arXiv subjects

Jean-Jacques E. Slotine

Publications and source records attributed to Jean-Jacques E. Slotine.

50 records · Page 3Linked to original sources

arXiv2008

Cooperative Robot Control and Concurrent Synchronization of Lagrangian Systems

Concurrent synchronization is a regime where diverse groups of fully synchronized dynamic systems stably coexist. We study global exponential synchronization and concurrent synchronization in the context of Lagrangian systems control. In a network constructed by adding diffusive couplings to robot manipulators or mobile robots, a decentralized tracking control law globally exponentially synchronizes an arbitrary number of robots, and represents a generalization of the average consensus problem. Exact nonlinear stability guarantees and synchronization conditions are derived by contraction analysis. The proposed decentralized strategy is further extended to adaptive synchronization and partial-state coupling.

math.OC↗

arXiv2006

Examples of Synchronization in Discrete Chaotic Systems

This paper presents an application of partial contraction analysis to the study of global synchronization in discrete chaotic systems. Explicit sufficient conditions on the coupling strength of networks of discrete oscillators are derived. Numerical examples and applications to simple systems are presented. Previous researches have shown numerically that the systems under study, when arranged in a network, exhibits rich and complex patterns that can dynamically change in response to variations in the environment. We show how this ``adaptation'' process strongly depends on the coupling characteristics of the network. Other potential applications of synchronized chaotic oscillators are discussed.

nlin.CD↗

arXiv2006

Stability and Robustness Analysis of Nonlinear Systems via Contraction Metrics and SOS Programming

Contraction analysis is a stability theory for nonlinear systems where stability is defined incrementally between two arbitrary trajectories. It provides an alternative framework in which to study uncertain interconnections or systems with external inputs, where it offers several significant advantages when compared with traditional Lyapunov analysis. Contraction-based methods are particularly useful for analyzing systems with uncertain parameters and for proving synchronization properties of nonlinear oscillators. Existence of a contraction metric for a given system is a necessary and sufficient condition for global exponential convergence of system trajectories. For systems with polynomial or rational dynamics, the search for contraction metrics can be made fully algorithmic through the use of convex optimization and sum of squares (SOS) programming. The search process is made computationally tractable by relaxing matrix definiteness constraints, whose feasibility indicate existence of a contraction metric, into SOS constraints on polynomial matrices. We illustrate the results through examples from the literature, emphasizing the advantages and contrasting the differences between the contraction approach and traditional Lyapunov techniques.

math.OC↗

arXiv2005

Contraction Analysis of Time-Delayed Communications Using Simplified Wave Variables

We study stability of interacting nonlinear systems with time-delayed communications, using contraction theory and a simplified wave variable design inspired by robotic teleoperation. We show that contraction is preserved through specific time-delayed feedback communications, and that this property is independent of the values of the delays. The approach is then applied to group cooperation with linear protocols, where it shown that synchronization can be made robust to arbitrary time delays.

nlin.PS↗

arXiv2005

Higher-Order Nonlinear Contraction Analysis

Nonlinear contraction theory is a comparatively recent dynamic control system design tool based on an exact differential analysis of convergence, in essence converting a nonlinear stability problem into a linear time-varying stability problem. Contraction analysis relies on finding a suitable metric to study a generally nonlinear and time-varying system. This paper shows that the computation of the metric may be largely simplified or indeed avoided altogether by extending the exact differential analysis to the higher-order dynamics of the nonlinear system. Simple applications in economics, classical mechanics, and process control are described.

nlin.PS↗

arXiv2004

Where To Go and How To Go: a Theoretical Study of Different Leader Roles in Networked Systems

This letter studies synchronization conditions for distributed dynamic networks with different types of leaders. The role of a leader specifying a desired global state trajectory through local interactions (the power leader) has long been recognized and modeled. This paper introduces the complementary notion of a knowledge leader holding information on the target dynamics, which is propagated to the entire network through local adaptation mechanisms. Knowledge-based leader-followers networks have many analogs in biology, e.g., in evolutionary processes and disease propagation. Different types of leaders can co-exist in the same network.

physics.bio-ph↗

arXiv2004

Adaptive Synchronization in Coupled Dynamic Networks

This paper studies synchronization in coupled nonlinear dynamic networks with unknown parameters. Adaptation can be added to one or several elements in the network, while preserving the global synchronization conditions derived in previously. This implies that new nodes can be added to the network without prior knowledge of the individual dynamics, and that nodes in an existing network have the ability to recover dynamic information if temporarily lost. In addition, when the individual elements feature sufficiently rich stable dynamics, as e.g. in the case of oscillators, then adaptation actually leads to an exact estimation of the unknown parameters. Different kinds of leaders are also discussed in this context - one type of leader can specify overall trajectories for the network, while another can concurrently specify dynamic parameters.

nlin.AO↗

arXiv2004

Contraction Analysis of Nonlinear Distributed Systems

Contraction theory is a recently developed dynamic analysis and nonlinear control system design tool based on an exact differential analysis of convergence. This paper extends contraction theory to local and global stability analysis of important classes of nonlinear distributed dynamics, such as convection-diffusion-reaction processes, Lagrangian and Hamilton-Jacobi dynamics, and optimal controllers and observers. The Hamilton-Jacobi-Bellman controller and a similar optimal nonlinear observer design are studied. Explicit stability conditions are given, which extend the well-known conditions on controllability and observability Grammians for linear time-varying systems. Stability of the Hamilton-Jacobi dynamics is assessed by evaluating the Hessian of the system state along system trajectories. In contrast to stability proofs based on energy dissipation,this principle allows to conclude on stability of energy-based systems that are excited by time-varying inputs. In this context, contraction can be regarded as describing new variational conservation laws and the stability of entropy producing processes.

math-ph↗

arXiv2004

Discrete Nonlinear Observers for Inertial Navigation

We derive an exact deterministic nonlinear observer to compute the continuous state of an inertial navigation system based on partial discrete measurements, the so-called strapdown problem. Nonlinear contraction is used as the main analysis tool, and the hierarchical structure of the system physics is sytematically exploited. The paper also discusses the use of nonlinear measurements, such as distances to time-varying reference points.

math.OC↗

arXiv2003

K-Winners-Take-All Computation with Neural Oscillators

Artificial spike-based computation, inspired by models of computation in the central nervous system, may present significant performance advantages over traditional methods for specific types of large scale problems. This paper describes very simple network architectures for k-winners-take-all and soft-winner-take-all computation using neural oscillators. Fast convergence is achieved from arbitrary initial conditions, which makes the networks particularly suitable to track time-varying inputs.

q-bio.NC↗

arXiv2003

Fast Computation with Neural Oscillators

Artificial spike-based computation, inspired by models of computations in the central nervous system, may present significant performance advantages over traditional methods for specific types of large scale problems. In this paper, we study new models for two common instances of such computation, winner-take-all and coincidence detection. In both cases, very fast convergence is achieved independent of initial conditions, and network complexity is linear in the number of inputs.

q-bio.NC↗

arXiv2003

Universal quantum interfaces

To observe or control a quantum system, one must interact with it via an interface. This letter exhibits simple universal quantum interfaces--quantum input/output ports consisting of a single two-state system or quantum bit that interacts with the system to be observed or controlled. It is shown that under very general conditions the ability to observe and control the quantum bit on its own implies the ability to observe and control the system itself. The interface can also be used as a quantum communication channel, and multiple quantum systems can be connected by interfaces to become an efficient universal quantum computer. Experimental realizations are proposed, and implications for controllability, observability, and quantum information processing are explored.

quant-ph↗

arXiv1999

Quantum feedback with weak measurements

The problem of feedback control of quantum systems by means of weak measurements is investigated in detail. When weak measurements are made on a set of identical quantum systems, the single-system density matrix can be determined to a high degree of accuracy while affecting each system only slightly. If this information is fed back into the systems by coherent operations, the single-system density matrix can be made to undergo an arbitrary nonlinear dynamics, including for example a dynamics governed by a nonlinear Schrödinger equation. We investigate the implications of such nonlinear quantum dynamics for various problems in quantum control and quantum information theory, including quantum computation. The nonlinear dynamics induced by weak quantum feedback could be used to create a novel form of quantum chaos in which the time evolution of the single-system wave function depends sensitively on initial conditions.

quant-ph↗

arXiv1997

Analog quantum error correction

Quantum error-correction routines are developed for continuous quantum variables such as position and momentum. The result of such analog quantum error correction is the construction of composite continuous quantum variables that are largely immune to the effects of noise and decoherence.

quant-ph↗