Discontinuity induced bifurcations of non-hyperbolic cycles in nonsmooth systems

We analyse three codimension-two bifurcations occurring in nonsmooth systems, when a non-hyperbolic cycle (fold, flip, and Neimark-Sacker cases, both in continuous- and discrete-time) interacts with one of the discontinuity boundaries characterising the system's dynamics. Rather than aiming at a complete unfolding of the three cases, which would require specific assumptions on both the class of nonsmooth system and the geometry of the involved boundary, we concentrate on the geometric features that are common to all scenarios. We show that, at a generic intersection between the smooth and discontinuity induced bifurcation curves, a third curve generically emanates tangentially to the former. This is the discontinuity induced bifurcation curve of the secondary invariant set (the other cycle, the double-period cycle, or the torus, respectively) involved in the smooth bifurcation. The result can be explained intuitively, but its validity is proven here rigorously under very general conditions. Three examples from different fields of science and engineering are also reported

Combined Global and Local Search for the Falsification of Hybrid Systems

In this paper we solve the problem of finding a trajectory that shows that a given hybrid dynamical system with deterministic evolution leaves a given set of states considered to be safe. The algorithm combines local with global search for achieving both efficiency and global convergence. In local search, it exploits derivatives for efficient computation. Unlike other methods for falsification of hybrid systems with deterministic evolution, we do not restrict our search to trajectories of a certain bounded length but search for error trajectories of arbitrary length

Task-Oriented Active Sensing via Action Entropy Minimization

This work is licensed under a Creative Commons Attribution 4.0 International License.In active sensing, sensing actions are typically chosen to minimize the uncertainty of the state according to some information-theoretic measure such as entropy, conditional entropy, mutual information, etc. This is reasonable for applications where the goal is to obtain information. However, when the information about the state is used to perform a task, minimizing state uncertainty may not lead to sensing actions that provide the information that is most useful to the task. This is because the uncertainty in some subspace of the state space could have more impact on the performance of the task than others, and this dependence can vary at different stages of the task. One way to combine task, uncertainty, and sensing, is to model the problem as a sequential decision making problem under uncertainty. Unfortunately, the solutions to these problems are computationally expensive. This paper presents a new task-oriented active sensing scheme, where the task is taken into account in sensing action selection by choosing sensing actions that minimize the uncertainty in future task-related actions instead of state uncertainty. The proposed method is validated via simulations

A general stability criterion for switched linear systems having stable and unstable subsystems

We report conditions on a switching signal that guarantee that solutions of a switched linear systems converge asymptotically to zero. These conditions are apply to continuous, discrete-time and hybrid switched linear systems, both those having stable subsystems and mixtures of stable and unstable subsystems

Changes in postural syntax characterize sensory modulation and natural variation of C. elegans locomotion

Locomotion is driven by shape changes coordinated by the nervous system through time; thus, enumerating an animal's complete repertoire of shape transitions would provide a basis for a comprehensive understanding of locomotor behaviour. Here we introduce a discrete representation of behaviour in the nematode C. elegans. At each point in time, the worm's posture is approximated by its closest matching template from a set of 90 postures and locomotion is represented as sequences of postures. The frequency distribution of postural sequences is heavy-tailed with a core of frequent behaviours and a much larger set of rarely used behaviours. Responses to optogenetic and environmental stimuli can be quantified as changes in postural syntax: worms show different preferences for different sequences of postures drawn from the same set of templates. A discrete representation of behaviour will enable the use of methods developed for other kinds of discrete data in bioinformatics and language processing to be harnessed for the study of behaviour

Application of the Actor-Critic Architecture to Functional Electrical Stimulation Control of a Human Arm

Clinical tests have shown that the dynamics of a human arm, controlled using Functional Electrical Stimulation (FES), can vary significantly between and during trials. In this paper, we study the application of the actor-critic architecture, with neural networks for the both the actor and the critic, as a controller that can adapt to these changing dynamics of a human arm. Development and tests were done in simulation using a planar arm model and Hill-based muscle dynamics. We begin by training it using a Proportional Derivative (PD) controller as a supervisor. We then make clinically relevant changes to the dynamics of the arm and test the actor-critic’s ability to adapt without supervision in a reasonable number of episodes. Finally, we devise methods for achieving both rapid learning and long-term stability

Suppressor analysis of the clk-1 mutants of Caenorhabditis elegans

clk-1 encodes a hydroxylase that is necessary for ubiquinone (UQ) biosynthesis. clk-1 mutants do not synthesize UQ, but instead accumulate the precursor demethoxyubiquinone (DMQ). When fed on bacteria that synthesize UQ the mutants are viable but display slow development, behaviours and aging. However, they arrest development when fed on UQ synthesis-deficient bacteria. I have taken a genetic suppressor approach to investigate the causes of the various phenotypes as well as of the dietary requirements of the clk-1 mutants.We identified two classes of mutants that suppress the defecation phenotypes of clk-1. All of these "dsc" mutants suppress the lengthened cycle of clk-1. Class I mutants also restore the ability to react normally to changes in temperature whereas the Class II mutants do not. The characterization of the Class I mutants suggests that part of the phenotype of clk-1 is due to an alteration of lipid metabolism, likely the level of lipid or lipoprotein oxidation. dsc-4 encodes the worm homolog of the Microsomal Triglyceride Transfer Protein (MTP), a protein required for the formation of low density lipoproteins (LDL) in vertebrates, and whose absence in people leads to abetalipoproteinemia. dsc-3 appears to be allelic to tat-2, which encodes a type IV P-type ATPase that is related to a family of human aminophospholipid transporters that includes ATP8B1/FIC1, whose inactivation results in cholestatic liver disease. dsc-3 and dsc-4 appear to affect distinct aspects of lipid metabolism. A general link between the Class II mutants and clk-1 remains elusive. dsc-1, a Class II gene, encodes a paired-like homeodomain transcription factor that is necessary for the GABA sensitivity of enteric muscles.We also identified 9 clk-1(e2519)-specific suppressors, which suppress most Clk phenotypes, including their requirement for dietary UQ. Our analysis of these suppressors reveals that it is the lack of UQ rather than the presence of DMQ that is responsible for most phenotypes. In addition, they allowed us to show that most Clk phenotypes can be uncoupled from each other. We cloned six suppressors and all encode missense tRNA(Glu) suppressor genes. To my knowledge, these represent the first missense tRNA suppressors identified in any metazoan

Creating a Reinforcement Learning Controller for Functional Electrical Stimulation of a Human Arm

Clinical tests have shown that the dynamics of a human arm, controlled using Functional Electrical Stimulation (FES), can vary significantly between and during trials. In this paper, we study the application of Reinforcement Learning to create a controller that can adapt to thesechanging dynamics of a human arm. Development and tests were done in simulation using a two-dimensional arm model and Hill-based muscle dynamics. An actor-critic architecture is used with artificial neural networks for both the actor and the critic. We begin by training it using a Proportional Derivative (PD) controller as a supervisor. We then make clinically relevant changesto the dynamics of the arm and test the actor-critic’s ability to adapt without supervision in a reasonable number of episodes