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Linear time-invariant Systems01:23

Linear time-invariant Systems

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A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
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Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
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System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
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Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
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Event-Triggered Adaptive NN Tracking Control for MIMO Nonlinear Discrete-Time Systems.

Wenqi Xu, Xiaoping Liu, Huanqing Wang

    IEEE Transactions on Neural Networks and Learning Systems
    |June 15, 2021
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    Summary

    This study introduces an event-based adaptive neural network (NN) control algorithm for MIMO nonlinear systems. The novel approach simplifies computation and ensures system stability using radial basis function NNs (RBFNNs).

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    Area of Science:

    • Control Systems Engineering
    • Artificial Intelligence
    • Nonlinear Dynamics

    Background:

    • Existing control algorithms for multiple-input-multiple-output (MIMO) nonlinear discrete-time systems often face challenges with computational complexity and reliance on virtual controls.
    • Adaptive neural networks (NNs) offer a powerful framework for approximating complex nonlinear functions, but their efficient implementation in event-triggered control remains an area of active research.

    Purpose of the Study:

    • To design a novel event-based adaptive neural network (NN) control algorithm for MIMO nonlinear discrete-time systems.
    • To reduce the computational burden and simplify the realization of adaptive NN controllers through an event-triggered mechanism.
    • To ensure the stability of the closed-loop system using a recursive design procedure that avoids virtual controls.

    Main Methods:

    • A recursive design procedure is employed to develop the controller, requiring only system states and eliminating the need for virtual controls.
    • Radial basis function neural networks (RBFNNs) are utilized to approximate the control input within an event-based adaptive framework.
    • The number of event-triggered conditions and online updated parameters per subsystem is minimized to one, enhancing computational efficiency.

    Main Results:

    • The proposed event-based adaptive NN control algorithm significantly reduces computational load and simplifies implementation.
    • Semiglobal uniformly ultimate boundedness (SGUUB) of all signals in the closed-loop system is rigorously proven using the Lyapunov difference approach.
    • Simulation results demonstrate the effectiveness and practical applicability of the developed control strategy.

    Conclusions:

    • The novel event-based adaptive NN control algorithm provides an effective and computationally efficient solution for MIMO nonlinear discrete-time systems.
    • The algorithm's ability to guarantee system stability and its simplified structure make it suitable for real-world applications.
    • This research contributes to the advancement of adaptive control techniques, particularly in the context of event-triggered systems and neural network applications.