Specific State Space Research Articles

PUMA: Deep Metric Imitation Learning for Stable Motion Primitives

Imitation learning (IL) facilitates intuitive robotic programming. However, ensuring the reliability of learned behaviors remains a challenge. In the context of reaching motions, a robot should consistently reach its goal, regardless of its initial conditions. To meet this requirement, IL methods often employ specialized function approximators that guarantee this property by construction. Although effective, these approaches come with some limitations: 1) they are typically restricted in the range of motions they can model, resulting in suboptimal IL capabilities, and 2) they require explicit extensions to account for the geometry of motions that consider orientations. To address these challenges, we introduce a novel stability loss function that does not constrain the function approximator's architecture and enables learning policies that yield accurate results. Furthermore, it is not restricted to a specific state space geometry; therefore, it can easily incorporate the geometry of the robot's state space. Proof of the stability properties induced by this loss is provided and the method is empirically validated in various settings. These settings include Euclidean and non‐Euclidean state spaces, as well as first‐order and second‐order motions, both in simulation and with real robots. More details about the experimental results can be found at https://youtu.be/ZWKLGntCI6w.

Universality Classes and Information-Theoretic Measures of Complexity via Group Entropies

We introduce a class of information measures based on group entropies, allowing us to describe the information-theoretical properties of complex systems. These entropic measures are nonadditive, and are mathematically deduced from a series of natural axioms. In addition, we require extensivity in order to ensure that our information measures are meaningful. The entropic measures proposed are suitably defined for describing universality classes of complex systems, each characterized by a specific state space growth rate function.

Application of multi-output Gaussian process regression for remaining useful life prediction of light emitting diodes

Light-emitting diodes (LEDs) are the preferred technology today when it comes to lighting both for indoor and outdoor applications, predominantly due to their high efficiency, environmental resilience and prolonged lifetime. Given their widespread use, there is a need to quickly qualify them and accurately predict the reliability of these devices. Due to their inherently long operational life, most LED reliability studies involve the use of degradation tests and application of filter-based prognostic techniques for dynamic update of degradation model parameters and estimation of the remaining useful life (RUL). Although they are in general very effective, the main drawback is the need for a specific state-space model that describes the degradation. In many cases, LED degradation trends are affected by a multitude of unknown factors such as unidentified failure modes, varying operational conditions, process and measurement variance, and environmental fluctuations. These variable factors that are hard to control tend to complicate the selection of a suitable state-space model and in some cases; there may not be a single model that could be used for the entire lifespan of the device. If the degradation patterns of LEDs under test deviate from the state space models, the resulting predictions will be inaccurate. This paper introduces a prognostics-based qualification method using a multi-output Gaussian process regression (MO-GPR) and applies it to RUL prediction of high-power LED devices. The main idea here is to use MO-GPR to learn the correlation between similar degradation patterns from multiple similar components under test and thereby, bypass the need for a specific state space model using available data of past units tested to failure.

Tensor network subspace identification of polynomial state space models

This article introduces a tensor network subspace algorithm for the identification of specific polynomial state space models. The polynomial nonlinearity in the state space model is completely written in terms of a tensor network, thus avoiding the curse of dimensionality. We also prove how the block Hankel data matrices in the subspace method can be exactly represented by low rank tensor networks, reducing the computational and storage complexity significantly. The performance and accuracy of our subspace identification algorithm are illustrated by experiments, showing that our tensor network implementation identifies a seventh degree polynomial state space model around 20 times faster than the standard matrix implementation before the latter fails due to insufficient memory. The proposed algorithm is also robust with respect to noise and therefore applicable to practical systems.

Toward Efficient Cascading Outage Simulation and Probability Analysis in Power Systems

This paper addresses how to improve the computational efficiency and estimation reliability in cascading outage analysis. Under mild assumptions, we first formulate a cascading outage as a Markov model with specific state space and transition probability by leveraging the Markov property of cascading outages. Such a model provides a rigorous formulation that allows analytic investigation on cascading outages in the framework of standard mathematical statistics. Then, we derive a sequential importance sampling (SIS)-based strategy for cascading outage simulations and blackout risk analysis with solid theoretical foundation. Numerical experiments manifest that the proposed SIS strategy can significantly enhance the efficiency of simulations and reduce the estimation variance of blackout probability/risk compared with the traditional Monte Carlo simulation strategy.

Delay-Dependent Stability Analysis of TS Fuzzy Switched Time-Delay Systems

This paper proposes a new approach to deal with the problem of stability under arbitrary switching of continuous-time switched time-delay systems represented by TS fuzzy models. The considered class of systems, initially described by delayed differential equations, is first put under a specific state space representation, called arrow form matrix. Then, by constructing a pseudo-overvaluing system, common to all fuzzy submodels and relative to a regular vector norm, we can obtain sufficient asymptotic stability conditions through the application of Borne and Gentina practical stability criterion. The stability criterion, hence obtained, is algebraic, is easy to use, and permits avoiding the problem of existence of a common Lyapunov-Krasovskii functional, considered as a difficult task even for some low-order linear switched systems. Finally, three numerical examples are given to show the effectiveness of the proposed method.

New stability conditions for nonlinear time varying delay systems

In this paper, new practical stability conditions for a class of nonlinear time varying delay systems are proposed. The study is based on the use of a specific state space description, known as the Benrejeb characteristic arrow form matrix, and aggregation techniques to obtain delay-dependent stability conditions. Application of this method to delayed Lurie–Postnikov nonlinear systems is given. Illustrative examples are presented to show the effectiveness of the proposed approach.

Modeling and Identification of the Restoring Force of a Marine Riser

The purpose of this paper is to provide a novel model to characterize the nonlinear restoring force of a marine vertical riser by using position-and-velocity-dependent polynomials. This model permits the obtaining of a specific state space representation—via the Liénard transformation—for the design of state observers that identify the structural parameters of vertical risers. The main results presented here are: (i) an approximation of the nonlinear restoring force by means of polynomials and its incorporation into a distributed parameter (DP) model, (ii) the transformation of the DP model into a Liénard system and (iii) an analysis of its observability and identifiability properties.

Mapping the dynamic repertoire of the resting brain

The resting state dynamics of the brain shows robust features of spatiotemporal pattern formation but the actual nature of its time evolution remains unclear. Computational models propose specific state space organization which defines the dynamic repertoire of the resting brain. Nevertheless, methods devoted to the characterization of the organization of brain state space from empirical data still lack and thus preclude comparison of the hypothetical dynamical repertoire of the brain with the actual one. We propose here an algorithm based on set oriented approach of dynamical system to extract a coarse-grained organization of brain state space on the basis of EEG signals. We use it for comparing the organization of the state space of large-scale simulation of brain dynamics with actual brain dynamics of resting activity in healthy subjects. The dynamical skeleton obtained for both simulated brain dynamics and EEG data depicts similar structures. The skeleton comprised chains of macro-states that are compatible with current interpretations of brain functioning as series of metastable states. Moreover, macro-scale dynamics depicts correlation features that differentiate them from random dynamics. We here propose a procedure for the extraction and characterization of brain dynamics at a macro-scale level. It allows for the comparison between models of brain dynamics and empirical measurements and leads to the definition of an effective coarse-grained dynamical skeleton of spatiotemporal brain dynamics.

Control Lyapunov Function Design by Cancelling Input Singularity

If one can find a control Lyapunov function (CLF) for a given nonlinear system, the control input stabilizing the system can be easily obtained. To find a CLF, the time derivative of an energy function should be negative definite. This procedure frequently requires a control input which is a rational function or includes an inverse function. The control input is not defined on the specific state-space where the denominator of the rational function is equal to 0 or the inverse function does not exist. In this region with singularities, the trajectory of the control system cannot be generated, which is one of the most important reasons why it is hard to make the origin of a nonlinear system be globally asymptotically stable. In this paper, we propose a smooth control law ensuring the globally asymptotic stability by means of cancelling the singularity in the control input.

Perturbation propagation in random and evolved Boolean networks

In this paper, we investigate the propagation of perturbations in Boolean networks by evaluating the Derrida plot and its modifications. We show that even small random Boolean networks agree well with the predictions of the annealed approximation, but nonrandom networks show a very different behaviour. We focus on networks that were evolved for high dynamical robustness. The most important conclusion is that the simple distinction between frozen, critical and chaotic networks is no longer useful, since such evolved networks can display the properties of all three types of networks. Furthermore, we evaluate a simplified empirical network and show how its specific state space properties are reflected in the modified Derrida plots.

Some Results on Dynamics of Special Double-Loop ΣΔ-Modulators

The dynamic behaviour of a specific two-dimensional state space model with discontinuity is studied. This model arises from the study of double-loop ΣΔ-modulators with constant input. Using mathematical tools we explain certain simulation results, and some properties are derived. Simulations based on time-varying input are also provided.