lpv_qmi
Data-Driven Control of Linear Parameter Varying (LPV) systems under Process Noise with Quadratic Matrix Inequalities (QMI).
Continuous-time systems supply noisy state-derivative-parameter observations. Discrete-time process require noisy state-parameter-next state observations.
A gain scheduling controller is synthesized by enforcing a QMI at each vertex of the parameter polytope.
The code is currently constructed for elementwise-L2 noise, but other types of noise models (energy bounds) may be enforced by modification of the QMIs.
Instructions
Generate a trajectory (with elementwise-L2 noise of bound epsilon) using lpvsim.sim. Define the vertices of the polytope (such as a manual definition or using lcon2vert from https://www.mathworks.com/matlabcentral/fileexchange/30892-analyze-n-dimensional-convex-polyhedra). Pass the trajectory into the lpvstab object for discrete-time stabilization, and then attempt generation of a gain scheduled controller on these vertices with the method lpvstab.stab.
For continuous-time systems use lpvstab_cont rather than lpvstab.
For H2 control in discrete-time, use lpvh2 rather than lpvstab.
Dependencies
- YALMIP: https://yalmip.github.io/
- Mosek: https://www.mosek.com/ (or any solver compatible with YALMIP)
All code is written and tested on Matlab R2021a.