Temporal Logic Disturbance Rejection Control of Nonlinear Systems Using Control Barrier Functions

The high level of autonomy within autonomous systems demands new control strategies to achieve more complex objectives while ensuring both safety and robustness, rather than relying solely on a given reference. To this end, this article addresses the problem of temporal logic disturbance rejection control (TLDRC) for a class of nonlinear systems subject to disturbances. Signal temporal logic (STL) specifications are introduced for the representation of complex tasks. A control barrier function (CBF), composed of a monotonic function characterizing the temporal behavior of the system and a predicate function, is constructed to encode the STL specifications. To guarantee robustness against disturbances, generalized proportional integral observers (GPIOs) are introduced for higher-accuracy disturbance estimation. It is shown that by fully exploiting the constructed CBF and the disturbance estimate, the developed TLDRC strategy is able to ensure the STL specifications and compensate undesirable effects caused by unknown disturbances, even if they are fast-time-varying. A numerical example is presented to illustrate the effectiveness of the proposed strategy.