A logical method for the synthesis of periodic trajectory in a binary dynamical system

A logic method for structural-parametric synthesis of a binary dynamical system with a given periodic trajectory is proposed. This method provides a constructive solution for the considered problem. The attraction region of such a trajectory must coincide with a given subset of the state space. An additional constraint sets the acceptable time for reaching this trajectory from its attraction region. As admissible structures for dynamical models of the synthesis, we consider the following systems: linear systems, systems with the disjunctive and conjunctive right sides. All conditions of the problem are written in the form of a quantified Boolean formula with subsequent verification of its truth using a specialized solver, which gives values of the required parameters of the dynamical model. The software implementation of the proposed method in the form of a composite service is presented. All stages of the parametric synthesis of a Boolean network based on the proposed method are demonstrated in the example of a one-step linear system.

Non-Attractive Periodic Trajectory Formation Mechanism on Random and Chaotic Time Series

Pseudo-random number series extracted from chaotic and random time series from the chaotic and random neural network (CRNN) with fixed-point arithmetic has been the focus of attention for protecting the information security of IoT devices. Pseudo-random number series generated by a computer is eventually periodic, practically. The produced closed trajectory is not a limit cycle, because which does not divide the phase space into 2 regions. The closed trajectory in this work is called a non-attractive periodic trajectory (NPT) because it hardly attracts trajectories within the neighborhood. The method of preventing the closed trajectory formation has been proposed on the basis of the NPT formation mechanism in this paper. The method has extended the period of NPT considerably. It is expected to apply security applications for IoT devices.

Nonlinear Trajectory Controller with Improved Performances for Waveriders

This paper presents a nonlinear trajectory controller with improved performances for a general model of the waverider based on feedback linearization theory and composite nonlinear feedback (CNF) technique. First, a nonlinear controller is presented using the dynamic inversion and CNF technique for the MIMO Model, and the robust stability of the proposed controller is proved. Then, the nonlinear model is established on the basis of hypersonic aerodynamic principle, and the dynamic characteristics are analyzed accordingly, and the periodic trajectory is designed and optimized in combination with a fuel optimization problem. Furthermore, the nonlinear controller is applied to the trajectory tracking of the waverider model, and the general design steps are provided the flight controller using this nonlinear control method. Finally, an illustrative example is given to verify the effectiveness of the nonlinear controller of the waverider, and the flight performances are improved accordingly, including system stability, robustness, and tracking ability.

Rotary Versus Flapping Flight: An Application Study for Optimal Periodic Control Theory

This paper uses optimal periodic control (OPC) theory as a framework for assessing the relative efficiency of revolving versus flapping wing trajectories in insect-sized flight problems. The literature already offers both experimental and simulation-based comparisons between these two flight modes. A collective conclusion from these studies is that the potential advantages of flapping flight depend on many factors such as Reynolds number, wing size/morphology, wing kinematic constraints, aerodynamic efficiency metrics, etc. This makes it necessary to develop a unified framework for comparing these flight modes under various conditions. We address this need by using the π test from OPC theory as a tool for analyzing the degree to which one can improve the efficiency of steady rotary hovering flight through periodic trajectory perturbations. A quasi-steady insect flight model from the literature is adopted as a case study. The paper applies the π test to this model. It then concludes by solving for the optimal lift-power Pareto fronts for both flight modes, and using these Pareto fronts to confirm the results predicted by the π test.