Design of a Suboptimal Controller based on Riccati Equation and State-dependent Impulsive Observer for a Robotic Manipulator

Abstract

In this paper, Riccati equation and state-dependent impulsive observer (SDIO) are combined to design a controller for the nonlinear dynamical system of a robotic manipulator. A state-dependent Riccati equation-based controller is similar to optimal linear quadratic regulator where its Riccati equation employs pseudo linearization. Pseudo-linearization is a technique to represent systems with a structure similar to a linear system while preserving all characteristics of the original nonlinear system. It is stronger than the linearization technique via Jacobin method and does not need to change the operating point. Here it is shown that, the impulsive observer is able to estimate system states even if they are not transmitted from the sensors with a regular sampling rate. Via the proposed design, the stability of the closed loop system is analyzed using comparison principle which results in less conservative stability criteria. Applying pseudo linearization technique to the system and combining the Riccati equation controller and SDIO, suboptimal observer based control is obtained for the nonlinear manipulator systems especially when the system output is not accessible at all moments. The simulation results indicate the performance and efficiency of the proposed method in controlling the system.