The article describes design principles of sensorless observing and control system of electrical submersible pump's induction motor based on dynamic state estimation using unscented Kalman filter. The artificial lift method with electrical submersible pumps in the oil industry is associated with measurements of technological parameters from which oil fluid flow rate is one of the most important. To develop sensorless control and parameters observing system the design principles of flow rate observers were proposed. The main possible scenarios for flow rate observation are considered, including those using surface-mounted sensors. The article also considers issues relating to the limitations in flow rate observation by usage pump catalog characteristics, involving control electric drive test signals changing the pump rotational speed. Overcoming these problems is proposed to the electrical submersible pump's flow rate observing system based on a machine learning model. The simulation results using a complex electrical submersible pump model confirming the efficiency of the proposed methods are provided.