Nonlinear System Level Synthesis for Polynomial Dynamical Systems

Abstract: This work introduces a controller synthesis method via system level synthesis for nonlinear systems characterized by polynomial dynamics. The resulting framework yields finite impulse response, time-invariant, closed-loop transfer functions with guaranteed disturbance cancellation. Our method generalizes feedback linearization to enable partial feedback linearization, where the cancellation of the nonlinearity is spread across a finite-time horizon. This provides flexibility to use the system dynamics to attenuate disturbances before cancellation via control, reducing the cost of control compared with feedback linearization while maintaining guarantees about disturbance rejection. This approach is illustrated on a benchmark example and on a common model for fluid flow control.