-varying reference trajectory of a hybrid system. To illustrate the possible use of this new error definition in the context of trajectory tracking, we outline how the standard linear trajectory tracking control for nonlinear systems -based on linear quadratic regulator (LQR) theory to compute the optimal feedback gain- could be generalized for hybrid systems.

math.OC↗

arXiv2012

Backstepping controller synthesis and characterizations of incremental stability

Incremental stability is a property of dynamical and control systems, requiring the uniform asymptotic stability of every trajectory, rather than that of an equilibrium point or a particular time-varying trajectory. Similarly to stability, Lyapunov functions and contraction metrics play important roles in the study of incremental stability. In this paper, we provide characterizations and descriptions of incremental stability in terms of existence of coordinate-invariant notions of incremental Lyapunov functions and contraction metrics, respectively. Most design techniques providing controllers rendering control systems incrementally stable have two main drawbacks: they can only be applied to control systems in either parametric-strict-feedback or strict-feedback form, and they require these control systems to be smooth. In this paper, we propose a design technique that is applicable to larger classes of (not necessarily smooth) control systems. Moreover, we propose a recursive way of constructing contraction metrics (for smooth control systems) and incremental Lyapunov functions which have been identified as a key tool enabling the construction of finite abstractions of nonlinear control systems, the approximation of stochastic hybrid systems, source-code model checking for nonlinear dynamical systems and so on. The effectiveness of the proposed results in this paper is illustrated by synthesizing a controller rendering a non-smooth control system incrementally stable as well as constructing its finite abstraction, using the computed incremental Lyapunov function.

math.OC↗