What are some good books or online resources for learning about optimization and probability focused control theory? A mathematician I was speaking to recently mentioned that a lot of the newest control theory relies mostly on optimization and probability theory (particularly stochastic processes), rather than the complex analysis upon which it used to be focused.
Could someone recommend books/resources for this more modern control theory? Also, is knowing about the old type necessary to learn about more modern control theory?
I know there are some other questions here requesting books for control theory, but I'm not sure which ones are about old control theory, and which are about the new type (so information on what terms to search for would also be helpful).
 A: Stephen Boyd, Craig Barratt, Linear Controller Design: Limits of Performance, Prentice-Hall, 1991.

The main topic of the book is closed-loop design and the computation of performance limits using convexity.  The book introduces a standard
  framework for the control design problem and describes many practical
  design specifications in this framework.  It is shown that many of
  these specifications are closed-loop convex; the corresponding control
  design problems can therefore be cast as infinite-dimensional
  nondifferentiable convex optimization problems.  The book shows how
  these problems can be solved using the ellipsoid and cutting-plane
  algorithms, using a Ritz approximation.
The book describes how the achievable performance can be computed
  numerically for any family of closed-loop convex specifications.
  Closed-loop convex specifications include, for example, H-two,
  H-infinity, or l-one norm bounds, entropy bounds, step response
  envelopes and asymptotic command decoupling.


Richard M. Murray, Optimization-Based Control, February 2010.

These notes serve as a supplement to Feedback Systems by Åström and
  Murray and expand on some of the topics introduced there. Our focus is
  on the use of optimization-based methods for control, including
  optimal control theory, receding horizon control and Kalman filtering.
  Each chapter is intended to be a standalone reference for advanced
  topics that are introduced in Feedback Systems.

A: Small contribution to the answer; Reinforcement learning is the bomb in these days. It is studied by a lot of different disciplines because it is a very general concept. Using learning techniques one could learn a control system how to steer itself. For instance, see this robot which learned itself to walk, https://www.youtube.com/watch?v=SBf5-eF-EIw. 
These type of techniques rely a lot on stochastic process and statistical theory. Some wikipedia pages; 
https://en.wikipedia.org/wiki/Markov_decision_process
https://en.wikipedia.org/wiki/Dynamic_programming (heavily used in reinforcement learning and originally invented by a control theorist Bellman)
https://en.wikipedia.org/wiki/Reinforcement_learning
