Course Outline for Optimal Control and Estimation (MAE 546)

Robert Stengel

School of Engineering and Applied Science
Princeton University

Spring 2009

Numbers in parentheses refer to sections of the book, OPTIMAL CONTROL AND ESTIMATION.

Week Number: Topics

1. Introduction [1]
   Scalars, vectors, and matrices [2.1]
   Matrix properties and operations [2.2]
   Dynamic system models and solutions [2.3]
   The optimal control problem [3.1]
   Cost functions [3.2]
   Parametric optimization [3.3]
2. Optimality conditions for control [3.4]
   Euler-Lagrange equations
3. Minimum principle
   Hamilton-Jacobi-Bellman equation
4. Numerical optimization [3.6]
5. Constraints and singular control [3.5]
   Simulated annealing
   Genetic algorithms
6. Neighboring-optimal control [3.7]
   Discrete-time systems
7. Least-squares estimation [4.1]
   Propagation of uncertainty [4.2]
8. Mid-term exam
   Discrete-time optimal filters [4.3]
9. Continuous-time optimal filters [4.5]
   Nonlinear state estimation [4.6]
   Adaptive filtering [4.7]
   Optimal control of nonlinear systems with random inputs and imperfect measurements [5.1, 5.2]
   Certainty-equivalence property of linear-quadratic-Gaussian controllers [5.3]
10. System stability [2.5]
    Linear, time-invariant systems with random inputs and imperfect measurements [5.4]
    Steady-state response to commands [6.2]
11. Cost function and controller structures [6.3]
    Frequency-domain modeling and analysis [2.6]
    
12. Modal properties of optimal control systems [6.4]
    Stability margins and disturbance response of linear-quadratic regulators [6.5]
13. Loop and cost transfer function matrices
    Multivariable Bode criterion
    Multivariable Nyquist criterion
    Stability margins of stochastic-optimal regulators [6.6]

Optimal Control and Estimation