9.X. Continuous-time optimal control – dynamic programming
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B(E)3M35ORR – Optimal and Robust Control
0. Introduction
What is optimal and robust control?
Course outline
Rules of the course
Software for the course
Literature for the course
Similar courses
1. Optimization – theory
Learning goals
Optimization problems
Problem reformulations
Unconstrained optimization
Constrained optimization
Optimization modelling languages
References
Homework
2. Optimization – algorithms
Learning goals
Computing the derivatives
Unconstrained optimization
Constrained optimization
Numerical solvers
References
Homework
3. Discrete-time optimal control – direct approach
Learning goals
General finite-horizon nonlinear optimal control as an NLP
Finite-horizon LQR as a QP
Model predictive control (MPC)
Numerical solvers for MPC
References
Homework
4. Discrete-time optimal control – indirect approach
Learning goals
General finite-horizon nonlinear optimal control as a TP-BVP
Discrete-time LQR on a finite horizon
Discrete-time LQR on an infinite horizon
Discrete-time algebraic Riccati equation (DARE)
References
Homework
5. Discrete-time optimal control – dynamic programming (DP)
Learning goals
DP and discrete-time optimal control
Tabular outcomes of DP
Solving LQR via DP
Differential dynamic programming (DDP)
References
Homework
6. More on MPC
Stability of MPC
Recursive feasibility
Economic MPC
Explicit MPC
References
Homework
7. Continuous-time optimal control - indirect approach via calculus of variations
Overview of continuous-time optimal control
Calculus of variations
Indirect approach to optimal control
Indirect approach to LQR on a finite horizon
Indirect approach to LQR on an infinite horizon
Continuous-time Riccati equation
Trajectory stabilization and neigboring extremals
References
Homework
8. Continuous-time optimal control - indirect approach via Pontryagin’s maximum principle
Pontryagin’s maximum principle
Constrained optimal control
Time-optimal control
References
Homework
9. Numerical methods for continuous-time optimal control - both indirect and direct approaches
Numerical methods for indirect approach
Numerical methods for direct approach
Software
References
Homework
9.X. Continuous-time optimal control – dynamic programming
Dynamic programming for continuous-time optimal control
Using HJB equation to solve the continuous-time LQR problem
Differential dynamic programming (DDP)
References
Homework
10. Some extensions: LQG, LTR, H2
LQR for stochastic systems
LQG control
Loop transfer recovery (LTR)
H2-optimal control
Software
References
Homework
11. Uncertainty modelling and robustness analysis
Uncertainty (in) modelling
Robustness analysis for unstructured uncertainty
Robustness analysis for structured uncertainty
Software
References
Homework
12. Robust control
Mixed sensitivity design
Hinfinity-optimal control
Mu synthesis
Software
References
Homework
13. Limitations of achievable performance
Limitations for SISO systems
Limitations for MIMO systems
References
Homework
14. Model and controller order reduction
Model order reduction
Controller order reduction
Benchmarks
References
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9.X. Continuous-time optimal control – dynamic programming
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References
LQR for stochastic systems