The Homicidal Chauffeur Problem With Time Delayed Feedback

2003 ◽  
Author(s):  
Nejat Olgac ◽  
Rifat Sipahi ◽  
Ali Fuat Ergenc
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Target Tracking ◽  
Critical Parameter ◽  
Delayed Feedback ◽  
Control Law ◽  
Pursuit Evasion ◽  
Parking Lot ◽  
Homicidal Chauffeur ◽  
Time Delayed Feedback

The classical pursuit-evasion scenario (target tracking) is studied with an interesting perspective. A homicidal chauffeur (pursuer) tries to capture an evader on a 2-dimensional platform (a parking lot). It utilizes a certain feedback control law, which enables the capture. If, however, a time delay is introduced for the sensory perception of the pursuer the performance of the pursuer can show dramatic changes. It may or may not capture its victim depending on this very critical parameter, the sensory time delay. The unique perspective is introduced at this feature.

BIFURCATION, CHAOS AND THEIR CONTROL IN A TIME-DELAY DIGITAL TANLOCK LOOP

2013 ◽  
Vol 23 (08) ◽  
pp. 1330029 ◽  
Author(s):  
TANMOY BANERJEE ◽  
BISHWAJIT PAUL ◽  
B. C. SARKAR
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Parameter Space ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Convergence Time ◽  
Stable Phase ◽  
Bifurcation And Chaos ◽  
Global Parameter ◽  
Time Delayed Feedback

This paper reports the detailed parameter space study of the nonlinear dynamical behaviors and their control in a time-delay digital tanlock loop (TDTL). At first, we explore the nonlinear dynamics of the TDTL in parameter space and show that beyond a certain value of loop gain parameter the system manifests bifurcation and chaos. Next, we consider two variants of the delayed feedback control (DFC) technique, namely, the time-delayed feedback control (TDFC) technique, and its modified version, the extended time-delayed feedback control (ETDFC) technique. Stability analyses are carried out to find out the stable phase-locked zone of the system for both the controlled cases. We employ two-parameter bifurcation diagrams and the Lyapunov exponent spectrum to explore the dynamics of the system in the global parameter space. We establish that the control techniques can extend the stable phase-locked region of operation by controlling the occurrence of bifurcation and chaos. We also derive an estimate of the optimum parameter values for which the controlled system has the fastest convergence time even for a larger acquisition range. The present study provides a necessary detailed parameter space study that will enable one to design an improved TDTL system.

A Partitioning Scheme for a Switched Feedback Control Law in Two Agent Pursuit-Evasion Scenarios

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Brian J. Goode ◽  
Andrew J. Kurdila ◽  
Michael J. Roan
Keyword(s):  
Feedback Control ◽  
State Space ◽  
The State ◽  
Theoretical Development ◽  
Control Law ◽  
Time Efficiency ◽  
True Solution ◽  
Pursuit Evasion ◽  
Graph Theoretical Approach ◽  
Homicidal Chauffeur

A switched feedback control law is derived for an autonomous pursuing agent that attempts to intercept an evading agent whose dynamics are initially unknown. The model of the pursuer’s dynamics is known perfectly, and the evader is modeled as a disturbance. A new method is presented to efficiently update the pursuer’s control law as measurements of the parameters that govern the evader’s dynamics are received. Using a graph theoretical approach, the control law updates are limited to specific partitions of the state space, which eliminate many unneeded calculations. Results show increases in the time efficiency of the update calculations compared to traditional control law generation methods with a minimal loss in accuracy. An 11.6% overall decrease in calculation time over traditional methods and a 1% error rate compared to the true solution is achieved when solving the homicidal chauffeur game. We show how actual gains in time efficiency depend on the specific application of the controller and the size of the state space grid approximation. Both the theoretical development and implementation of the switched feedback controller are discussed.

TIME-DELAYED FEEDBACK CONTROL OF TIME-DELAY CHAOTIC SYSTEMS

2003 ◽  
Vol 13 (01) ◽  
pp. 193-205 ◽  
Author(s):  
XINPING GUAN ◽  
CAILIAN CHEN ◽  
HAIPENG PENG ◽  
ZHENGPING FAN
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Error Control ◽  
Chaotic Systems ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Control Technique ◽  
Time Delayed Feedback

This paper addresses time-delayed feedback control (DFC) of time-delay chaotic systems. To extend the DFC approach to time-delay chaotic system, alter having been successfully used in chaotic systems without time-delays, the standard feedback control (SFC) method is firstly employed to show the main control technique in this paper based on one error control system. Then sufficient conditions for stabilization and tracking problems via DFC are derived from the results based on SFC. Also, the systematic and analytic controller design method can be obtained to stabilize the system to an unstable fixed point and to tracking an unstable periodic orbit, respectively. Some numerical examples are provided to demonstrate the effectiveness of the presented method.

Stochastic Stability of Mathieu-Van Der Pol System with Delayed Feedback Control

2011 ◽  
Vol 105-107 ◽  
pp. 132-138
Author(s):  
Chang Shui Feng ◽  
Shuang Lin Chen
Keyword(s):  
Time Delay ◽  
Lyapunov Exponent ◽  
Feedback Control ◽  
Lyapunov Stability ◽  
Original System ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Control Force ◽  
Van Der Pol ◽  
Time Delayed Feedback

The asymptotic Lyapunov stability with probability one of Mathieu-Van der Pol system with time-delayed feedback control under wide-band noise parametric excitation is studied. First, the time-delayed feedback control force is expressed approximately in terms of the system state variables without time delay. Then, the averaged Itô stochastic differential equations for the system are derived by using the stochastic averaging method and the expression for the Lyapunov exponent of the linearized averaged Itô equations is derived. It is inferred that the Lyapunov exponent so obtained is the first approximation of the largest Lyapunov exponent of the original system, and the asymptotic Lyapunov stability with probability one of the original system can be determined approximately by using the Lyapunov exponent. Finally, the effects of time delay in feedback control on the Lyapunov exponent and the stability of the system are analyzed. The theoretical results are well verified through digital simulation.

CHAOTIFICATION OF A NONLINEAR VIBRATION ISOLATION SYSTEM BY DUAL TIME DELAYED FEEDBACK CONTROL

2013 ◽  
Vol 23 (06) ◽  
pp. 1350096 ◽  
Author(s):  
YINGLI LI ◽  
DAOLIN XU ◽  
YIMING FU ◽  
JIAXI ZHOU
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Vibration Isolation ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Stable Region ◽  
Control Parameters ◽  
Isolation System ◽  
Vibration Isolation System ◽  
Time Delayed Feedback

Line spectrum of noise radiated from machinery vibrations of underwater vehicles is one of the most harmful signals that expose the characteristics of vehicles and locations. In order to distort the features and restrain the intensity of the line spectra, we attempt to chaotify the vibration system by time delay control. To avoid blindly numerical testing of the control parameters, stability of a two-dimensional vibration isolation floating raft system with two time-delayed feedback control is studied in this paper, aiming to provide guidance for chaotification. The system with dual equal time delay is investigated by the generalized strum method and the polynomial eigenvalues are adopted to analyze the stability of the controlled vibration isolation system with two unequal time delays. The critical control gains and delays for stability switches are obtained. By adjusting the control parameters beyond stable region, it is feasible to chaotify the system. Numerical simulations are conducted to compare the effect of two time delay with different control parameters and different control scheme to complicate the vibration isolation system.

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