A Concise Introduction

**Daniel Liberzon**
*University of Illinois at Urbana-Champaign*

7. Advanced Topics

In this chapter we discuss four additional topics (independent from one another) which extend the developments of Chapters 4-6. The objective of the present chapter is twofold: to enhance the reader's understanding of the earlier material, and to indicate some of the possible avenues for further study. We will not strive for the same level of completeness and rigor here as in the previous chapters, and instead will limit ourselves to an introductory discussion. The references provided at the end of the chapter, as usual, can be consulted for precise statements of technical results and other details.

- 7.1 Maximum principle on manifolds
- 7.1.1 Differentiable manifolds
- 7.1.2 Re-interpreting the maximum principle
- 7.1.3 Symplectic geometry and Hamiltonian flows

- 7.2 HJB equation, canonical equations, and characteristics

- 7.3 Riccati equations and inequalities in robust control

- 7.4 Maximum principle for hybrid control systems

- 7.5 Notes and references for Chapter 7

Daniel 2010-12-20