Optimal Trajectory Tracking for Uncertain Linear Discrete-time Systems using Time-varying Q-learning
Abstract
This Article Introduces a Novel Optimal Trajectory Tracking Control Scheme Designed for Uncertain Linear Discrete-Time (DT) Systems. in Contrast to Traditional Tracking Control Methods, Our Approach Removes the Requirement for the Reference Trajectory to Align with the Generator Dynamics of an Autonomous Dynamical System. Moreover, It Does Not Demand the Complete Desired Trajectory to Be Known in Advance, Whether through the Generator Model or Any Other Means. Instead, Our Approach Can Dynamically Incorporate Segments (Finite Horizons) of Reference Trajectories and Autonomously Learn an Optimal Control Policy to Track Them in Real Time. to Achieve This, We Address the Tracking Problem by Learning a Time-Varying (Formula Presented.) -Function through State Feedback. This (Formula Presented.) -Function is Then Utilized to Calculate the Optimal Feedback Gain and Explicitly Time-Varying Feedforward Control Input, All Without the Need for Prior Knowledge of the System Dynamics or Having the Complete Reference Trajectory in Advance. Additionally, We Introduce an Adaptive Observer to Extend the Applicability of the Tracking Control Scheme to Situations Where Full State Measurements Are Unavailable. We Rigorously Establish the Closed-Loop Stability of Our Optimal Adaptive Control Approach, Both with and Without the Adaptive Observer, Employing Lyapunov Theory. Moreover, We Characterize the Optimality of the Controller with Respect to the Finite Horizon Length of the Known Components of the Desired Trajectory. to Further Enhance the Controller's Adaptability and Effectiveness in Multitask Environments, We Employ the Efficient Lifelong Learning Algorithm, Which Leverages a Shared Knowledge Base within the Recursive Least Squares Algorithm for Multitask (Formula Presented.) -Learning. the Efficacy of Our Approach is Substantiated through a Comprehensive Set of Simulation Results by using a Power System Example.
Recommended Citation
M. Geiger et al., "Optimal Trajectory Tracking for Uncertain Linear Discrete-time Systems using Time-varying Q-learning," International Journal of Adaptive Control and Signal Processing, Wiley, Jan 2024.
The definitive version is available at https://doi.org/10.1002/acs.3807
Department(s)
Electrical and Computer Engineering
Second Department
Computer Science
Publication Status
Full Access
International Standard Serial Number (ISSN)
1099-1115; 0890-6327
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 Wiley, All rights reserved.
Publication Date
01 Jan 2024
Comments
Office of Naval Research, Grant N00014‐21‐1‐2232