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Henk Nijmeijer

Publications and source records attributed to Henk Nijmeijer.

11 recordsLinked to original sources
arXiv2023

Model Validation of a Low-Speed and Reverse Driving Articulated Vehicle

For the autonomous operation of articulated vehicles at distribution centers, accurate positioning of the vehicle is of the utmost importance. Automation of these vehicle poses several challenges, e.g. large swept path, asymmetric steering response, large slide slip angles of non-steered trailer axles and trailer instability while reversing. Therefore, a validated vehicle model is required that accurately and efficiently predicts the states of the vehicle. Unlike forward driving, open-loop validation methods can not be used for reverse driving of articulated vehicles due to their unstable dynamics. This paper proposes an approach to stabilize the unstable pole of the system and compares three vehicle models (kinematic, non-linear single track and multibody dynamics model) against real-world test data obtained from low-speed experiments at a distribution center. It is concluded that single track non-linear model has a better performance in comparison to other models for large articulation angles and reverse driving maneuvers.

cs.RO↗
arXiv2023

Nonlinear Tracking and Rejection using Linear Parameter-Varying Control

The Linear Parameter-Varying (LPV) framework has been introduced with the intention to provide stability and performance guarantees for analysis and controller synthesis for Nonlinear (NL) systems via convex methods. By extending results of the Linear Time-Invariant framework, mainly based on quadratic stability and performance using dissipativity theory, it has been assumed that they generalize tracking and disturbance rejection guarantees for NL systems. However, as has been shown in literature, stability and performance through standard dissipativity is not sufficient in order to satisfy the desired guarantees in case of reference tracking and disturbance rejection for nonlinear systems. We propose to solve this problem by the application of incremental dissipativity, which does ensure these specifications. A novel approach is proposed to synthesize and realize an NL controller which is able to guarantee incremental stability and performance for NL systems via convex optimization using methods from the LPV framework. Through simulations and experiments, the presented method is compared to standard LPV controller designs, showing significant performance improvements.

eess.SY↗
arXiv2019

A Stochastic Model Predictive Control Approach for Driver-Aided Intersection Crossing With Uncertain Driver Time Delay

We investigate the problem of coordinating human-driven vehicles in road intersections without any traffic lights or signs by issuing speed advices. The vehicles in the intersection are assumed to move along an a priori known path and to be connected via vehicle-to-vehicle communication. The challenge arises with the uncertain driver reaction to a speed advice, especially in terms of the driver reaction time delay, as it might lead to unstable system dynamics. For this control problem, a distributed stochastic model predictive control concept is designed which accounts for driver uncertainties. By optimizing over scenarios, which are sequences of independent and identically distributed samples of the uncertainty over the prediction horizon, we can give probabilistic guarantees on constraint satisfaction. Simulation results demonstrate that the scenario-based approach is able to avoid collisions in spite of uncertainty while the non-stochastic baseline controller is not.

math.OC↗
arXiv2017

Synchronization in Networks of Diffusively Coupled Nonlinear Systems: Robustness Against Time-Delays

In this manuscript, we study the problem of robust synchronization in networks of diffusively time-delayed coupled nonlinear systems. In particular, we prove that, under some mild conditions on the input-output dynamics of the systems and the network topology, there always exists a unimodal region in the parameter space (coupling strength versus time-delay), such that if they belong to this region, the systems synchronize. Moreover, we show how this unimodal region scales with the network topology, which, in turn, provides useful insights on how to design the network topology to maximize robustness against time-delays. The results are illustrated by extensive simulation experiments of time-delayed coupled Hindmarsh-Rose neural chaotic oscillators.

eess.SY↗
arXiv2017

On Centroidal Dynamics and Integrability of Average Angular Velocity

In the literature on robotics and multibody dynamics, the concept of average angular velocity has received considerable attention in recent years. We address the question of whether the average angular velocity defines an orientation framethat depends only on the current robot configuration and provide a simple algebraic condition to check whether this holds. In the language of geometric mechanics, this condition corresponds to requiring the flatness of the mechanical connection associated to the robotic system. Here, however, we provide both a reinterpretation and a proof of this result accessible to readers with a background in rigid body kinematics and multibody dynamics but not necessarily acquainted with differential geometry, still providing precise links to the geometric mechanics literature. This should help spreading the algebraic condition beyond the scope of geometric mechanics,contributing to a proper utilization and understanding of the concept of average angular velocity.

cs.RO↗
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↗
arXiv2013

Adaptive Observers and Parameter Estimation for a Class of Systems Nonlinear in the Parameters

We consider the problem of asymptotic reconstruction of the state and parameter values in systems of ordinary differential equations. A solution to this problem is proposed for a class of systems of which the unknowns are allowed to be nonlinearly parameterized functions of state and time. Reconstruction of state and parameter values is based on the concepts of weakly attracting sets and non-uniform convergence and is subjected to persistency of excitation conditions. In absence of nonlinear parametrization the resulting observers reduce to standard estimation schemes. In this respect, the proposed method constitutes a generalization of the conventional canonical adaptive observer design.

math.OC↗
arXiv2010

Observers for canonic models of neural oscillators

We consider the problem of state and parameter estimation for a wide class of nonlinear oscillators. Observable variables are limited to a few components of state vector and an input signal. The problem of state and parameter reconstruction is viewed within the classical framework of observer design. This framework offers computationally-efficient solutions to the problem of state and parameter reconstruction of a system of nonlinear differential equations, provided that these equations are in the so-called adaptive observer canonic form. We show that despite typical neural oscillators being locally observable they are not in the adaptive canonic observer form. Furthermore, we show that no parameter-independent diffeomorphism exists such that the original equations of these models can be transformed into the adaptive canonic observer form. We demonstrate, however, that for the class of Hindmarsh-Rose and FitzHugh-Nagumo models, parameter-dependent coordinate transformations can be used to render these systems into the adaptive observer canonical form. This allows reconstruction, at least partially and up to a (bi)linear transformation, of unknown state and parameter values with exponential rate of convergence. In order to avoid the problem of only partial reconstruction and to deal with more general nonlinear models in which the unknown parameters enter the system nonlinearly, we present a new method for state and parameter reconstruction for these systems. The method combines advantages of standard Lyapunov-based design with more flexible design and analysis techniques based on the non-uniform small-gain theorems. Effectiveness of the method is illustrated with simple numerical examples.

q-bio.NC↗
arXiv2009

Semi-passivity and synchronization of diffusively coupled neuronal oscillators

We discuss synchronization in networks of neuronal oscillators which are interconnected via diffusive coupling, i.e. linearly coupled via gap junctions. In particular, we present sufficient conditions for synchronization in these networks using the theory of semi-passive and passive systems. We show that the conductance-based neuronal models of Hodgkin-Huxley, Morris-Lecar, and the popular reduced models of FitzHugh-Nagumo and Hindmarsh-Rose all satisfy a semi-passivity property, i.e. that is the state trajectories of such a model remain oscillatory but bounded provided that the supplied (electrical) energy is bounded. As a result, for a wide range of coupling configurations, networks of these oscillators are guaranteed to possess ultimately bounded solutions. Moreover, we demonstrate that when the coupling is strong enough the oscillators become synchronized. Our theoretical conclusions are confirmed by computer simulations with coupled \HR and \ML oscillators. Finally we discuss possible "instabilities" in networks of oscillators induced by the diffusive coupling.

nlin.PS↗
arXiv2006

Non-uniform Small-gain Theorems for Systems with Unstable Invariant Sets

We consider the problem of asymptotic convergence to invariant sets in interconnected nonlinear dynamic systems. Standard approaches often require that the invariant sets be uniformly attracting. e.g. stable in the Lyapunov sense. This, however, is neither a necessary requirement, nor is it always useful. Systems may, for instance, be inherently unstable (e.g. intermittent, itinerant, meta-stable) or the problem statement may include requirements that cannot be satisfied with stable solutions. This is often the case in general optimization problems and in nonlinear parameter identification or adaptation. Conventional techniques for these cases rely either on detailed knowledge of the system's vector-fields or require boundeness of its states. The presently proposed method relies only on estimates of the input-output maps and steady-state characteristics. The method requires the possibility of representing the system as an interconnection of a stable, contracting, and an unstable, exploratory part. We illustrate with examples how the method can be applied to problems of analyzing the asymptotic behavior of locally unstable systems as well as to problems of parameter identification and adaptation in the presence of nonlinear parametrizations. The relation of our results to conventional small-gain theorems is discussed.

math.DS↗