Experimental Investigation of a Time Scales-Based Stability Criterion Over Finite Time Horizons

2015 ◽  
Author(s):  
Matthew Mosley ◽  
Ian Gravagne ◽  
Dylan Poulsen ◽  
John Davis
Keyword(s):  
Feedback Control ◽  
Exponential Stability ◽  
Control Systems ◽  
Time Scales ◽  
Stability Criterion ◽  
Finite Time ◽  
Time Horizon ◽  
Large Area ◽  
Feedback Control Systems ◽  
Finite Time Horizon

Feedback control systems that employ large area networks or other unpredictable or unreliable communications protocols between sensors, actuators, and controllers may experience nonuniform sampling characteristics. Previous work by Poulsen, et. al. gives a criterion for exponential stability of non-uniformly discretized feedback control systems, assuming sample periods drawn from a known statistical distribution. However, the given stability theorem assumes an infinite time horizon. This work therefore examines the exponential stability criterion experimentally, over a finite time horizon, on a 2nd-order servo mechanism. This paper is the first to experimentally investigate the validity of this time scales stability criterion.

scholarly journals Some Differential Inequalities on Time Scales and Their Applications to Feedback Control Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Yonghong Fan ◽  
Yangyang Yu ◽  
Linlin Wang
Keyword(s):  
Feedback Control ◽  
Control Systems ◽  
Time Scales ◽  
New Method ◽  
Differential Inequalities ◽  
Boundedness Of Solutions ◽  
Ultimate Boundedness ◽  
Uniform Ultimate Boundedness ◽  
Feedback Control Systems

This paper deals with feedback control systems on time scales. Firstly, we generalize the semicycle concept to time scales and then establish some differential inequalities on time scales. Secondly, as applications of these inequalities, we study the uniform ultimate boundedness of solutions of these systems. We give a new method to investigate the permanence of ecosystem on time scales. And some known results have been generalized. Finally, an example is given to support the result.

scholarly journals A Constrained Markovian Diffusion Model for Controlling the Pollution Accumulation

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1466
Author(s):  
Beatris Adriana Escobedo-Trujillo ◽  
José Daniel López-Barrientos ◽  
Javier Garrido-Meléndez
Keyword(s):  
Dynamic Programming ◽  
Dirichlet Problem ◽  
Stochastic Control ◽  
Finite Time ◽  
Time Horizon ◽  
Closed Loop ◽  
Programming Techniques ◽  
Pollution Accumulation ◽  
Finite Time Horizon ◽  
The Cost

This work presents a study of a finite-time horizon stochastic control problem with restrictions on both the reward and the cost functions. To this end, it uses standard dynamic programming techniques, and an extension of the classic Lagrange multipliers approach. The coefficients considered here are supposed to be unbounded, and the obtained strategies are of non-stationary closed-loop type. The driving thread of the paper is a sequence of examples on a pollution accumulation model, which is used for the purpose of showing three algorithms for the purpose of replicating the results. There, the reader can find a result on the interchangeability of limits in a Dirichlet problem.

Sign in / Sign up

Export Citation Format

Share Document