Discretization, Bifurcation and Control for a Class of Predator–Prey Interactions

The present study focuses on the dynamical aspects of a discrete-time Leslie–Gower predator–prey model accompanied by a Holling type III functional response. Discretization is conducted by applying a piecewise constant argument method of differential equations. Moreover, boundedness, existence, uniqueness, and a local stability analysis of biologically feasible equilibria were investigated. By implementing the center manifold theorem and bifurcation theory, our study reveals that the given system undergoes period-doubling and Neimark–Sacker bifurcation around the interior equilibrium point. By contrast, chaotic attractors ensure chaos. To avoid these unpredictable situations, we establish a feedback-control strategy to control the chaos created under the influence of bifurcation. The fractal dimensions of the proposed model are calculated. The maximum Lyapunov exponents and phase portraits are depicted to further confirm the complexity and chaotic behavior. Finally, numerical simulations are presented to confirm the theoretical and analytical findings.

Mathematical Analysis of a Fractional-Order Predator-Prey Network with Feedback Control Strategy

This paper examines the bifurcation control problem of a class of delayed fractional-order predator-prey models in accordance with an enhancing feedback controller. Firstly, the bifurcation points of the devised model are precisely figured out via theoretical derivation taking time delay as a bifurcation parameter. Secondly, a set comparative analysis on the influence of bifurcation control is numerically studied containing enhancing feedback, dislocated feedback, and eliminating feedback approaches. It can be seen that the stability performance of the proposed model can be immensely heightened by the enhancing feedback approach. At the end, a numerical example is given to illustrate the feasibility of the theoretical results.

Study on the Lyapunov Stability of a Time-Discrete Macro Traffic System with Variable Delay and Feedback Control

This paper constructs and analyzes a time-discrete macro traffic system with bounded variable delay and feedback control strategy. By theoretical analysis using the Lyapunov theorem, a stable condition of the macro traffic system is derived under which traffic jams can be suppressed. The traffic developing properties of the new traffic system for different variable delay and feedback control parameters are illustrated through simulation. The results show that variable delay can easily lead a traffic system to evolve into a traffic jam, and the feedback control strategy can enhance the stability of the traffic system with respect to variable delay. Moreover, the traffic unstable level caused by variable delay is less than the unstable extent caused by the constant upper bound of variable delay; still it is more serious than the traffic fluctuation caused by the constant lower bound of variable delay.

Methane production from food waste using a feedback control strategy in a sequencing batch reactor

The performance of a feedback control strategy in the operation of a sequencing batch reactor was evaluated. This strategy uses the online biogas flow measurements to define the duration of the reaction phase of each operating cycle, thereby increasing the energy production of the system and maximizing the methane production rate. The reaction phase is ended when the biogas flow rate reaches a sustained value significantly lower value than the maximum flow rate achieved, as a consequence of the depletion of the CODsoluble. The implementation of the depletion-time control was successful and reached a maximum methane production rate of 1.22 LCH4/d, showing an average productivity of 0.73 ± 0.3 LCH4/d. The reaction phase varied from 1.2 to 6 days with hydraulic retention times from 6 to 30 days. The use of this feedback control strategy increased the methane production and the energy production in 80% of the evaluated cycles (from 10.4 to 43.8%) compared to the operation of conventional anaerobic digestion without a control strategy. Furthermore, the strategy is easy to implement since it does not require complex calculations and uses a readily available biogas flow rate sensor.

Model predictive control with random batch methods for a guiding problem

We model, simulate and control the guiding problem for a herd of evaders under the action of repulsive drivers. The problem is formulated in an optimal control framework, where the drivers (controls) aim to guide the evaders (states) to a desired region of the Euclidean space. The numerical simulation of such models quickly becomes unfeasible for a large number of interacting agents, as the number of interactions grows [Formula: see text] for [Formula: see text] agents. For reducing the computational cost to [Formula: see text], we use the Random Batch Method (RBM), which provides a computationally feasible approximation of the dynamics. First, the considered time interval is divided into a number of subintervals. In each subinterval, the RBM randomly divides the set of particles into small subsets (batches), considering only the interactions inside each batch. Due to the averaging effect, the RBM approximation converges to the exact dynamics in the [Formula: see text]-expectation norm as the length of subintervals goes to zero. For this approximated dynamics, the corresponding optimal control can be computed efficiently using a classical gradient descent. The resulting control is not optimal for the original system, but for a reduced RBM model. We therefore adopt a Model Predictive Control (MPC) strategy to handle the error in the dynamics. This leads to a semi-feedback control strategy, where the control is applied only for a short time interval to the original system, and then compute the optimal control for the next time interval with the state of the (controlled) original dynamics. Through numerical experiments we show that the combination of RBM and MPC leads to a significant reduction of the computational cost, preserving the capacity of controlling the overall dynamics.

An Integrated Dynamic Simulation Platform for Assistive Human-Robot Interaction: Application to Upper Limb Exosuit

Soft exosuits are wearable robotic devices that assist or enhance the human muscle performance. A human machine interface simulation platform based on MATLAB-OpenSim interface is developed in this paper for closed loop dynamic simulation with feedback control strategy and to study its effect on human physiology. The proposed simulation model is based on Computed Muscle Control (CMC) algorithm and is implemented using the MATLAB -OpenSim interface. A Gravity Compensation (GC) controller has been implemented on the external device and the resulting decrease in the physiological torques, muscle activations and metabolic costs during a simple load lifting task with two different speeds is investigated.

An Integrated Dynamic Simulation Platform for Assistive Human-Robot Interaction: Application to Upper Limb Exosuit

Soft exosuits are wearable robotic devices that assist or enhance the human muscle performance. A human machine interface simulation platform based on MATLAB-OpenSim interface is developed in this paper for closed loop dynamic simulation with feedback control strategy and to study its effect on human physiology. The proposed simulation model is based on Computed Muscle Control (CMC) algorithm and is implemented using the MATLAB -OpenSim interface. A Gravity Compensation (GC) controller has been implemented on the external device and the resulting decrease in the physiological torques, muscle activations and metabolic costs during a simple load lifting task with two different speeds is investigated.

Embedded control of cell growth using tunable genetic systems

We present an embedded feedback control strategy to control the density of a bacterial population, allowing cells to self-regulate their growth rate so as to reach a desired density at steady state. We consider a static culture condition, where cells are provided with a limited amount of space and nutrients. The control strategy is built using a tunable expression system (TES), which controls the production of a growth inhibitor protein, complemented with a quorum sensing mechanism for the sensing of the population density. We show on a simplified population-level model that the TES endows the control system with additional flexibility by allowing the set-point to be changed online. Finally, we validate the effectiveness of the proposed control strategy by means of realistic in silico experiments conducted in BSim, an agent-based simulator explicitly designed to simulate bacterial populations, and we test the robustness of our design to disturbances and parameters' variations due, for instance, to cell-to-cell variability.