Design and analysis of a novel command governor architecture for shaping the transient response of nonlinear uncertain dynamical systems

In this paper, we develop a new control framework for nonlinear uncertain dynamical systems. The proposed methodology consists of a novel command governor architecture and an adaptive controller. The command governor is a linear dynamical system which 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 approximates the ideal reference system by properly choosing the design parameter of the command governor. In addition, the purpose of the adaptive controller is to asymptotically assure that the error between the controlled nonlinear uncertain dynamical system and the ideal reference system vanishes in steady state. 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.