[Paper Review] Adaptive Control: Algorithms, Analysis and Applications

Ioan Doré Landau, Rogelio Lozano+2 more|arXiv (Cornell University)|Jun 11, 2024

Advanced Control Systems Optimization292 citations

TL;DR

A comprehensive, discrete-time treatment of adaptive control that unifies basic techniques with synthesis, analysis, and real-world applications, emphasizing mathematical foundations for practical use.

ABSTRACT

Adaptive control provides techniques for adjusting control parameters in real time to maintain system performance despite unknown or changing process parameters. These methods use real data to tune controllers and adjust plant models or controller parameters. The field has progressed significantly since the 1970s, helped by digital computers. Early applications offered essential feedback, and theoretical advances solved many basic problems. This book comprehensively treats adaptive control, guiding readers from basic problems to analytical solutions with practical applications. Presenting a unified view is challenging due to various design steps and applications. However, a coherent presentation of basic techniques is now possible. The book uses a discrete-time approach to reflect the role of digital computers and shares practical experiences and understanding of different control designs. Mathematical aspects of synthesizing and analyzing algorithms are emphasized, though they alone may not solve practical problems. The book includes applications of control techniques but stresses that a solid mathematical understanding is crucial for creatively applying them to new challenges. Mathematical synthesis and analysis are highlighted, but they must be supplemented with practical problem-solving and algorithm modifications for specific applications.

Motivation & Objective

• Motivate the need for real-time parameter adaptation to cope with unknown or changing process parameters.
• Provide a unified presentation of adaptive control techniques suitable for digital computers.
• Bridge mathematical synthesis/analysis with practical control design and implementation.
• Highlight the role of discrete-time modeling to reflect modern computational environments.

Proposed method

• Adopt a discrete-time framework to reflect digital computation in control design and analysis.
• Emphasize mathematical synthesis and analytical techniques behind adaptive algorithms.
• Combine theory with practical considerations and real-data tuning of controllers.
• Discuss applications while maintaining a solid mathematical foundation for creative problem-solving.

Experimental results

Research questions

• RQ1 What are the core adaptive control techniques that form a cohesive, unified framework in discrete time?
• RQ2 How can adaptive algorithms be synthesized and analyzed to ensure performance under parameter uncertainty?
• RQ3 What is the role of mathematical rigor in translating adaptive control methods into practical, real-world applications?
• RQ4 How do practical considerations and digital implementation influence the design of adaptive controllers?

Key findings

• The book presents a coherent, unified view of basic adaptive control techniques.
• A discrete-time approach is used to reflect the role of digital computers in control design.
• Mathematical synthesis and analysis are emphasized as essential for effectively applying adaptive control to real problems.
• Applications are discussed with an emphasis on practical experience and problem-solving beyond theory.