A new command governor architecture for transient response shaping

In this paper, we develop a control framework for stabilization and command following of nonlinear uncertain dynamical systems. The proposed methodology consists of a new command governor architecture and an adaptive controller. The command governor is a dynamical system that adjusts the trajectory of a given command to follow an ideal reference system capturing a desired closed-loop dynamical system behavior in transient time. Specifically, we show that the controlled nonlinear uncertain dynamical system can approach the ideal reference system by choosing the design parameter of the command governor. In addition, an adaptive element is used to asymptotically assure that the error between the controlled nonlinear uncertain dynamical system and the ideal reference system is reduced in long term. Therefore, the proposed methodology not only has closed-loop transient and steady-state performance guarantees but can also shape the transient response by adjusting the trajectory of the given command with the command governor. We highlight that there exists a trade-off between the adaptive controller's learning rate and the command governor's design parameter. This key feature of our framework allows rapid suppression of system uncertainties without resorting to a high learning rate in the adaptive controller. Furthermore, we discuss the robustness properties of the proposed approach with respect to high-frequency dynamical system content such as measurement noise and / or unmodeled dynamics. A numerical example is provided to demonstrate the efficacy of the proposed architecture.