Current Projects

 

To set the foundation for robust adaptive control, reading notes and teaching notes are input into latex documents and revised.   The book “Measure-Theoretic Calculus in Abstract Spaces: On the Playground of Infinite-Dimensional Spaces” has been published by Birkhäuser, an imprint of Springer-Nature in January 2024.  Comments are very welcome.  This book is the Holy Grail in analysis and now it is available for the public. 

I have begun to write a reading note on “Nonlinear Systems”. The note is tentatively titled “Nonlinear and Inverse Optimal Systems – a game theoretic view point.”  Currently, it contains a complete proof of my 2001 IEEE Transaction on Automatic Control paper coauthored with Ezal, Krener, and Kokotović.  This book is under development. 

Based on my book “Measure-Theoretic Calculus in Abstract Spaces: on the playground of infinite-dimensional spaces”, my earlier research for linear stochastic system seemed to be correct, but those for nonlinear stochastic systems are missing key technical assumptions, and therefore considered not correct.  Those results for nonlinear stochastic systems can only serve as pointers to what one might achieve for those systems. 

 

My main goal is to study robust adaptive control theory in detail, give it a solid foundation, solve for MIMO systems, and generalize to nonlinear and possibly infinite-dimensional systems.  Currently, I am advancing toward this goal from many fronts.

First of all, it is envisioned that the approach adopted by the project works on finite-dimensional minimum phase linear systems (necessary and sufficient condition).  The characterization of minimum phase linear systems is studied in the working paper:  MinPhaseSIAM.pdf (an abridged version had appeared in 57th IEEE Conference on Decision and Control). Further properties of minimum phase linear systems are studied in the working papers MinPhase2ACC.pdf and MinPhaseICS.pdf.  Minimum phase property for multiple-input and multiple-output linear systems have also be obtained in the working paper MinPhaseMIMOSIAM.pdf (an abridged version has appeared in IFAC World Congress 2020), the rest of this paper is to be submitted MinPhaseMIMO2-IFAC2020.pdf.  These papers, together with the vectorized version of these working papers and  the SISO adaptive control paper linadaptpub.pdf, then solves the robust adaptive control problem for finite-dimensional continuous-time square MIMO linear time invariant system completely in the paper MIMOlinadapt-IJACSP-2023-08-21.pdf (which had appeared in the International Journal of Adaptive Control and Signal Processing, October, 2023.) 

A new result on parallel interconnected linear systems where each one of the subsystem admit uniform vector relative degree and uniform observability indices (and thus is robust adaptive control design ready) but the subsystems do not share a uniform vector relative degree is studied, and the extended zero dynamics canonical form for the composite system is obtained.  This result is summarized in the working paper EZDCF-MIMO-PI-IFAC2023.pdf.   Thus, if one can show that the composite system is minimum phase, then robust adaptive control design can be performed on the composite system with nonuniform vector relative degrees.  This work is ongoing.  Comments are very welcome.  

Project 2: Teaching notes development

Project 1: Robust adaptive control