Online Feedback Optimization

Automatic Control Laboratory

How can we operate a complex system optimally?

How can we decide the system inputs that maximize a performance metric defined on the system output?

Complex system

Controllable inputs

System output

Models for complex systems are known to be unreliable.

Pre-computing the optimal input based on a model of the system leads to suboptimal and possibly unsafe operation of the system.

Complex system

Controllable inputs

System output

Controllable inputs

System output

Online

Feedback

Optimization

Instead, we can iteratively

 

Controllable inputs

System output

Online

Feedback

Optimization

Instead, we can iteratively

 

1. Measure the system output

Controllable inputs

System output

Online

Feedback

Optimization

Instead, we can iteratively

 

1. Measure the system output

 

2. Compute an incremental step towards the optimum

Instead, we can iteratively

 

1. Measure the system output

 

2. Compute an incremental step towards the optimum

 

3. Actuate the system and observe its response

Controllable inputs

System output

Online

Feedback

Optimization

Controllable inputs

System output

Active research directions

• How to translate optimization algorithms into feedback controllers?
  
  
• How to certify stability of the closed-loop system?
  
  
• How to guarantee safe operation of the system during the entire trajectory towards the optimum?

Online

Feedback

Optimization

 Online feedback optimization
 

• is extremely robust against model mismatch, disturbances, unknown dynamics
   
• drives the system to the optimum
   
• satisfies system constraints at all times
   
• is computationally tractable even for complex large-scale systems

Initial condition

Optimum

System trajectory

Safe region

Main application domain:
Smart electrical power grids

• a complex real-time optimization problem
• a complex large-scale system to control
• a large number of inputs and outputs
• abundant measurements
• need for dependable decision mechanisms

Automatic Control Laboratory

Saverio Bolognani

Adrian Hauswirth

Giuseppe Belgioioso

Lukas Ortmann

Miguel Picallo Cruz

Dominic Liao-Mc Pherson