Some Control Studies of Dynamical Systems with Time Delay

2010 ◽  
pp. 135-155
Author(s):  
Bo Song ◽  
Jian-Qiao Sun
Keyword(s):  
Time Delay ◽  
Dynamical Systems

LDG method for reaction–diffusion dynamical systems with time delay

2011 ◽  
Vol 217 (22) ◽  
pp. 9173-9181 ◽  
Author(s):  
Dongfang Li ◽  
Chengjian Zhang ◽  
Hongyu Qin
Keyword(s):  
Time Delay ◽  
Dynamical Systems ◽  
Reaction Diffusion ◽  
Ldg Method

Dynamics of Neural Networks as Nonlinear Systems with Several Equilibria

2011 ◽  
pp. 331-357 ◽  
Author(s):  
Daniela Danciu
Keyword(s):  
Neural Network ◽  
Dynamical System ◽  
Neural Networks ◽  
Time Delay ◽  
Dynamical Systems ◽  
Qualitative Properties ◽  
The Neural Network ◽  
The Neural Networks ◽  
Global Asymptotics ◽  
Dynamical Properties

Neural networks—both natural and artificial, are characterized by two kinds of dynamics. The first one is concerned with what we would call “learning dynamics”. The second one is the intrinsic dynamics of the neural network viewed as a dynamical system after the weights have been established via learning. The chapter deals with the second kind of dynamics. More precisely, since the emergent computational capabilities of a recurrent neural network can be achieved provided it has suitable dynamical properties when viewed as a system with several equilibria, the chapter deals with those qualitative properties connected to the achievement of such dynamical properties as global asymptotics and gradient-like behavior. In the case of the neural networks with delays, these aspects are reformulated in accordance with the state of the art of the theory of time delay dynamical systems.

scholarly journals A Panoramic Sketch about the Robust Stability of Time-Delay Systems and Its Applications

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-26
Author(s):  
Baltazar Aguirre-Hernández ◽  
Raúl Villafuerte-Segura ◽  
Alberto Luviano-Juárez ◽  
Carlos Arturo Loredo-Villalobos ◽  
Edgar Cristian Díaz-González
Keyword(s):  
Time Delay ◽  
Dynamical Systems ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Complex Dynamical Systems ◽  
The Stability ◽  
Numerical Approaches

This paper presents a brief review on the current applications and perspectives on the stability of complex dynamical systems, with an emphasis on three main classes of systems such as delay-free systems, time-delay systems, and systems with uncertainties in its parameters, which lead to some criteria with necessary and/or sufficient conditions to determine stability and/or stabilization in the domains of frequency and time. Besides, criteria on robust stability and stability of nonlinear time-delay systems are presented, including some numerical approaches.

Optimally designed Lyapunov–Krasovskii terminal costs for robust stable–feasible model predictive control of uncertain time-delay nonlinear dynamical systems

2020 ◽  
pp. 095965182095219
Author(s):  
S Yaqubi ◽  
MR Homaeinezhad
Keyword(s):  
Time Delay ◽  
Dynamical Systems ◽  
Model Predictive Control ◽  
Predictive Control ◽  
Robust Stability ◽  
Control Algorithm ◽  
Nonlinear Dynamical Systems ◽  
Prediction Horizon ◽  
Delay Effects ◽  
Uncertain Time

This article details a new Model Predictive Control algorithm ensuring robust stability and control feasibility for uncertain nonlinear multi-input multi-output dynamical systems considering uncertain time-delay effects. The proposed control algorithm is based on construction of a Lyapunov–Krasovskii functional as terminal cost. Incorporation of this terminal cost into the Model Predictive Control optimization problem and calculation of the associated admissible set result in robust feasibility and robust stability of closed-loop system in presence of uncertain time-delay effects and bounded disturbance signals. The Lyapunov–Krasovskii functional term is constructed with respect to predicted sliding functions over the prediction horizon and considers the effects of dynamical variations over the prediction horizon in generation of control inputs. As dynamical variations are investigated in a sample-to-sample basis, feasible sliding regions are updated at each sample as well. Finally, based on expression of sliding functions as a combination of dynamical variations and input-based terms, required control inputs are calculated in the admissible bound by the optimization algorithm. Construction of control scheme on this basis permits straightforward calculation of robust stability and feasibility conditions for a general class of uncertain nonlinear system in finite prediction horizon whereas in the previous works, often-restrictive conditions were considered for the investigated dynamical systems. Numerical illustrations indicate precision and efficiency of control algorithm and improved stability and convergence rate for multivariable nonlinear dynamical systems considering uncertain time-delay effects. Finally, hardware-in-the-loop implementation indicates applicability of the proposed scheme in real-time control applications particularly in case appropriate compromises between optimality and calculation speed are considered.

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