Feedback Control and Parameter Invasion for a Discrete Competitive Lotka–Volterra System

Abstract

State feedback is used to stabilize the Turing instability at the unstable equilibrium point of a discrete competitive Lotka-Volterra system. In addition, a regularization method is applied to parameter inversion for the given Turing system and numerical simulation can verify the effectiveness of the algorithm. Furthermore, how less or more sample data and dependence on the initial state affect estimation procedure are tested.

Parametrical Non-Complex Tests to Evaluate Partial Decentralized Linear-Output Feedback Control Stabilization Conditions from Their Centralized Stabilization Counterparts

“…Now, rewrite the system matrices of closed-loop dynamics of Equations (7) and (10), equivalently Equation (A7), with A = A c = A d and its incremental value as follows:…”

“…Some extra constraints inherent to some systems, like solution positivity in the case of biological systems or human migrations or the needed behavior robustness against parametrical changes of disturbance actions add additional complexity to the related investigations and need the use of additional mathematical or engineering tools for the research development, [5][6][7]. A large variety of modeling and design tools have to be invoked and developed in the analysis depending on the concrete systems under study and their potential applications as, for instance, the presence of internal and external delays, discretization, dynamics modeling based on fractional calculus, the existence of complex systems with interconnected subsystems, [8][9][10][11][12][13], hybrid coupled continuous/digital tandems, nonlinear systems and optimization and estimation techniques [14][15][16][17][18][19] as well as robotic and fuzzy-logic based systems, [20,21]. In particular, decentralized control is a useful tool for controlling dynamic systems by cutting some links between the dynamics coupling a set of subsystems integrated in the whole system at hand.…”

“…To assess the behavior of the controlled system, a model of such a nonlinear plant is controlled by a fractional proportional/integral/derivative control device through a linearization of its set points, the fractional part being relevant in the approach on the controller derivative actions. In addition, a set of applied complex control problems are studied, for instance, in [10][11][12][13][14][15][16] with the aim of giving different ad hoc simplification tools to deal with the appropriate control methodologies. In particular, a decentralized control approach is proposed in [16].…”

Global Stability for a Discrete Space-Time Lotka–Volterra System with Feedback Control

“…ere also may exist a situation where the equilibrium of the dynamical model is not the desirable one (or affordable) and a smaller value of the equilibrium is required; then, altering the model structure so as to make the population stabilize at a lower value is necessary [22]. Feedback control will be an effective one and can alter the positions of positive equilibrium or obtain its stability.…”

Global Stability for a Semidiscrete Logistic System with Feedback Control

“…ere may exist a situation where the equilibrium of the dynamical model is not the desirable one (or affordable) and a smaller value of the equilibrium is required. en, altering the model structure so as to make the population stabilize at a lower value is necessary [14].…”