Current Projects

Current Projects

To set the foundation for robust adaptive control, reading notes and teaching notes are input into latex documents and revised. The most recent version of the reading notes on “Real Analysis” can be downloaded here: Realanalysis.pdf. Comments are very welcome. Tentatively, the title of the notes is set to be “Measure Theoretic Calculus in Abstract Spaces”.

In the process of my learning, I had been accumulating some nuggets in nonlinear systems that are of interest to the control community. I am collecting them in 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. Before now, this exercise is fertile since whenever I reference some result in my Real Analysis reading notes, that reference got messed up after I update Real Analysis. Now, this work can proceed fruitfully.

In the near future, my focus will be on trying to work out Probability Theory. I want to make sure that the tools I used in my stochastic control research are correct. I will try to prove these tools rigorously and then continue to control research.

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 CDC). Further properties of minimum phase linear systems are studied in the working paper MinPhase2SIAM.pdf. Comments are very welcome.

In the estimation part of robust adaptive control, the cost-to-come function method is employed. In the control design step of robust adaptive control, the integrator backstepping methodology is employed. A softer backstepping method is under study.

Project 1: Robust adaptive control

Project 2: Teaching notes development