A Note on the Sequential Linear Fractional Dynamical Systems from the Control System Viewpoint and L 2 -Theory

2011 ◽  
pp. 73-83
Author(s):  
Abolhassan Razminia ◽  
Vahid Johari Majd ◽  
Ahmad Feiz Dizaji
Keyword(s):  
Control System ◽  
Dynamical Systems

Performance Standards in Dynamics

1977 ◽  
Vol 99 (2) ◽  
pp. 118-122
Author(s):  
N. Komaroff
Keyword(s):  
Control System ◽  
Phase Space ◽  
Dynamical Systems ◽  
System Performance ◽  
Performance Standards ◽  
Design Specifications ◽  
Analysis And Synthesis ◽  
Comprehensive Manner ◽  
Averaging Functions ◽  
And Control

A method to evaluate the performance of dynamical systems governed by ordinary differential equations is presented. It is based on averaging functions describing system behaviour (e.g. velocities) over prescribed domains (e.g. surfaces) in phase space. Quantitative measures of motion are introduced to indicate e.g. how oscillatory or how monotone would be the response following a disturbance. Examples demonstrate how these measures serve as new design specifications whose role is to define, compare and control system performance in a more comprehensive manner. Another application of the work is to qualitative studies in both the analysis and synthesis contexts.

Use of Simulated Annealing for Adaptive Control System

2013 ◽  
Vol 2 (3) ◽  
pp. 42-54 ◽  
Author(s):  
Tran Trong Dao ◽  
Ivan Zelinka ◽  
Vo Hoang Duy
Keyword(s):  
Artificial Intelligence ◽  
Adaptive Control ◽  
Simulated Annealing ◽  
Control System ◽  
Dynamical Systems ◽  
Adaptive Control System ◽  
And Control

This work deals with using a method of artificial intelligence, mainly the generic probabilistic meta-algorithm can be used in such a difficult task which is analyzed and control of dynamical systems. Simulated annealing (SA) is used in this investigation. The adaptive control system was used in simulations with optimization by Simulated Annealing and the results are presented in graphs.

The Dynamical Systems Safety Analysis by SQMD Method

2014 ◽  
Vol 693 ◽  
pp. 92-97
Author(s):  
Pavol Tanuska ◽  
Milan Strbo ◽  
Augustin Gese ◽  
Barbora Zahradnikova
Keyword(s):  
Dynamical System ◽  
Control System ◽  
Dynamical Systems ◽  
Critical Points ◽  
Safety Analysis ◽  
Critical System ◽  
Safety Critical ◽  
Qualitative And Quantitative ◽  
Safety Critical System

The objective of the article is to demonstrate the principle of the SQMD method concept for performing safety analysis on the example of a dynamical system. The safety analysis is performed in the process of designing a control system for safety-critical system processes. The safety analysis is aimed at using the models to monitor different critical points of the system. For the purpose of modelling, we suggest using the SQMD method combining qualitative and quantitative procedures of modelling and taking both methods advantages.

scholarly journals CONTROL AND ESTIMATION FOR A CLASS OF IMPULSIVE DYNAMICAL SYSTEMS

2019 ◽  
Vol 5 (2) ◽  
pp. 21
Author(s):  
Tatiana F. Filippova
Keyword(s):  
Control System ◽  
Dynamical Systems ◽  
Quadratic Forms ◽  
Evolution Equations ◽  
System Modeling ◽  
Vector Measures ◽  
Nonlinear Dynamical ◽  
Theory Of Evolution ◽  
Control Functions ◽  
Dynamical Control

The nonlinear dynamical control system with uncertainty in initial states and parameters is studied. It is assumed that the dynamic system has a special structure in which the system nonlinearity is due to the presence of quadratic forms in system velocities. The case of combined controls is studied here when both classical measurable control functions and the controls generated by vector measures are allowed.  We present several theoretical schemes and the estimating algorithms allowing to find the upper bounds for reachable sets of the studied control system.   The research develops the techniques of the ellipsoidal calculus and of the theory of evolution equations for set-valued states of dynamical systems having in their description the uncertainty of set-membership kind.  Numerical results of system modeling based on the proposed methods are included.

Symbolic Computation of Quantities Associated With Time-Periodic Dynamical Systems

2015 ◽  
Author(s):  
W. Grant Kirkland ◽  
S. C. Sinha
Keyword(s):  
Control System ◽  
Dynamical Systems ◽  
System Design ◽  
Symbolic Computation ◽  
Picard Iteration ◽  
Control System Design ◽  
Symbolic Form ◽  
Varying Coefficients ◽  
And Control ◽  
Time Periodic

Many dynamical systems can be modeled by a set of linear/nonlinear ordinary differential equations with periodic time-varying coefficients. The state transition matrix Φ(t,α) associated with the linear part of the equation can be expressed in terms of the periodic Lyapunov-Floquét transformation matrix Q(t,α) and a time-invariant matrix R(α). Computation of Q(t,α) and R(α) in a symbolic form as a function of system parameters α is of paramount importance in stability, bifurcation analysis, and control system design. In the past, a methodology has been presented for computing Φ(t,α) in a symbolic form, however Q(t,α) and R(α) have never been calculated in a symbolic form. Since Q(t,α) and R(α) were available only in numerical forms, general results for parameter unfolding and control system design could not be obtained in the entire parameter space. In this work a technique for symbolic computation of Q(t,α), and R(α) matrices is presented. First, Φ(t,α) is computed symbolically using the shifted Chebyshev polynomials and Picard iteration method as suggested in the literature. Then R(α) is computed using the Gaussian quadrature integral formula. Finally Q(t,α) is computed using the matrix exponential summation method. Using Mathematica, this approach has successfully been applied to the well-known Mathieu equation and a four dimensional time-periodic system in order to demonstrate the applications of the proposed method to linear as well as nonlinear problems.

SINGLE STATE-FEEDBACK CHAOTIFICATION OF DISCRETE DYNAMICAL SYSTEMS

2004 ◽  
Vol 14 (01) ◽  
pp. 279-284 ◽  
Author(s):  
YONGAI ZHENG ◽  
GUANRONG CHEN
Keyword(s):  
Control System ◽  
Dynamical Systems ◽  
Feedback Control ◽  
Nonlinear System ◽  
State Feedback ◽  
Discrete Dynamical Systems ◽  
State Feedback Control ◽  
Sine Function ◽  
System State ◽  
Single State

In this paper, the problem of making a nonlinear system chaotic by using state-feedback control is studied, where the feedback controller uses a simple sine function of the system state with only one single component in each dimension. It is proved that the designed control system generates chaos in the sense of Li and Yorke.

Ramp Tracking in Systems With Nonminimum Phase Zeros: One-and-a-Half Integrator Approach

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Mohammad Saleh Tavazoei
Keyword(s):  
Control System ◽  
Dynamical Systems ◽  
Transfer Function ◽  
Fractional Calculus ◽  
Control Law ◽  
Nonminimum Phase ◽  
Numerical Examples ◽  
Loop Transfer Function ◽  
Asymptotic Tracking

In this paper, a simple fractional calculus-based control law is proposed for asymptotic tracking of ramp reference inputs in dynamical systems. Without need to add any zero to the loop transfer function, the proposed technique can guarantee asymptotic ramp tracking in plants having nonminimum phase zeros. The appropriate range for determining the parameters of the proposed control law is also specified. Moreover, the performance of the designed control system in tracking ramp reference inputs is illustrated by different numerical examples.

The Methodology Proposal for the Model-Oriented Safety Analysis of Dynamical Systems

2014 ◽  
Vol 693 ◽  
pp. 86-91 ◽  
Author(s):  
Milan Strbo ◽  
Pavol Tanuska ◽  
Augustin Gese ◽  
Lukas Smolarik
Keyword(s):  
Control System ◽  
Dynamical Systems ◽  
Process Monitoring ◽  
System Development ◽  
Safety Analysis ◽  
System Operation ◽  
Safety Critical ◽  
Model Driven ◽  
The Individual ◽  
Critical Process

The aim of the article is to propose a methodology for implementing a model-driven safety analysis of dynamical technology systems. The safety analysis is performed in the process of control system development, especially aiming at safety-critical processes of system operation. The methodology was divided into six basic steps. The individual steps of the methodology are carried out in a hierarchical sequence. Further, roles of individual methodology steps are detailed. In the next part of the article, the principle of safety-critical process monitoring based on models is described.

scholarly journals Trajectory Controllability of Dynamical Systems with Non-instantaneous Impulses

YMER Digital ◽  
2021 ◽  
Vol 20 (11) ◽  
pp. 371-381
Author(s):  
Vishant Shah ◽  
◽  
Jaita Sharma ◽  
Prakash H Patel ◽  
◽  
...  
Keyword(s):  
Banach Space ◽  
Control System ◽  
Dynamical Systems ◽  
Initial Conditions ◽  
Operator Semigroup ◽  
Nonlocal Initial Conditions ◽  
Gronwall’S Inequality ◽  
Evolution Control ◽  
General Banach Space

This manuscript considered the system governed by the non-instantaneous impulsive evolution control system and discusses trajectory controllability of the governed system with classical and nonlocal initial conditions over the general Banach space. The results of the trajectory controllability for governed systems are obtained through the concept of operator semigroup and Gronwall’s inequality. This manuscript is also equipped with examples to illustrate the applications of derived results.

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