Content
1 Introduction to Optimal Control (OC)
- Some examples
- Problems statement of Optimal Control
- Admissible control and associated trajectory
- Optimal Control problems
- Calculus of Variation problems
2 The simplest problem of OC
- The necessary condition of Pontryagin
- The proof in a particular situation
- Sufficient conditions
- First generalizations
- Initial/final conditions on the trajectory
- On minimum problems
- The case of Calculus of Variation
- Examples and applications
- The curve of minimal length
- A problem of business strategy I
- A two-sector model
- A problem of inventory and production I
- Singular and bang-bang controls
3 General problems of OC
- Problems of Bolza, Mayer and Lagrange
- Problems with fixed or free final time
- Fixed final time
- Free final time
- The proof of the necessary condition
- The Bolza problem in Calculus of Variations
- Labor adjustment model of Hamermesh
- Time optimal problem
- The classical example of Pontryagin and its boat
- Existence and controllability results
- Infinite horizon problems
- The model of Ramsey
- Autonomous problems
- Current Hamiltonian in model of optimal consumption
4 Constrained problems of OC
- The general case
- Pure state constraints
- Commodity trading
- Isoperimetric problems in CoV
- Necessary conditions with regular constraints
- The multiplier ν as shadow price
- The foundation of Cartagena
- The Hotelling model of socially optimal extraction
5 OC with dynamic programming
- The value function: necessary conditions
- The final condition
- Bellman's Principle of optimality
- The Bellman-Hamilton-Jacobi equation
- The value function: sufficient conditions
- More general problems of OC
- Examples and applications
- Infinite horizon problems
- A model of optimal consumption
- Problems with discounting and salvage value