Derivative-Based Koopman Operators for Real-Time Control of Robotic Systems

This article presents a generalizable methodology for data-driven identification of nonlinear dynamics that bounds the model error in terms prediction horizon and magnitude derivatives system states. Using higher order general need not be known, we construct Koopman-operator-based linear representation utilize Taylor series accuracy analysis to derive an bound. The resulting formula is used choose basis functions obtain Koopman using closed-form expression can computed real time. inverted pendulum system, illustrate robustness given noisy measurements unknown dynamics, where are estimated numerically. When combined with control, has marginally better performance than competing modeling methods, such as SINDy NARX. In addition, model, approach lends itself readily efficient control design tools, linear–quadratic regulator, whereas other approaches require methods. efficacy further demonstrated simulation experimental results on tail-actuated robotic fish. Experimental show proposed outperforms tuned proportional–integral–derivative controller updating online significantly improves presence unmodeled fluid disturbance. complemented video available at https://youtu.be/9_wx0tdDta0 .