Current Projects

 

To set the foundation for robust adaptive control, reading notes and teaching notes are input into latex documents and revised.   The final draft version of the book “Measure Theoretic Calculus in Abstract Spaces” has been submitted for review.  Comments are still very welcome at this stage. 

I have begun to write a reading note on “Nonlinear Systems”.  The book by Prof. H. Khalil on nonlinear systems is absolutely the best in this topic.  Now that the measure-theoretic foundation for nonlinear system has been done, I will continue to collect results in nonlinear systems and enter into the reading note. 

Based on my book, 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 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 the working paper linadaptpub.pdf then solves the robust adaptive control problem for finite-dimensional continuous-time square MIMO linear time invariant system completely.  Comments are very welcome.  

 

Project 1: Robust adaptive control

Project 2: Teaching notes development