Learning stabilising policies for constrained nonlinear systems
This work addresses control challenges for constrained nonlinear systems, such as in industrial processes, but appears incremental as it builds on existing control principles.
The authors tackled the problem of controlling constrained nonlinear systems with disturbances by proposing a two-layered control scheme that ensures stability and constraint satisfaction while improving performance via a trainable neural network. Simulation results on a pH-neutralisation benchmark demonstrated its effectiveness.
This work proposes a two-layered control scheme for constrained nonlinear systems represented by a class of recurrent neural networks and affected by additive disturbances. In particular, a base controller ensures global or regional closed-loop l_p-stability of the error in tracking a desired equilibrium and the satisfaction of input and output constraints within a robustly positive invariant set. An additional control contribution, derived by combining the internal model control principle with a stable operator, is introduced to improve system performance. This operator, implemented as a stable neural network, can be trained via unconstrained optimisation on a chosen performance metric, without compromising closed-loop equilibrium tracking or constraint satisfaction, even if the optimisation is stopped prematurely. In addition, we characterise the class of closed-loop stable behaviours that can be achieved with the proposed architecture. Simulation results on a pH-neutralisation benchmark demonstrate the effectiveness of the proposed approach.