Memristor Chaotic Oscillator Predefined-Time Synchronization

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Solution Overview

Problem

Conventional secure communication systems using chaotic synchronization face challenges with predefined-time synchronization, handling unknown inputs, and transmission channel noise, leading to synchronization issues and inaccurate message recovery.

Innovation Solution

A secure encryption-decryption system employing a single-channel predefined-time synchronization method using a memristor chaotic system, where a high-gain observer is constructed to demodulate chaotic signals, allowing for arbitrary settling time independent of initial conditions and system parameters, and a filtered observer is used to mitigate noise effects.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If conventional synchronization techniques are used, then synchronization can be achieved, but all state variables of the drive system must be transmitted through the communication channel, leading to channel overload

Engineering Contradiction:

Improvesynchronization accuracyVSAvoidcommunication channel load

Core Design Contradiction:

ReliabilityVSQuantity of substance

Solution Approach 1:

The invention extracts only the necessary information (single output variable) from the drive system for transmission, rather than transmitting all state variables. This is achieved by designing an observer at the receiver side that can reconstruct the full state from this single transmitted variable, thereby reducing channel load while maintaining synchronization accuracy

Inventive Principle:

Principle #2Taking out (Extraction)

Solution Approach 2:

The invention introduces an observer as an intermediary system at the receiver side that mediates between the received single-channel signal and the required full state information. The observer reconstructs the complete state vector from the limited transmitted information, enabling synchronization without direct transmission of all state variables

Inventive Principle:

Principle #24Intermediary (Mediator)

2Adaptability or versatility

If conventional techniques are used, then basic encryption can be performed, but they cannot adequately handle unknown inputs representing secret messages in chaotic dynamics

Engineering Contradiction:

Improvehandling unknown inputVSAvoidmessage recovery accuracy

Core Design Contradiction:

Adaptability or versatilityVSReliability

Solution Approach 1:

The invention implements a feedback mechanism where the receiver's observer continuously adjusts its state estimation based on the difference between the received signal and its own generated signal. This feedback loop enables the system to track and recover the unknown input (secret message) embedded in the chaotic signal, achieving accurate message recovery despite the unknown input nature

Inventive Principle:

Principle #23Feedback

3Reliability

If conventional synchronization methods are used, then synchronization can be maintained, but transmission channel noise destroys the predefined-time synchronization and makes message recovery inaccurate or impossible

Engineering Contradiction:

Improvesynchronization stabilityVSAvoidtransmission channel noise

Core Design Contradiction:

ReliabilityVSObject-affected harmful factors

Solution Approach 1:

The invention converts the harmful effect of noise into a manageable disturbance by designing an observer that explicitly accounts for noise in its design. The observer structure and gain selection are optimized to filter out noise effects while maintaining the ability to track the underlying synchronous signal and recover the secret message, thus transforming noise from a destructive factor into a controlled parameter

Inventive Principle:

Principle #22Blessing in disguise (Convert harm into benefit)

4Speed

If predefined-time synchronization is implemented, then fast synchronization is achieved, but the settling time depends on initial conditions and system parameters

Engineering Contradiction:

Improvesynchronization speedVSAvoidsettling time independence

Core Design Contradiction:

SpeedVSAdaptability or versatility

Solution Approach 1:

The invention employs dynamic gain scheduling in the observer design, where the observer gains are adjusted dynamically based on the current synchronization error and system state. This dynamic adaptation allows the system to achieve fast convergence from any initial condition while maintaining predefined-time performance, as the gains are optimized during the transient phase to ensure rapid error reduction regardless of starting conditions

Inventive Principle:

Principle #15Dynamics

Data Source

PatentUS11424906B1Secure encryption and decryption method and system

Publication Date: 2022.08.23 KING ABDULAZIZ UNIV

AI summary

Memristor based chaotic oscillators exhibit complex dynamics. They are often chosen for secure communication owing to their interesting feature. In chaos-based secure communication applications using the master-slave configuration, synchronization is a central issue. Most of the synchronization methods proposed in the literature are asymptotic. In practice, it is desirable that synchronization be established in a predefined time. This invention provides new developments in the design of high-gain observers with an unknown input dedicated for predefined-time synchronization of memristor based chaotic systems. The proposed predefined-time extended high gain observer is constructed on the basis of a time-dependent coordinates transformation based on modulating functions that annihilate the effect of initial conditions on the synchronization time. Both noise-free channel and noisy channel are considered. Simulations performed on a numerical example illustrated the efficiency of proposed approaches.