7. Continuous-time optimal control - indirect approach via calculus of variations
Indirect approach to LQR on a finite horizon
B(E)3M35ORR – Optimal and Robust Control
1. Optimization – theory
Optimization problems
Problem reformulations
Theory for unconstrained optimization
Theory for constrained optimization
Optimization modelling languages
References
2. Optimization – algorithms
Computing derivatives
Algorithms for unconstrained optimization
Algorithms for constrained optimization
Numerical solvers
References
3. Discrete-time optimal control – direct approach
General finite-horizon nonlinear discrete-time optimal control as a nonlinear program
Finite-horizon LQR-optimal control as a QP
Model predictive control (MPC)
Numerical solvers for MPC
References
4. Discrete-time optimal control – indirect approach
General nonlinear discrete-time optimal control
Discrete-time LQR on a finite horizon
Discrete-time LQR-optimal control on an infinite horizon
Discrete-time algebraic Riccati equation (DARE)
References
5. Discrete-time optimal control – dynamic programming
Dynamic programming and discrete-time optimal control
Tables as outcomes of dynamic programming
Solving LQR via dynamic programming
Differential dynamic programming (DDP)
References
6. More on MPC
Stability of MPC
Recursive feasibility
Economic MPC
Explicit MPC
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
8. Continuous-time optimal control - indirect approach via Pontryagin’s maximum principle
Pontryagin’s maximum principle
Constrained optimal control
Time-optimal control
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
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
10. Some extensions: LQG, LTR, H2
LQR for stochastic systems
LQG control
Loop transfer recovery (LTR)
H2-optimal control
11. Uncertainty modelling and robustness analysis
Uncertainty (in) modelling
Robustness analysis for unstructured uncertainty
Robustness analysis for structured uncertainty
Software
References
12. Robust control
Mixed sensitivity design
Hinfinity-optimal control
Mu synthesis
Software
References
13. Limitations of achievable performance
Limitations for SISO systems
Limitations for MIMO systems
References
14. Model and controller order reduction
Model order reduction
Controller order reduction
Benchmarks
References
7. Continuous-time optimal control - indirect approach via calculus of variations
Indirect approach to LQR on a finite horizon
Indirect approach to LQR on a finite horizon
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Indirect approach to optimal control
Indirect approach to LQR on an infinite horizon