BIOMECHANICAL STABILITY ANALYSIS OF THE λ-MODEL CONTROLLING ONE JOINT

Predicting Perturbed Human Arm Movements in a Neuro-Musculoskeletal Model to Investigate the Muscular Force Response

Human movement is generated by a dynamic interplay between the nervous system, the biomechanical structures, and the environment. To investigate this interaction, we propose a neuro-musculoskeletal model of human goal-directed arm movements. Using this model, we simulated static perturbations of the inertia and damping properties of the arm, as well as dynamic torque perturbations for one-degree-of freedom movements around the elbow joint. The controller consists of a feed-forward motor command and feedback based on muscle fiber length and contraction velocity representing short-latency (25 ms) or long-latency (50 ms) stretch reflexes as the first neuronal responses elicited by an external perturbation. To determine the open-loop control signal, we parameterized the control signal resulting in a piecewise constant stimulation over time for each muscle. Interestingly, such an intermittent open-loop signal results in a smooth movement that is close to experimental observations. So, our model can generate the unperturbed point-to-point movement solely by the feed-forward command. The feedback only contributed to the stimulation in perturbed movements. We found that the relative contribution of this feedback is small compared to the feed-forward control and that the characteristics of the musculoskeletal system create an immediate and beneficial reaction to the investigated perturbations. The novelty of these findings is (1) the reproduction of static as well as dynamic perturbation experiments in one neuro-musculoskeletal model with only one set of basic parameters. This allows to investigate the model's neuro-muscular response to the perturbations that-at least to some degree-represent stereotypical interactions with the environment; (2) the demonstration that in feed-forward driven movements the muscle characteristics generate a mechanical response with zero-time delay which helps to compensate for the perturbations; (3) that this model provides enough biomechanical detail to allow for the prediction of internal forces, including joint loads and muscle-bone contact forces which are relevant in ergonomics and for the development of assistive devices but cannot be observed in experiments.

INDIRECT ADAPTIVE CONTROL OF UNKNOWN MULTI VARIABLE NONLINEAR SYSTEMS WITH PARAMETRIC AND DYNAMIC UNCERTAINTIES USING A NEW NEURO-FUZZY SYSTEM DESCRIPTION

The indirect adaptive regulation of unknown nonlinear dynamical systems with multiple inputs and states (MIMS) under the presence of dynamic and parameter uncertainties, is considered in this paper. The method is based on a new neuro-fuzzy dynamical systems description, which uses the fuzzy partitioning of an underlying fuzzy systems outputs and high order neural networks (HONN's) associated with the centers of these partitions. Every high order neural network approximates a group of fuzzy rules associated with each center. The indirect regulation is achieved by first identifying the system around the current operation point, and then using its parameters to device the control law. Weight updating laws for the involved HONN's are provided, which guarantee that, under the presence of both parameter and dynamic uncertainties, both the identification error and the system states reach zero, while keeping all signals in the closed loop bounded. The control signal is constructed to be valid for both square and non square systems by using a pseudoinverse, in Moore-Penrose sense. The existence of the control signal is always assured by employing a novel method of parameter hopping instead of the conventional projection method. The applicability is tested on well known benchmarks.

Weak resonant double Hopf bifurcations in an inertial four-neuron model with time delay

In this paper, a four-neuron delayed bidirectional associative memory (BAM) model with inertia is considered. Weak resonant double Hopf bifurcations are completely analyzed in the parameter space of the coupling weight and the coupling delay by the perturbation-incremental scheme (PIS). Numerical simulations are given for justifying the theoretical results. To the best of our knowledge, the paper is the first one to introduce inertia to a four-neuron delayed system and clarify the relationship between system parameters and dynamical behaviors.

BURSTING NEAR BAUTIN BIFURCATION IN A NEURAL NETWORK WITH DELAY COUPLING

Bursting behavior is one of the most important firing activities of neural system and plays an important role in signal encoding and transmission. In the present paper, a neural network with delay coupling is modeled to investigate the generation mechanism of bursting behavior. The Andronov-Hopf bifurcation is firstly studied and then the degenerated Andronov-Hopf bifurcation, namely Bautin bifurcation, is analyzed with the external input varying. Classifying dynamics in the neighborhood of the Bautin bifurcation, we obtain the bifurcation sets where the supercritical/subcritical Andronov-Hopf, or the fold limit cycle bifurcation may happen in the system under consideration. For a periodic disturbance occurring in the neighborhood of the Bautin bifurcation, it is seen that the Andronov-Hopf bifurcation and fold limit cycle bifurcation may lead to the transition from quiescent state to firing activities. Complex bursting phenomena, including Hopf/Hopf bursting, Hopf/Fold cycle bursting, SubHopf/Hopf bursting and SubHopf/Fold cycle bursting are found in the firing area. The results show that the dynamical properties of different burstings are related to the dynamical behaviors derived from the bifurcations of the system. Finally, it is seen that the bursting disappears but the periodic spiking appears in the delayed neural network for large values of delay.