Related Experiment Video
Updated: Jul 7, 2026
06:52
Deep-Learning Based Multi-Joint Synchronous Tracking for Objective Quantification of Hindlimb Locomotor Kinematics in Rats
Published on: April 3, 2026
Nonlinear adaptive trajectory tracking using dynamic neural networks
A S Poznyak1, W Yu, E N Sanchez
1Departamento de Control Automatico, CINVESTAV-IPN, Mexico D.F., 07360, Mexico.
IEEE Transactions on Neural Networks
|February 7, 2008
Summary
This study introduces dynamic neural networks for adaptive nonlinear identification and trajectory tracking. We establish theorems bounding identification and tracking errors, validated with relay and chaotic Duffing systems.
Area of Science:
- Control Systems Engineering
- Artificial Intelligence
- Nonlinear Dynamics
Background:
- Adaptive nonlinear systems require robust identification and precise trajectory tracking.
- Dynamic neural networks offer a promising approach for complex system control.
- Stability and error bounds are critical for validating control strategies.
Purpose of the Study:
- To develop and analyze adaptive nonlinear identification and trajectory tracking using dynamic neural networks.
- To establish theoretical bounds for identification and tracking errors.
- To demonstrate the practical application of the proposed methods on complex systems.
Main Methods:
- Lyapunov-like analysis for determining stability conditions of identification error.
- Local optimal controller for analyzing trajectory tracking error.
- Utilizing algebraic and differential Riccati equations for error analysis.
- Formulating two original theorems to bound identification and tracking errors.
Main Results:
- Established stability conditions for the identification error using Lyapunov-like analysis.
- Derived bounds for both the identification error and the trajectory tracking error through two novel theorems.
- Successfully illustrated the effectiveness of the proposed methods on a second-order relay system and the chaotic Duffing equation.
Conclusions:
- The proposed dynamic neural network approach provides effective adaptive nonlinear identification and trajectory tracking.
- The derived error bounds offer theoretical guarantees for system performance.
- The validated examples highlight the method's applicability to diverse and challenging nonlinear systems.
Related Concept Videos
01:26Orthogonal Trajectories
Orthogonal trajectories describe the geometric relationship between two families of curves that intersect each other at right angles. One illustrative case involves a family of parabolas that open sideways along the x-axis. These curves share a common shape but differ by a scaling parameter, resulting in a set of curves that all pass through the origin and widen at different rates.Determining Orthogonal TrajectoriesTo identify the orthogonal trajectories for these parabolas, the first step...
01:30Vector Functions and Motion: Problem Solving
Accurate position tracking is fundamental to the safe and effective operation of unmanned aerial vehicles (UAVs), particularly during precision maneuvers near complex structures. In this scenario, a drone is programmed to perform a high-precision inspection of a vertical structure, starting at position ((x, y, z) = (3, 0, 0)), with an initial velocity oriented in the positive z-direction. The trajectory of the drone is governed by a time-dependent acceleration function a(t), which is predefined...