Abstract: A collaborative control method for tracking Lagrangian coherent structures (LCSs) and manifolds on flows employs at least three autonomous sensors each equipped with a local flow sensor for sensing flow in a designated fluid medium, e.g. water or air. A first flow sensor is a tracking sensor while the other sensors are herding sensors for controlling and determining the actions of the tracking sensor. The tracking sensor is positioned with respect to the herding sensors in the fluid medium such that the herding sensors maintain a straddle formation across a boundary; obtaining a local fluid flow velocity measurement from each sensor. A global fluid flow structure is predicted based on the local flow velocity measurements. In a water medium, mobile autonomous underwater flow sensors may be deployed with each tethered to a watersurface craft.

Abstract: A collaborative control method for tracking Lagrangian coherent structures (LCSs) and manifolds on flows employs at least three autonomous underwater vehicles (AUVs) each equipped with a local flow sensor. A first flow sensor is a tracking sensor and the other sensors are herding sensors for controlling and determining the actions of the tracking sensor. The AUVs are deployed in a body of water whereby the tracking sensor is positioned with respect to the herding sensors such that the herding sensors maintain a straddle formation across a boundary. A local flow velocity measurement is obtained from each AUV; and based on the local flow velocity measurements a global flow structure that is useful for plotting an optimal course for a vessel between two or more locations is predicted.

Abstract: A collaborative control method for tracking Lagrangian coherent structures (LCSs) and manifolds on flows employs at least three autonomous sensors each equipped with a local flow sensor for sensing flow in a designated fluid medium, e.g. water or air. A first flow sensor is a tracking sensor while the other sensors are herding sensors for controlling and determining the actions of the tracking sensor. The tracking sensor is positioned with respect to the herding sensors in the fluid medium such that the herding sensors maintain a straddle formation across a boundary; obtaining a local fluid flow velocity measurement from each sensor. A global fluid flow structure is predicted based on the local flow velocity measurements. In a water medium, mobile autonomous underwater flow sensors may be deployed with each tethered to a watersurface craft.

Abstract: A collaborative control method for tracking Lagrangian coherent structures (LCSs) and manifolds on flows employs at least three autonomous underwater vehicles (AUVs) each equipped with a local flow sensor. A first flow sensor is a tracking sensor and the other sensors are herding sensors for controlling and determining the actions of the tracking sensor. The AUVs are deployed in a body of water whereby the tracking sensor is positioned with respect to the herding sensors such that the herding sensors maintain a straddle formation across a boundary. A local flow velocity measurement is obtained from each AUV; and based on the local flow velocity measurements a global flow structure that is useful for plotting an optimal course for a vessel between two or more locations is predicted.

Abstract: A synchronized delay-coupled laser system includes at least two lasers. Each laser includes a laser fiber with a coupling means for coupling to a laser pump. The lasers are coupled to each other by way of two optical fibers. Each laser also includes a self-feedback section. The optical fibers interconnecting the lasers and the self-feedback sections are configured to provide a substantially identical delay time. The lasers may be ring lasers, may be semi-conductor or solid state, and may include components such as a fiber amplifier, a polarization controller, and a nonlinear oscillator. The system includes multiple interconnected lasers and also employ cross-coupling connections.

Abstract: A control method and system are provided to sustain chaos in a nonlinear dynamic system. A sustained transient that is tracked as a system parameter is substantially varied thereby allowing sustained chaotic transients to exist far away from the crisis parameter values. The method includes targeting points near a chaotic transient once the iterates reach a neighborhood of an undesired attractor. Targeting is done so that the natural dynamics of the system would not engage again the iterations and chaotic motion. A brief parameter fluctuation forces the attractor to be a repeller so that a point which lies on the previously existing chaotic transient can be targeted. Consequently, instead of landing on the attractor, the iterations will reach a region of phase space where a chaotic transient is present, causing the chaotic motion to be reexcited.

Abstract: A control method and system are provided to sustain chaos in a nonlinear dynamic system. A sustained transient that is tracked as a system parameter is substantially varied thereby allowing sustained chaotic transients to exist far away from the crisis parameter values. The method includes targeting points near a chaotic transient once the iterates reach a neighborhood of an undesired attractor. Targeting is done so that the natural dynamics of the system would not engage again the iterations and chaotic motion. A brief parameter fluctuation forces the attractor to be a repeller so that a point which lies on the previously existing chaotic transient can be targeted. Consequently, instead of landing on the attractor, the iterations will reach a region of phase space where a chaotic transient is present, causing the chaotic motion to be reexcited.

Abstract: A method and apparatus for accessing anti-phase states in a nonlinear system by globally coupling an array of oscillators. For N number of oscillators in the system, there are (N-1)| anti-phase (AP) states in phase space. AP states exist where each waveform is staggered out-of-phase with every other wave form. The system is controlled between AP states by means of a linear parameter and a hyper-switch. In an out-of-phase (OP) state the orbit remains on a basin boundary between or among AP states. As the linear parameter is decreased to a specific value, the orbit leaves the basin boundary and enters a canonical invariant region (CIR) towards an attractor. Each CIR contains one AP state and one attractor. Once the orbit has reached an attractor within the CIR it shall remain there until the linear parameter is increased and system again becomes unstable.

Abstract: A control system for tracking the operation of a nonlinear system has two parts: a tracking subsystem and a controlling subsystem. The tracking subsystem generates a parametric signal and the controlling subsystem controls and stabilizes the nonlinear system operating under operating conditions corresponding to that parametric signal. The controlling subsystem includes a modulator responsive to the parametric signal and to a feedback signal for producing and applying an input signal to the nonlinear system to cause the nonlinear system to produce an output signal. The controlling subsystem also includes means responsive to the output signal for producing the feedback signal.

Abstract: A method and apparatus for sustaining chaos in a system by using the natural dynamics of the system to redirect flow towards a chaotic region along unstable manifolds of basin boundary saddles by utilizing small, infrequent parameter perturbations. The perturbations are determined based on the location of an unstable state, which is used as a control reference. The location of the unstable state, which is unobservable, is estimated by calculating a theoretical branch connecting the current state of the system to the target unstable state.