scholarly journals On the Approximated Reachability of a Class of Time-Varying Nonlinear Dynamic Systems Based on Their Linearized Behavior about the Equilibria: Applications to Epidemic Models

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1045 ◽  
Author(s):  
Sen
Keyword(s):  
Nonlinear Dynamics ◽  
Linear Time ◽  
Epidemic Models ◽  
Control Input ◽  
Time Varying ◽  
Controllability Gramian ◽  
Linearized System ◽  
Time Invariant ◽  
Theoretical Results ◽  
Linear Parameterization

This paper formulates the properties of point reachability and approximate point reachability of either a targeted state or output values in a general dynamic system which possess a linear time-varying dynamics with respect to a given reference nominal one and, eventually, an unknown structured nonlinear dynamics. Such a dynamics is upper-bounded by a function of the state and input. The results are obtained for the case when the time-invariant nominal dynamics is perfectly known while its time-varying deviations together with the nonlinear dynamics are not precisely known and also for the case when only the nonlinear dynamics is not precisely known. Either the controllability gramian of the nominal linearized system with constant linear parameterization or that of the current linearized system (which includes the time-varying linear dynamics) are assumed to be non-singular. Also, some further results are obtained for the case when the control input is eventually saturated and for the case when the controllability gramians of the linear parts are singular. Examples of the derived theoretical results for some epidemic models are also discussed.

The Swing Control of Cranes with Variable Rope Length Based on Linear Time Varying System Theory

2012 ◽  
Vol 461 ◽  
pp. 763-767
Author(s):  
Li Fu Wang ◽  
Zhi Kong ◽  
Xin Gang Wang ◽  
Zhao Xia Wu
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Linear Time ◽  
Feedback Stabilization ◽  
Time Varying ◽  
Closed Loop System ◽  
Overhead Cranes ◽  
Time Varying Systems ◽  
Time Invariant ◽  
Time Invariant System

In this paper, following the state-feedback stabilization for time-varying systems proposed by Wolovich, a controller is designed for the overhead cranes with a linearized parameter-varying model. The resulting closed-loop system is equivalent, via a Lyapunov transformation, to a stable time-invariant system of assigned eigenvalues. The simulation results show the validity of this method.

Periodic controller for guaranteed simultaneous stabilization of two plants with robust zero error tracking

2018 ◽  
Vol 233 (5) ◽  
pp. 480-490
Author(s):  
Arindam Chakraborty ◽  
Jayati Dey
Keyword(s):  
Design Methodology ◽  
Linear Time ◽  
Pole Placement ◽  
Control Input ◽  
Efficient Design ◽  
Simultaneous Stabilization ◽  
Bounded Control ◽  
Linear Time Invariant ◽  
Time Invariant ◽  
Time Periodic

The guaranteed simultaneous stabilization of two linear time-invariant plants is achieved by continuous-time periodic controller with high controller frequency. Simultaneous stabilization is accomplished by means of pole-placement along with robust zero error tracking to either of two plants. The present work also proposes an efficient design methodology for the same. The periodic controller designed and synthesized for realizable bounded control input with the proposed methodology is always possible to implement with guaranteed simultaneous stabilization for two plants. Simulation and experimental results establish the veracity of the claim.

scholarly journals Intermittent Time-Varying Formation Control for High-Order Networked Agents Subject to Discontinuous Communications

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Lixin Wang ◽  
Zhe Luo ◽  
Xiaoqiang Li ◽  
Xinsan Li ◽  
Xiaogang Yang
Keyword(s):  
Formation Control ◽  
Linear Matrix ◽  
Control Input ◽  
Intermittent Control ◽  
Movement Trajectory ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Communication Time ◽  
Theoretical Results ◽  
Formation Design

This paper investigates the leaderless and leader-follower time-varying formation design and analysis problems for a group of networked agents subject to discontinuous communications. Firstly, a leaderless time-varying formation control protocol is proposed via the intermittent control strategy, where the control input of each agent is constructed by the distributed local state information and formation instructions in the communication time unit, but it is zero in the noncommunication time unit. Then, an explicit formulation of the formation center function is determined to describe the formation movement trajectory of the whole networked agents. Leaderless time-varying formation design and analysis with discontinuous communications are given in the form of linear matrix inequalities. Moreover, the main results of the leaderless cases are extended to the leader-follower cases. Finally, two numerical examples are provided to illustrate the theoretical results of leaderless and leader-follower cases, respectively.

scholarly journals FE Analysis of Communications Systems for Drive-Thru Restaurants in a Business Dispute Over Specifications and Design Process

2021 ◽  
Vol 38 (1) ◽  
Author(s):  
Robert Peruzzi
Keyword(s):  
Communication System ◽  
Communication Systems ◽  
Linear Time ◽  
Forensic Analysis ◽  
Time Varying ◽  
Audio Quality ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Quick Service ◽  
Time Invariant

Forensic analysis in this case involves the design of a communication system intended for use in Quick Service Restaurant (QSR) drive-thru lanes. This paper provides an overview of QSR communication system components and operation and introduces communication systems and channels. This paper provides an overview of non-linear, time-varying system design as contrasted with linear, time-invariant systems and discusses best design practices. It also provides the details of how audio quality was defined and compared for two potentially competing systems. Conclusions include that one of the systems was clearly inferior to the other — mainly due to not following design techniques that were available at the time of the project.

Linear Approximations for Swing Leg Motion During Gait

1984 ◽  
Vol 106 (2) ◽  
pp. 137-143 ◽  
Author(s):  
W. H. Lee ◽  
J. M. Mansour
Keyword(s):  
Linear Systems ◽  
System Analysis ◽  
Linear Time ◽  
Time Varying ◽  
Two Dimensional ◽  
State Variables ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Leg Motion ◽  
Time Invariant

The applicability of a linear systems analysis of two-dimensional swing leg motion was investigated. Two different linear systems were developed. A linear time-varying system was developed by linearizing the nonlinear equations describing swing leg motion about a set of nominal system and control trajectories. Linear time invariant systems were developed by linearizing about three different fixed limb positions. Simulations of swing leg motion were performed with each of these linear systems. These simulations were compared to previously performed nonlinear simulations of two-dimensional swing leg motion and the actual subject motion. Additionally, a linear system analysis was used to gain some insight into the interdependency of the state variables and controls. It was shown that the linear time varying approximation yielded an accurate representation of limb motion for the thigh and shank but with diminished accuracy for the foot. In contrast, all the linear time invariant systems, if used to simulate more than a quarter of the swing phase, yielded generally inaccurate results for thigh shank and foot motion.

scholarly journals Decentralized Suboptimal State Feedback Integral Tracking Control Design for Coupled Linear Time-Varying Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Mohamed Sadok Attia ◽  
Mohamed Karim Bouafoura ◽  
Naceur Benhadj Braiek
Keyword(s):  
Tracking Control ◽  
State Feedback ◽  
Linear Time ◽  
Least Square ◽  
Control Synthesis ◽  
Operational Matrices ◽  
Control Input ◽  
Time Varying ◽  
State Equations ◽  
Integral Control

In this paper, a suboptimal state feedback integral decentralized tracking control synthesis for interconnected linear time-variant systems is proposed by using orthogonal polynomials. Particularly, the use of operational matrices allows, by expanding the subsystem input states and outputs over a shifted Legendre polynomial basis, the conversion of time-varying parameter differential state equations to a set of time-independent algebraic ones. Hence, optimal open-loop state and control input coefficients are forwardly determined. These data are used to formulate a least-square problem, allowing the synthesis of decentralized state feedback integral control gains. Closed-loop asymptotic stability LMI conditions are given. The proposed approach effectiveness is proved by solving a nonconstant reference tracking problem for coupled inverted pendulums.

Floquet Experimental Modal Analysis for System Identification of Linear Time-Periodic Systems

2007 ◽  
Author(s):  
Matthew S. Allen
Keyword(s):  
System Identification ◽  
Linear Time ◽  
Time Varying ◽  
Response Model ◽  
State Matrix ◽  
Linear Time Invariant ◽  
Response Data ◽  
Time Varying Systems ◽  
Time Invariant ◽  
Time Periodic

A variety of systems can be faithfully modeled as linear with coefficients that vary periodically with time or Linear Time-Periodic (LTP). Examples include anisotropic rotorbearing systems, wind turbines, satellite systems, etc… A number of powerful techniques have been presented in the past few decades, so that one might expect to model or control an LTP system with relative ease compared to time varying systems in general. However, few, if any, methods exist for experimentally characterizing LTP systems. This work seeks to produce a set of tools that can be used to characterize LTP systems completely through experiment. While such an approach is commonplace for LTI systems, all current methods for time varying systems require either that the system parameters vary slowly with time or else simply identify a few parameters of a pre-defined model to response data. A previous work presented two methods by which system identification techniques for linear time invariant (LTI) systems could be used to identify a response model for an LTP system from free response data. One of these allows the system’s model order to be determined exactly as if the system were linear time-invariant. This work presents a means whereby the response model identified in the previous work can be used to generate the full state transition matrix and the underlying time varying state matrix from an identified LTP response model and illustrates the entire system-identification process using simulated response data for a Jeffcott rotor in anisotropic bearings.

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