2nd Order Dynamics Research Articles

Meta neurons improve spiking neural networks for efficient spatio-temporal learning

Spiking neural networks (SNNs) have incorporated many biologically-plausible structures and learning principles, and hence are playing critical roles in bridging the gap between artificial and natural neural networks. The spike is a sparse membrane-potential signal describing the above-threshold event-based firing and under-threshold dynamic integration, which might be considered an alternative uniformed and efficient way of spatio-temporal information representation and computation. Nowadays, most SNNs have selected the leaky integrated-and-fire (LIF) neuron with 1st-order dynamics as a key feature of membrane potential integration. The LIF neuron is efficient in dynamic coding but still too simple compared to its biological counterpart, which could generate various types of firing patterns. Here we run further by defining some “meta” neuron models that contain 1st- or 2nd-order dynamics and a recovery variable to simulate the hyperpolarization. Both shallow and deep SNNs were used to test the efficiency and flexibility of meta neuron models in various benchmark machine learning tasks, containing spatial learning (e.g., MNIST, Fashion-MNIST, NETtalk, Cifar-10), temporal learning (e.g., TIDigits, TIMIT), and spatio-temporal learning (e.g., N-MNIST). SNNs using these meta neurons were optimized by backpropagation with approximate gradient, and achieved markedly higher spatio-temporal capability without affecting accuracy, compared to those using regular LIF models.

Adaptive robot navigation with collision avoidance subject to 2nd-order uncertain dynamics

This paper considers the problem of robot motion planning in a workspace with obstacles for systems with uncertain 2nd-order dynamics. In particular, we combine closed form potential-based feedback controllers with adaptive control techniques to guarantee the collision-free robot navigation to a predefined goal while compensating for the dynamic model uncertainties. We base our findings on sphere world-based configuration spaces, but extend our results to arbitrary star-shaped environments by using previous results on configuration space transformations. Moreover, we propose an algorithm for extending the control scheme to decentralized multi-robot systems. Finally, extensive simulation results verify the theoretical findings.

Gain scheduled constrained controller for SISO plants

The paper considers design and tuning of simple constrained controllers for plants with dominant 2nd order dynamics. They represent hybrid solutions with dynamics ranging from the relay minimum time systems to linear pole assignment ones. There understanding requires just basic knowledge of the 2nd order trajectories patterns. In contrast to the other known solutions the controllers derived are appropriate also for extremely fast application and easy to tune by a procedure that generalizes the well-known method by Ziegler and Nichols.

Parameter Estimation Algorithms for Hierarchical Distributed Systems

There has been a great deal of research activity in the area of identification of distributed parameter systems over the past two decades. An extensive treatment of off-line schemes ( e.g. , output least squares, estimation error, etc. ) together with a comprehensive survey of the literature can be found in the monograph by Banks and Kunisch [4] . In the case of on-line, or adaptive, schemes, the available literature is less extensive and more recent ( Isermann et al . [7] ). The on-line methods give estimates recursively as the measurements are obtained within the time limit imposed by the sampling period. These include recursive projection algorithm ( Baumeister et al. [5] ), recursive least squares algorithm ( Glentis et al . [6] ), on-line excitation algorithms ( Ludwig et al. [8] ), etc . In this paper an equivalent 2nd order dynamical system is formulated from a given trajectory representing the pattern to be recognised and simulated in order to estimate the parameters for hierarchical distributed systems using 1st and 2nd order dynamics. Recommendations for the best estimation strategy are given.

Saturating Pole Assignment Controller Construction and Geometrical Interpretation in the Phase Plane

This paper deals with the pole assignment controller design under consideration of the control signal saturation. The controller synthesis developed for the double integrator plant is based on the decomposition of the 2nd order dynamics into two particular 1st order movements witch enables, together with the newly introduced geometrical interpretation of closed loop poles, an easy handling of saturation effects and yields a simlpe explicite controller fully respecting the given saturation limits. So, the specification of the closed loop poles can be made quite indipendently from the saturation effect, i.e. they only have to respect different parasitic effects like quantization and measurement noice, neclected dynamics, etc. It gives to the designer a new “degree of freedom” in comparing with the “linear” pole assignment controllers, where this choice has to take into account also the allowed control signal amplitudes.

Identification of processes with direction-dependent dynamic responses

Many processes have dynamic responses which are dependent on the direction in which the response variable is moving. The effects of such nonlinear behaviour on the weighting-function model of the process obtained by crosscorrelation and on the difference-equation model obtained by a generalised least-squares procedure are determined theoretically for a process with 1st-order dynamics perturbed with pseudorandom binary signals. The theory is confirmed by results from a hybrid-computer simulation, and computer-simulated results for processes with 2nd-order dynamics are also presented. Experimental work on two pilot-scale processes with direction-dependent dynamics is reported, and two further examples from the literature are examined.