Optimal placement of sensor and actuator for controlling low-dimensional chaotic systems based on global modeling

Controlling chaos is fundamental in many applications, and for this reason, many techniques have been proposed to address this problem. Here, we propose a strategy based on an optimal placement of the sensor and actuator providing global observability of the state space and global controllability to any desired state. The first of these two conditions enables the derivation of a model of the system by using a global modeling technique. In turn, this permits the use of feedback linearization for designing the control law based on the equations of the obtained model and providing a zero-flat system. The procedure is applied to three case studies, including two piecewise linear circuits, namely, the Carroll circuit and the Chua circuit whose governing equations are approximated by a continuous global model. The sensitivity of the procedure to the time constant of the dynamics is also discussed.

Automated summary

Controlling chaos is important in many applications, and various techniques have been proposed for this purpose. In this study, we propose a strategy that involves optimal placement of sensors and actuators to achieve global observability and controllability. This strategy allows for the derivation of a system model using a global modeling technique, which is then used for designing a control law through feedback linearization. The effectiveness of this strategy is demonstrated through the application to three case studies, including two piecewise linear circuits, and the sensitivity to the system dynamics' time constant is also discussed.