Learning-Based Adaptive Control for Stochastic Linear Systems with Input Constraints
This work addresses control design for uncertain systems with constraints, but it appears incremental as it builds on certainty-equivalence schemes without major breakthroughs.
The paper tackles adaptive control of stochastic linear systems with input constraints and unknown parameters, proving mean square boundedness of states under worst-case marginal stability assumptions.
We propose a certainty-equivalence scheme for adaptive control of scalar linear systems subject to additive, i.i.d. Gaussian disturbances and bounded control input constraints, without requiring prior knowledge of the bounds of the system parameters, nor the control direction. Assuming that the system is at-worst marginally stable, mean square boundedness of the closed-loop system states is proven. Lastly, numerical examples are presented to illustrate our results.