A paper on convex optimization in system identification (aka learning dynamical systems), written by Mark Tobenkin, myself, and Alex Megretski, has been published in IEEE Transactions on Automatic Control. This paper reports some of the key findings of the work we did when all three of us were MIT, but has taken a while to get into a final form for publishing.
It is available open-access here:
This paper provides methods to address two major challenges in nonlinear system identification: guaranteeing model stability, and identifying long-term dependence between inputs and outputs. In particular, we provide convex parameterizations of flexible sets of nonlinear models with guaranteed stability, and also convex upper bounds on simulation error. Taken together, these allow tools such as sum-of-squares programming to be used to identify highly accurate nonlinear models from data.
A paper by my student Mounir Boudali, in collaboration with Peter Sinclair and Richard Smith of the University of Sydney Biomechanics Research Team, has been accepted to the IEEE Engineering in Medicine and Biology Conference.
The main idea is to generate predictive computational models of the relationship between different limbs during human motion, with the objective that these models can be used for control and motion planning within assistive devices and prosthetics. In this paper, we investigated using the Koopman operator to generate models.
A. Mounir Boudali, Peter J. Sinclair, Richard Smith, Ian R. Manchester, “Human Locomotion Analysis: Identifying a Dynamic Mapping Between Upper and Lower Limb Joints Using the Koopman Operator”, Proceedings of the 39th Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC’17), JeJu Island, S. Korea, July 2017.
My paper with Jean-Jacques Slotine introducing control contraction metrics has just been published in IEEE Transactions on Automatic Control
The main result of this paper is that difficult problems in nonlinear control design can be made easier by thinking about them in terms of differential (local) dynamics and contraction metrics. Roughly speaking, local stabilizability of all trajectories implies global stabilizability of all trajectories.
The search for a metric that verifies this fact can be written as a convex optimization problem, very similar to well-known formulations for linear control design. In particular, problems with polynomial dynamics can easily be solved using sum-of-squares, e.g. via Yalmip