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In this paper, a feedback control law based on two time‐scale assignment and state extension is implemented for the nonlinear non‐minimum phase dynamics of three degree‐of‐freedom autonomo...

Objective:We assessed the delay times in the interaction between the autonomic regulatory loop of Heart Rate Variability (HRV) and autonomic regulatory loop of photoplethysmographic waveform variability (PPGV), showing low-frequency oscillations.Material and Methods:In eight healthy subjects aged 25–30 years (3 male, 5 female), we studied at rest (in a supine position) the simultaneously recorded two-hour signals of RR intervals (RRIs) chain and finger photoplethysmogram (PPG). To extract the low-frequency components of RRIs and PPG signal, associated with the low-frequency oscillations in HRV and PPGV with a frequency of about 0.1 Hz, we filtered RRIs and PPG with a bandpass 0.05-0.15 Hz filter. We used a method for the detection of coupling between oscillatory systems, based on the construction of predictive models of instantaneous phase dynamics, for the estimation of delay times in the interaction between the studied regulatory loops.Results:Averaged value of delay time in coupling from the regulatory loop of HRV to the loop of PPGV was 0.9±0.4 seconds (mean ± standard error of the means) and averaged value of delay time in coupling from PPGV to HRV was 4.1±1.1 seconds.Conclusion:Analysis of two-hour experimental time series of healthy subjects revealed the presence of delay times in the interaction between regulatory loops of HRV and PPGV. Estimated delay time in coupling regulatory loops from HRV to PPGV was about one second or even less, while the delay time in coupling from PPGV to HRV was about several seconds. The difference in delay times is explained by the fact that PPGV to HRV response is mediated through the autonomic nervous system (baroreflex), while the HRV to PPGV response is mediated mechanically via cardiac output.

The problem of interval estimation of the time delay of the coupling between oscillatory systems from observed time series is considered. It is shown that the known asymptotic estimates based on the empirical model in the form of a system of first-order phase oscillators and the maximum likelihood formalism can lead to false inferences of the value of the time delay in two typical situations: 1) nonlinear low-dimensional systems whose phases are well-determined but, as a result of significant amplitude fluctuations, the phase approximation is insufficient for describing the dynamics and 2) systems whose phases are defined not quite well because of too large amplitude fluctuations. A method for empirical diagnostics of problematic situations and its modification (coarse estimation) providing a low probability of false inferences in these situation are proposed. The efficiency of the diagnostic criterion and coarse estimation suggested is demonstrated on reference systems with different dynamic properties (linear stochastic oscillators, van der Pol oscillators, and Ressler and Lorenz chaotic systems).

First order phase reduced model is a good approximation of the dynamics of forced nonlinear oscillators near its limit cycle. The phase evolution is determined by the unforced frequency, the forcing term, and the phase response curve (PRC). Such models arise in biological oscillations such as in circadian rhythm, neural signaling, heart beat, etc. This technical note focuses on the phase regulation of the circadian rhythm using light intensity as the input. Though the model is simple, the circle topology of the state space needs to be carefully addressed. The most common entrainment method is to use a periodic input, such as in our daily light-dark cycle. We obtain the complete stable entrainment condition based on the entraiment input and the PRC. Motivated by the jet-lag problem, we also consider the minimum time entrainment control to achieve a specified phase shift. Application of the Pontryagin Minimum Principle leads to an efficient solution strategy for the optimal control, without solving the two-point boundary value problem. The optimal control may be further represented as a feedback control law based on the current and desired phases. Our analysis allows the answer to questions such as: When traveling from New York to Paris, is it faster to use light to shift the phase forward by 6 hours or delay the phase by 18 hours? The answer is somewhat counter-intuitive—delaying by 18 hours requires less time. The general answer depends on the light intensity level and the shape of the PRC. PRCs for human and Drosophila from the literature are used to illustrate the results.

In multi-modular process architectures with independent but interacting subsystems, identification may not be the first choice at hand for closed loop control. A robust relay-based PID autotuning strategy is presented and validated on a quadruple tank system with non-minimum phase dynamics. The controller ensures a specified closed loop robustness, which is of great benefit to the overall performance. The experimental results suggest that the proposed method fulfils the robustness requirement and performs well in various operating conditions of the testbench.

Rider models are employed to gain insight into bicycle rider steering behaviour and to improve characteristic properties of bicycles. In this paper, stability properties as well as basic dynamic characteristics of the passive (uncontrolled) bicycle-rider system and consequences on the rider control modelling are addressed. In particular, the unstable motion of the system at low velocities and bandwidth limitations caused by non-minimum phase dynamics are emphasized. To analyse the effectiveness of the steering torque and the lean torque as possible rider's inputs to control the dynamics of the bicycle, a controllability analysis of the bicycle-rider system has been performed. It turns out that lean torque input, in contrast to steering torque input, has marginal impact on the dynamics of the system. Finally, a bicycle rider control model considering human rider properties is presented, and its capabilities are demonstrated by performing a curve entering manoeuvre.

This paper proposes distributed control laws for formations of swimming robotic fish generating antiphase sinusoidal body waves. The control laws are inspired by the mathematical model for the hydrodynamics of schools of cruising fish, which reveals that fish swimming in diamond-shape formations with synchronized antiphase body waves can benefit greatly from energy saving. The phase dynamics of the body waves of the robotic fish are modeled by coupled Kuramoto oscillators and the stability analysis for the phase dynamics are carried out for coupling topologies corresponding to diamond-shape formations. It is proven that the body waves can be synchronized in specific antiphase patterns. Simulations and experiments further validate the effectiveness of the proposed control laws.

Single-track vehicles such as motorcycles or bicycles provide an agile mobile platform. Control of motorcycles is challenging due to its underactuation and non-minimum phase dynamics properties. In this paper, we present a maneuver regulation control design for autonomous motorcycles. The maneuver regulation control guides the vehicle to follow a desired path and automatically tunes the desired velocity. We extend the motorcycle dynamics by including the coupled longitudinal/lateral tire/road interaction. We then design a velocity field for regulating vehicle maneuvers. The velocity field-based maneuver regulation design is integrated with the previously established trajectory tracking controller for motorcycle systems. Simulation results are presented to illustrate the maneuver regulation design.

We study a learning and recalling model of phase patterns in a two- or three-coupled BVP oscillators system with a time delay δ. The coupling strengths are modulated by the Hebbian learning rule. Assuming the first-order approximation, we calculate the optimal condition of δ for exact recall by applying the phase dynamics theory. When α = 0, where α represents the coupling from activator to inhibitor, the correlation between the learning and the retrieval phase depends on δ. When α = 1, exact recall is achieved independent of δ. The results can be explained by the phase dynamics theory.

The statistics of the instantaneous phase of oscillations in dynamic systems with a noisy limit cycle is compared to the statistics of the instantaneous phase of oscillations in dynamic systems with a spiral chaotic attractor. Simulation of the phase dynamics of chaotic self-sustained oscillations by a Wiener process is considered. The results provided by various methods of determination of the instantaneous phase are analyzed.

This paper proposes a new feed-forward control strategy for a plant with non-minimum phase dynamics. A Feed-Forward controller is very essential for controlling plants with time-varying reference signals. However, designing this type of controller is a non-trivial problem in case the plant dynamics is non-minimum-phase. This is because, this controller design involves the concept of inversion of the plant model and inverse of a non-minimum-phase plant model is unstable or non-causal. For this problem, usually an approximate inversion of a plant model is applied. An approach with corrected-approximate-inverse (CAI) method is available for feed forward controller design. After analyzing the results and discussion of this CAI technique, it is seen that although it seems to be working perfectly for small duration of time but its performance is unsatisfactory in case of large span of time. Therefore, in this paper, a new feed-forward control strategy has been designed to erase the above said problem. This method has adopted a simple version of an internal plant-model structure in its time domain. The fixed-structure feed forward controller that is constructed using this method is usually a linear amalgamation of a reference trajectory and its time-derivatives with suitable weighting factors. This control strategy has been verified with appropriate simulation results applied to a studied plant and results are compared with that of the CAI technique.

Chronotaxic systems represent deterministic nonautonomous oscillatory systems which are capable of resisting continuous external perturbations while having a complex time-dependent dynamics. Until their recent introduction in \emph{Phys. Rev. Lett.} \textbf{111}, 024101 (2013) chronotaxic systems had often been treated as stochastic, inappropriately, and the deterministic component had been ignored. While the previous work addressed the case of the decoupled amplitude and phase dynamics, in this paper we develop a generalized theory of chronotaxic systems where such decoupling is not required. The theory presented is based on the concept of a time-dependent point attractor or a driven steady state and on the contraction theory of dynamical systems. This simplifies the analysis of chronotaxic systems and makes possible the identification of chronotaxic systems with time-varying parameters. All types of chronotaxic dynamics are classified and their properties are discussed using the nonautonomous Poincar\'e oscillator as an example. We demonstrate that these types differ in their transient dynamics towards a driven steady state and according to their response to external perturbations. Various possible realizations of chronotaxic systems are discussed, including systems with temporal chronotaxicity and interacting chronotaxic systems., Comment: 9 pages, 8 figures

We apply retrospective cost adaptive control (RCAC) to a linearized aircraft dynamics with an unknown transition to nonminimum-phase (NMP) dynamics. In prior work, RCAC was used for command-following with unknown NMP zeros. In this work we extend those results to command following for cases where the dynamics transition from minimum-phase to NMP. We use system identification techniques to identify the NMP zero, and use this information in RCAC. We consider both full-state feedback and output feedback, and in both cases we follow step commands with transitioning dynamics. We first consider the case where RCAC is unaware of the change and NMP zero identification is unavailable to RCAC. We then assume that NMP zero information is available to RCAC from system identification.

The simplified models of neural networks based on biophysical Hodgkin–Huxley neurons are studied with a focus on coherent-phase dynamics. In our approach, each neuron is considered as a nonlinear oscillator, and collective dynamics of a mesoscopic network of neural oscillators are studied using the methods of nonlinear dynamics. We explore the mechanisms for synchrony, clustering and their breakup in the synaptic parameter space and discuss implications to temporal aspects of neural-information processing.

Based on neurophysiological evidence, studies modeling human locomotion system have shown that a bipedal walking is generated by mutual entrainments between the oscillatory activities of a central pattern generator (CPG) and a Body. The walking model could well reproduce human walking. However, it has been also shown that time delay in the sensorimotor loop destabilizes mutual entrainments, which leads a failure to walk. Recently, theoretical studies have discovered a phenomenon in which a CPG can induce the phase of its oscillatory activity to shift forward according to time delay. This self-organized phenomenon overcoming time delay is called “flexible-phase locking”. Then, theoretical studies have hypothesized that one of the essential mechanisms to yield of flexible-phase locking is a stable limit cycle of CPG activity. This study demonstrates the hypothesis in walking models through computer simulation by replacing the CPG model with the one having different oscillation properties.

This paper introduces an extension of the Internal Model Control algorithm for efficient disturbance rejection. The approach is based on ideas from model based predictive control and diophantine equation derivation. As an illustration of the power of the extension, an example from the process industry is borrowed, namely a drum boiler. The process is challenging for control since it has an integrator and non-minimum phase dynamics. The performance of the proposed extension is compared against nominal IMC design and PID. The simulation results suggest that the proposed algorithm outperforms the other implementations in terms of effective disturbance rejections.

International audience; Motivated by neuroscience applications, we rigorously derive the phase dynamics of an ensemble of interconnected nonlinear oscillators under the effect of a proportional feedback. We individuate the critical parameters determining the validity of the phase approximation and derive bounds on the accuracy of the latter in reproducing the behavior of the original system. We use these results to study the existence of oscillating phase-locked solutions in the original oscillator model.

In this paper we consider limits of achievable performance for a class of scramjet-powered hypersonic aircraft. A simple 3-DOF model is used to illustrate the main ideas. The vehicle is characterized by unstable and non-minimum phase dynamics. The limitations introduced by the right-half plane zero and actuator saturation on achievable trajectories has been examined. In addition, we examine several vehicle configurations and consider fundamental limitations for the plant and closed loop performance. An optimization methodology that explicitly incorporates performance specifications into the design of vehicle is explored. The advantages of such an approach is illustrated with examples.

In this paper, we propose a framework for generating coordinated periodic movements of robotic systems with external inputs. We developed an adaptive pattern generator model that is composed of a two-factor observation model with a style parameter and phase dynamics with a phase variable. The style parameter controls the spatial patterns of the generated trajectories, and the phase variable controls its temporal profiles. To validate the effectiveness of our proposed method, we applied it to a simulated humanoid model to perform biped walking behaviors coordinated with observed walking patterns and the environment. The robot successfully performed stable biped walking behaviors even when the style of the observed walking pattern and the period were suddenly changed.

Phase models are a powerful method to quantify the coupled dynamics of nonlinear oscillators from measured data. We use two phase modeling methods to quantify the dynamics of pairs of coupled electrochemical oscillators, based on the phases of the two oscillators independently and the phase difference, respectively. We discuss the benefits of the two-dimensional approach relative to the one-dimensional approach using phase difference. We quantify the dependence of the coupling functions on the coupling magnitude and coupling time delay. We show differences in synchronization predictions of the two models using a toy model. We show that the two-dimensional approach reveals behavior not detected by the one-dimensional model in a driven experimental oscillator. This approach is broadly applicable to quantify interactions between nonlinear oscillators, especially where intrinsic oscillator sensitivity and coupling evolve with time.

We develop an effective description of noise-induced oscillations based on deterministic phase dynamics. The phase equation is constructed to exhibit correct frequency and distribution density of noise-induced oscillations. In the simplest one-dimensional case the effective phase equation is obtained analytically, whereas for more complex situations a simple method of data processing is suggested. As an application an effective coupling function is constructed that quantitatively describes periodically forced noise-induced oscillations., This paper has been withdrawn by the author due to errors in Fig. 3 and faulty conclusions drawn from Fig. 4

In this paper a control configuration for inverse-response processes is presented. It results in a Smith-type predictor scheme that aims to put the non-minimum phase dynamics out of the feedback loop. The design is carried out analytically by solving an H ∞ weighted optimization problem assuming a second order stable process with one positive zero. The performance of the proposed control configuration is compared by simulation with two different approaches to show its applicability.

This work concerns output trajectory tracking for the McDonnell Dougglas YAV68B Harrier VSTOL aircraft. This system can perform three distinct flight modes, and is modelled with a Lagrangian nonlinear hybrid non-minimum phase dynamics. Output tracking is solved using classical input/output linearization scheme associated to an internal dynamics stable inversion for each flight mode dynamics. The performance of the global switched control law is discussed and validated through simulation tests.

A phased-array two-dimensional CPLL array is introduced. The phase dynamics are analyzed and an approximate solution are obtained using the method of continuum phase. By detuning the free-running frequencies of edge elements, linear phase distribution can be achieved among the array. An experimental CPLL array circuit is also shown and tested, proceedings.

We address an important problem in neurophysiology concerning the characterization of coupled neural oscillators from experimental data. The approach employs the formal mathematical description of the dynamics of weakly coupled oscillators by the phase model, and the recently developed methods for identification of directionality of coupling and estimation of coupling delays. We study neuron oscillator models with synaptic coupling and diffusively coupled ensembles of neurons, incorporating time delays in coupling. Results of directionality analysis closely reflect the coupling strength asymmetry. In comparison with the standard cross-correlation analysis, the phase dynamics based time delays estimation provides more accurate estimates of coupling delays

A model-based robust control approach is proposed that significantly improves imaging bandwidth for the dynamic mode atomic force microscopy. A model for cantilever oscillation amplitude and phase dynamics is derived and used for the control design. In particular, the control design is based on a linearized model and robust H(∞) control theory. This design yields a significant improvement when compared to the conventional proportional-integral designs and verified by experiments.

We study the dynamics of an array of Stuart-Landau oscillators with repulsive coupling. Autonomous network with global repulsive coupling settles on one from a continuum of synchronized regimes characterized by zero mean field. Driving this array by an external oscillatory signal produces a nonzero mean field that follows the driving signal even when the oscillators are not locked to the external signal. At sufficiently large amplitude the external signal synchronizes the oscillators and locks the phases of the array oscillations. Application of this system as a beam-forming element of a phase array antenna is considered. The phase dynamics of the oscillator array synchronization is used to reshape the phases of signals received from the phase array antenna and improve its beam pattern characteristics.

The phase difference in coupled chaotic oscillators exhibits a small noiselike fast fluctuation in long-term phase dynamics. The fast fluctuation can cause an error in the measurement of the period of the temporary phase locking state. We discuss why we should filter out the fast fluctuation on determination of periodic phase synchronization.

Complex-valued Hopfield networks which possess the energy function are analyzed. The dynamics of the network with certain forms of an activation function is decomposable into the dynamics of the amplitude and phase of each neuron. Then the phase dynamics is described as a coupled system of phase oscillators with a pair-wise sinusoidal interaction. Therefore its phase synchronization mechanism is useful for the area-wide offset control of the traffic signals. The computer simulations show the effectiveness under the various traffic conditions.

Cross-spectral and synchronization analysis of two independent, identical chaotic R\"ossler systems suggest a coupling although there is no interaction. This spuriously detected interaction can either be explained by the absence of mixing or by finite size effects. To decide which alternative holds the phase dynamics is studied by a model of the fluctuations derived from the system's equations. The basic assumption of the model is a diffusive character for the system which corresponds to mixing. Comparison of theoretical properties of the model with empirical properties of the R\"ossler system suggests that the system is mixing but the rate of mixing appears to be rather low.

Focusing on the mechanisms underlying the appearance of phase multistability, the paper examines a variety of phase-locked patterns in the bursting behavior of a model of coupled pancreatic cells. In particular, we show how the number of spikes per train and the proximity of a neighboring equilibrium point can influence the formation of coexisting regimes.

New formulations of active vibration isolation problems for multiple degree-of-freedom (DOF) systems are presented. A position-tracking approach via partial emulation is proposed to take advantage of the natural dynamics of a particular type of actuator: the electrohydraulic actuator. A specific 2DOF system with nonminimum phase dynamics and a noncollocated sensor and actuator pair is chosen to implement this position-tracking approach. Experimental results demonstrate good vibration isolation performance.

We consider the phase dynamics of an ensemble of Kuramoto oscillators whose eigenfrequencies are perturbed to model the openness of living systems, and we show that it exhibits time-localized epochs of synchrony. A new quantitative measure is used to show that the model compares well with electroencephalography data recorded from a healthy awake human.