Robust adaptive control for a class of uncertain nonlinear systems with time-varying delay
Ruliang Wang1, Jie Li, Shanshan Zhang
1Computer and Information Engineering College, Guangxi Teachers Education University, Nanning 530023, China. wrl@gxtc.edu.cn
Thescientificworldjournal
|July 16, 2013
Summary
This study introduces adaptive neural control for complex nonlinear systems with time delays. The new method ensures system stability and accurate trajectory tracking, demonstrating effectiveness through simulations.
Area of Science:
- Control Systems Engineering
- Nonlinear Dynamics
- Artificial Intelligence in Control
Background:
- Perturbed nonlinear Multiple-Input Multiple-Output (MIMO) systems with time-varying delays present significant control challenges.
- Existing control strategies often struggle with controller singularity and ensuring bounded closed-loop signals.
Purpose of the Study:
- To design an adaptive neural control scheme for a specific class of perturbed nonlinear MIMO time-varying delay systems.
- To address controller singularity and ensure robust system performance.
Main Methods:
- Development of a neural controller based on a quadratic-type Lyapunov-Krasovskii functional.
- Utilizing a block-triangular system structure for controller design.
Main Results:
- The proposed control scheme effectively avoids controller singularity.
- All closed-loop signals are guaranteed to remain bounded.
- Output tracking error dynamics converge to a neighborhood of the desired trajectories.
Conclusions:
- The adaptive neural control design is effective for the targeted complex systems.
- The method provides a robust solution for systems with nonlinearities, perturbations, and time delays.
Related Concept Videos
01:26Feedback control systems
Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
01:23Linear time-invariant Systems
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 calculated...
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 calculated...
01:07Time-Domain Interpretation of PD Control
Proportional-Derivative (PD) control is a widely used control method in various engineering systems to enhance stability and performance. In a system with only proportional control, common issues include high maximum overshoot and oscillation, observed in both the error signal and its rate of change. This behavior can be divided into three distinct phases: initial overshoot, subsequent undershoot, and gradual stabilization.
Consider the example of control of motor torque. Initially, a positive...
Consider the example of control of motor torque. Initially, a positive...
01:31Classification of Systems-II
Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
01:24BIBO stability of continuous and discrete -time systems
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.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
01:27State Space Representation
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
Consider an RLC circuit, a...