Surviving disturbances: a predictive control framework with guaranteed safety

Rejecting all disturbances is an extravagant hope in safety-critical control systems, hence surviving them where possible is a sensible objective a controller can deliver. In order to build a theoretical framework starting from surviving all disturbances but taking the appropriate opportunity to reject them, a sufficient condition on surviving disturbances is first established by exploring the relation among steady sets of state, input, and disturbance, followed by an output reachability condition on rejecting disturbances. A new robust safety-critical model prediction control (MPC) framework is then developed by embedding the quartet of pseudo steady input, output, state, and disturbance (IOSD) into the optimisation. Unlike most existing tracking MPC setups, a new and unique formulation is adopted by taking the pseudo steady disturbance as an optimisation decision variable, rather than directly driven by the disturbance estimate. This new setup is able to decouple estimation error dynamics, significantly contributing to the guarantee of recursive feasibility, even if the disturbance or its estimate changes rapidly. Moreover, towards optimal coexistence with disturbances, offset-free tracking of a compromised reference can be achieved, if rejecting the disturbance conflicts with safety-critical specifications. Finally, the benefits of the proposed method have been demonstrated by both numerical simulations and experiments on aerial physical interaction.