1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/596B270197FE27DE5FABB598B6210622/S0025557200150892a.pdf/div-class-title-span-class-italic-the-geometry-of-biological-time-span-by-a-t-winfree-pp-544-dm68-corrected-second-printing-1990-isbn-3-540-52528-9-springer-div.pdf

The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)

This brief addresses the fixed-time event/self-triggered leader–follower consensus problems for networked multi-agent systems subject to nonlinear dynamics. First, we present an event-triggered control strategy to achieve the fixed-time consensus, and a new measurement error is designed to avoid Zeno behavior. Then, two new self-triggered control strategies are presented to avoid continuous triggering condition monitoring. Moreover, under the proposed self-triggered control strategies, a strictly positive minimal triggering interval of each follower is given to exclude Zeno behavior. Compared with the existing fixed-time event-triggered results, we propose two new self-triggered control strategies, and the nonlinear term is more general. Finally, the performances of the consensus tracking algorithms are illustrated by a simulation example.

Fixed-Time Leader–Follower Consensus of Networked Nonlinear Systems via Event/Self-Triggered Control

Fixed-time consensus of multi-agent systems with input delay and uncertain disturbances via event-triggered control

This article is concerned with fixed-time leader–follower consensus problem for multiagent systems (MASs) with output constraints, unknown control direction, unknown system dynamics, unknown external disturbance, and dead-zone control input. First, a fixed-time distributed observer is presented for each follower to estimate the leader’s states. Next, using a modified nonlinear mapping, an output-constrained system is transformed into an unconstrained system. Then, by adopting adding a power integrator technique, radial basis function neural network (RBFNN) approximation, and adaptive method, the ideal fixed-time stable virtual control protocol is derived and the issues of unknown control direction, unknown system dynamics, and unknown external disturbance are addressed. Finally, the actual control protocol is developed using the bound of dead-zone parameters. It is shown that the proposed control scheme achieves fixed-time leader–follower consensus of the studied MAS. The presented control protocol is applied to the leader–follower consensus of inverted pendulums and simulation results verify its effectiveness.

Adaptive Neural Network Fixed-Time Leader–Follower Consensus for Multiagent Systems With Constraints and Disturbances

This article addresses the team-triggered fixed-time consensus problems for a class of double-integrator agents subject to uncertain disturbance Compared with the finite-time results, the convergence time of the fixed-time results is independent of the initial conditions Furthermore, a novel team-triggered control (TTC) strategy is presented This control strategy incorporates the event-triggered control (ETC) and self-triggered control (STC) The ETC and STC are proposed to achieve the fixed-time consensus of second-order multiagent systems (MASs), and no Zeno behavior occurs The TTC scheme, derived by combining the ETC scheme and the STC scheme, is able to relax the requirement of continuous communication and thus lowering the energy consumption of communication while ensuring the performance of the system The effectiveness of the proposed algorithms is validated by numerical simulations

Team-Triggered Practical Fixed-Time Consensus of Double-Integrator Agents With Uncertain Disturbance

In this paper, a deep reinforcement learning-based robust control strategy for quadrotor helicopters is proposed. The quadrotor is controlled by a learned neural network which directly maps the system states to control commands in an end-to-end style. The learning algorithm is developed based on the deterministic policy gradient algorithm. By introducing an integral compensator to the actor-critic structure, the tracking accuracy and robustness have been greatly enhanced. Moreover, a two-phase learning protocol which includes both offline and online learning phase is proposed for practical implementation. An offline policy is first learned based on a simplified quadrotor model. Then, the policy is online optimized in actual flight. The proposed approach is evaluated in the flight simulator. The results demonstrate that the offline learned policy is highly robust to model errors and external disturbances. It also shows that the online learning could significantly improve the control performance.

Deterministic Policy Gradient With Integral Compensator for Robust Quadrotor Control

Distributed event-triggered fixed-time consensus for leader-follower multiagent systems with nonlinear dynamics and uncertain disturbances

Fixed-time event-triggered synchronization of a multilayer Kuramoto-oscillator network

In this paper, a nonlinear robust control method is developed for trajectory tracking of a quadrotor aircraft. The proposed approach combines the robust signal compensation method and the backstepping technique. First, the quadrotor dynamic system with multiple disturbances and uncertainties is divided into four subsystems. Then, the nominal controllers are constructed for the subsystems without disturbance terms, while the robust signal compensators are introduced to compensate for the effect of nonlinearities and uncertainties. Furthermore, the Lyapunov analysis has shown that the proposed controller can achieve stable tracking in the presence of violent discontinuous disturbances and uncertainties. The tracking error converges to an arbitrarily small neighborhood of zero. Finally, the proposed control design is validated with real flight experiments. The results show superior trajectory tracking performance of the quadrotor system affected by external disturbances.

/pdf/nonlinear-robust-compensation-method-for-trajectory-tracking-ngqexhl8zf.pdf

Nonlinear Robust Compensation Method for Trajectory Tracking Control of Quadrotors

In this paper, a distributed formation control protocol for a multi-quadrotor system is proposed. The nonlinear dynamic model and the communication model of the multi-quadrotor system are established first. Then, for the lower-level motion control of each quadrotor, the feedback linearization technique is employed. For the higher-level formation, we use a leader-follower structure. The formation control protocol based on the consensus theory and the observer technique are proposed to guide the follower quadrotors to their desired formation positions. The proposed protocol only requires the position information from neighbors. Finally, the simulation result shows that a fast-response and high-precision formation can be achieved by the proposed protocol.

Jia Sun

Papers

Deterministic Policy Gradient With Integral Compensator for Robust Quadrotor Control

Distributed event-triggered fixed-time consensus for leader-follower multiagent systems with nonlinear dynamics and uncertain disturbances

Fixed-time event-triggered synchronization of a multilayer Kuramoto-oscillator network

Nonlinear Robust Compensation Method for Trajectory Tracking Control of Quadrotors

Distributed Formation Control for Multi-quadrotor System