1,840 research outputs found

    Controlling Chaos Faster

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    Predictive Feedback Control is an easy-to-implement method to stabilize unknown unstable periodic orbits in chaotic dynamical systems. Predictive Feedback Control is severely limited because asymptotic convergence speed decreases with stronger instabilities which in turn are typical for larger target periods, rendering it harder to effectively stabilize periodic orbits of large period. Here, we study stalled chaos control, where the application of control is stalled to make use of the chaotic, uncontrolled dynamics, and introduce an adaptation paradigm to overcome this limitation and speed up convergence. This modified control scheme is not only capable of stabilizing more periodic orbits than the original Predictive Feedback Control but also speeds up convergence for typical chaotic maps, as illustrated in both theory and application. The proposed adaptation scheme provides a way to tune parameters online, yielding a broadly applicable, fast chaos control that converges reliably, even for periodic orbits of large period

    Adapting Predictive Feedback Chaos Control for Optimal Convergence Speed

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    Stabilizing unstable periodic orbits in a chaotic invariant set not only reveals information about its structure but also leads to various interesting applications. For the successful application of a chaos control scheme, convergence speed is of crucial importance. Here we present a predictive feedback chaos control method that adapts a control parameter online to yield optimal asymptotic convergence speed. We study the adaptive control map both analytically and numerically and prove that it converges at least linearly to a value determined by the spectral radius of the control map at the periodic orbit to be stabilized. The method is easy to implement algorithmically and may find applications for adaptive online control of biological and engineering systems.Comment: 21 pages, 6 figure

    Chaotic exploration and learning of locomotion behaviours

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    We present a general and fully dynamic neural system, which exploits intrinsic chaotic dynamics, for the real-time goal-directed exploration and learning of the possible locomotion patterns of an articulated robot of an arbitrary morphology in an unknown environment. The controller is modeled as a network of neural oscillators that are initially coupled only through physical embodiment, and goal-directed exploration of coordinated motor patterns is achieved by chaotic search using adaptive bifurcation. The phase space of the indirectly coupled neural-body-environment system contains multiple transient or permanent self-organized dynamics, each of which is a candidate for a locomotion behavior. The adaptive bifurcation enables the system orbit to wander through various phase-coordinated states, using its intrinsic chaotic dynamics as a driving force, and stabilizes on to one of the states matching the given goal criteria. In order to improve the sustainability of useful transient patterns, sensory homeostasis has been introduced, which results in an increased diversity of motor outputs, thus achieving multiscale exploration. A rhythmic pattern discovered by this process is memorized and sustained by changing the wiring between initially disconnected oscillators using an adaptive synchronization method. Our results show that the novel neurorobotic system is able to create and learn multiple locomotion behaviors for a wide range of body configurations and physical environments and can readapt in realtime after sustaining damage

    Optimal Neuro-Controller Synthesis for Impulse-Driven System

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    This paper presents a new controller design technique for systems driven with impulse inputs. Necessary conditions for optimal impulse control are derived. A neural network structure to solve the resulting equations is presented. The solution concepts are illustrated with a few example problems that exhibit increasing levels of difficulty. Two linear problems-one scalar and one vector-and a benchmark nonlinear problem-Van Der Pol oscillator-are used as case studies. Numerical results show the efficacy of the new solution process for impulse driven systems. Since the theoretical development and the design technique are free from restrictive assumptions, this technique is applicable to many problems in engineering and science

    full-FORCE: A Target-Based Method for Training Recurrent Networks

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    Trained recurrent networks are powerful tools for modeling dynamic neural computations. We present a target-based method for modifying the full connectivity matrix of a recurrent network to train it to perform tasks involving temporally complex input/output transformations. The method introduces a second network during training to provide suitable "target" dynamics useful for performing the task. Because it exploits the full recurrent connectivity, the method produces networks that perform tasks with fewer neurons and greater noise robustness than traditional least-squares (FORCE) approaches. In addition, we show how introducing additional input signals into the target-generating network, which act as task hints, greatly extends the range of tasks that can be learned and provides control over the complexity and nature of the dynamics of the trained, task-performing network.Comment: 20 pages, 8 figure

    Stability and Diversity in Collective Adaptation

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    We derive a class of macroscopic differential equations that describe collective adaptation, starting from a discrete-time stochastic microscopic model. The behavior of each agent is a dynamic balance between adaptation that locally achieves the best action and memory loss that leads to randomized behavior. We show that, although individual agents interact with their environment and other agents in a purely self-interested way, macroscopic behavior can be interpreted as game dynamics. Application to several familiar, explicit game interactions shows that the adaptation dynamics exhibits a diversity of collective behaviors. The simplicity of the assumptions underlying the macroscopic equations suggests that these behaviors should be expected broadly in collective adaptation. We also analyze the adaptation dynamics from an information-theoretic viewpoint and discuss self-organization induced by information flux between agents, giving a novel view of collective adaptation.Comment: 22 pages, 23 figures; updated references, corrected typos, changed conten

    Incremental embodied chaotic exploration of self-organized motor behaviors with proprioceptor adaptation

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    This paper presents a general and fully dynamic embodied artificial neural system, which incrementally explores and learns motor behaviors through an integrated combination of chaotic search and reflex learning. The former uses adaptive bifurcation to exploit the intrinsic chaotic dynamics arising from neuro-body-environment interactions, while the latter is based around proprioceptor adaptation. The overall iterative search process formed from this combination is shown to have a close relationship to evolutionary methods. The architecture developed here allows realtime goal-directed exploration and learning of the possible motor patterns (e.g., for locomotion) of embodied systems of arbitrary morphology. Examples of its successful application to a simple biomechanical model, a simulated swimming robot, and a simulated quadruped robot are given. The tractability of the biomechanical systems allows detailed analysis of the overall dynamics of the search process. This analysis sheds light on the strong parallels with evolutionary search
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