Transient-Robust Reference Governors: An Extension to Systems with Non-invertible Steady-State Mappings

In our previous work, we presented a constraint management technique, referred to as the Transient-Robust Reference Governor (TR-RG), to enforce state, output, and control constraints in closed-loop nonlinear systems. One of the key assumptions behind the TR-RG is that the input-output mapping of the nonlinear system is available at steady-state and, furthermore, this mapping is invertible. While this assumption holds in some situations (e.g., engine control in automotive applications), it does not hold in general (e.g., inverted pendulum control problem). To overcome this limitation, this paper extends TR-RG to a wider class of nonlinear systems, namely those with non-invertible or uncertain steady-state characterizations. Theoretical guarantees of constraint enforcement using this scheme are provided. Finally, the scheme is illustrated using two practical examples.