Implicit Regularization and Momentum Algorithms in Nonlinearly Parameterized Adaptive Control and Prediction.

Stable concurrent learning and control of dynamical systems is the subject of adaptive control. Despite being an established field with many practical applications and a rich theory, much of the development in adaptive control for nonlinear systems revolves around a few key algorithms. By exploiting strong connections between classical adaptive nonlinear control techniques and recent progress in optimization and machine learning, we show that there exists considerable untapped potential in algorithm development for both adaptive nonlinear control and adaptive dynamics prediction.

A Continuous-Time Analysis of Distributed Stochastic Gradient.

We analyze the effect of synchronization on distributed stochastic gradient algorithms. By exploiting an analogy with dynamical models of biological quorum sensing, where synchronization between agents is induced through communication with a common signal, we quantify how synchronization can significantly reduce the magnitude of the noise felt by the individual distributed agents and their spatial mean. This noise reduction is in turn associated with a reduction in the smoothing of the loss function imposed by the stochastic gradient approximation.

Optimal dynamic soaring consists of successive shallow arcs.

Albatrosses can travel a thousand kilometres daily over the oceans. They extract their propulsive energy from horizontal wind shears with a flight strategy called dynamic soaring. While thermal soaring, exploited by birds of prey and sports gliders, consists of simply remaining in updrafts, extracting energy from horizontal winds necessitates redistributing momentum across the wind shear layer, by means of an intricate and dynamic flight manoeuvre.

Symmetries, stability, and control in nonlinear systems and networks.

This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and equivariance with recent convergence analysis tools based on nonlinear contraction theory and virtual dynamical systems. This synergy between structural properties (symmetries) and convergence properties (contraction) is illustrated in the contexts of network motifs arising, for example, in genetic networks, from invariance to environmental symmetries, and from imposing different patterns of synchrony in a network.

Global convergence of quorum-sensing networks.

In many natural synchronization phenomena, communication between individual elements occurs not directly but rather through the environment. One of these instances is bacterial quorum sensing, where bacteria release signaling molecules in the environment which in turn are sensed and used for population coordination. Extending this motivation to a general nonlinear dynamical system context, this paper analyzes synchronization phenomena in networks where communication and coupling between nodes are mediated by shared dynamical quantities, typically provided by the nodes' environment.

Does the brain make waves to improve stability?

In many ways, roboticians and the human brain are faced with the same problem: How does one control movement from a distance? In both cases, delays in the transmission of information play an important role, either because the distances to be covered are long (imagine controlling a robot arm on the moon from a command center on Earth), or because the underlying hardware is slow (nerves transmit information much more slowly than wires, radio waves or light). Delays have a debilitating effect on feedback control systems; causes and effects can bounce back and forth between distant sites, resulting in oscillatory behavior that can grow without bound. Control engineers have developed the concept of wave variables to combat this problem-by mimicking a flexible rod, wave variables constrain movement of the master and slave during the delay, ensuring stable overall behavior [G.

Intrinsic musculoskeletal properties stabilize wiping movements in the spinalized frog.

The mechanical stability properties of hindlimb-hindlimb wiping movements of the spinalized frog were examined. One hindlimb, the wiping limb, was implanted with 12 electromyographic (EMG) electrodes and attached to a robot that both recorded its trajectory and applied brief force perturbations. Cutaneous electrical stimulation was applied to the other hindlimb, the target limb, to evoke the hindlimb-hindlimb wiping reflex.

On partial contraction analysis for coupled nonlinear oscillators.

We describe a simple yet general method to analyze networks of coupled identical nonlinear oscillators and study applications to fast synchronization, locomotion, and schooling. Specifically, we use nonlinear contraction theory to derive exact and global (rather than linearized) results on synchronization, antisynchronization, and oscillator death. The method can be applied to coupled networks of various structures and arbitrary size.