Forwarding Control Design for Strict-Feedforward Systems

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
K. D. Do
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Lyapunov Function ◽  
Control Design ◽  
Linear Partial Differential Equation ◽  
Asymptotically Stable ◽  
Bounded Control ◽  
Control Laws ◽  
Globally Asymptotically Stable ◽  
Control Designs

This paper presents a new recursive forwarding method to design control laws that globally asymptotically stabilize strict-feedforward systems, of which Jacobian linearization at the origin might not be stabilizable. At each step, a Lyapunov function is constructed based on a solution of a linear partial differential equation (PDE) or a system of globally asymptotically stable (GAS) ordinary differential equations (ODEs). Optimal and bounded control designs are also addressed. The flexibility of the proposed design is illustrated via five examples.

scholarly journals EVOLUTION OF MODULATIONAL INSTABILITY IN TRAVELLING WAVE SOLUTION OF NON-LINEAR PARTIAL DIFFERENTIAL EQUATION

2020 ◽  
Vol 5 (1) ◽  
pp. 1-7
Author(s):  
Ram Dayal Pankaj ◽  
Arun Kumar ◽  
Chandrawati Sindhi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Wave Solution ◽  
Modulational Instability ◽  
Nonlinear Partial Differential Equation ◽  
Linear Partial Differential Equation ◽  
Travelling Wave ◽  
Travelling Wave Solution ◽  
Partial Differential ◽  
Jacobian Elliptic Functions

The Ritz variational method has been applied to the nonlinear partial differential equation to construct a model for travelling wave solution. The spatially periodic trial function was chosen in the form of combination of Jacobian Elliptic functions, with the dependence of its parameters

Recent Advances in the Knowledge of Transonic Air Flow

1956 ◽  
Vol 60 (544) ◽  
pp. 241-252 ◽  
Author(s):  
C. H. E. Warren
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Layers ◽  
Velocity Potential ◽  
Fluid Velocity ◽  
Linear Partial Differential Equation ◽  
Inviscid Flow ◽  
Stream Velocity ◽  
Linear Boundary ◽  
Small Perturbations

The most powerful theoretical tool in the solution of the aerodynamic problems of aircraft is the theory of small perturbations, which states that if a wing is thin (or a body slender), and if the incidence is small, then in inviscid flow the fluid velocity at any point can be treated as a small perturbation from the stream velocity. The backbone of our knowledge of the aerodynamics of aircraft is provided by this theory, to which the effects of thick wings and large incidences, and the effect of viscosity, introducing as it does the concept of boundary layers, can be added as additional or correction effects. It is known that at subsonic and again at supersonic speeds, the theory of small perturbations is a linear theory; that is, the assumptions implicit in it lead to a linear partial differential equation for the velocity potential, with linear boundary conditions.

scholarly journals Global Dynamics of an SIQR Model with Vaccination and Elimination Hybrid Strategies

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 328 ◽  
Author(s):  
Yanli Ma ◽  
Jia-Bao Liu ◽  
Haixia Li
Keyword(s):  
Lyapunov Function ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, an SIQR (Susceptible, Infected, Quarantined, Recovered) epidemic model with vaccination, elimination, and quarantine hybrid strategies is proposed, and the dynamics of this model are analyzed by both theoretical and numerical means. Firstly, the basic reproduction number R 0 , which determines whether the disease is extinct or not, is derived. Secondly, by LaSalles invariance principle, it is proved that the disease-free equilibrium is globally asymptotically stable when R 0 < 1 , and the disease dies out. By Routh-Hurwitz criterion theory, we also prove that the disease-free equilibrium is unstable and the unique endemic equilibrium is locally asymptotically stable when R 0 > 1 . Thirdly, by constructing a suitable Lyapunov function, we obtain that the unique endemic equilibrium is globally asymptotically stable and the disease persists at this endemic equilibrium if it initially exists when R 0 > 1 . Finally, some numerical simulations are presented to illustrate the analysis results.

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