H2−H∞ control of continuous-time nonlinear systems using the state-dependent Riccati equation approach

This paper presents a novel $ {H_2} - {H_\infty } $ state-dependent Riccati equation (SDRE) control approach with the purpose of providing a more effective control design framework for continuous-time nonlinear systems to achieve a mixed nonlinear quadratic regulator and H∞ control performance criteria. By solving the generalized SDRE, the optimal control solution is found to achieve mixed performance objectives guaranteeing nonlinear quadratic optimality with inherent stability property in combination with H∞ type of disturbance reduction. An efficient computational algorithm is given to find the solution to the $ {H_2} - {H_\infty } $ SDRE. The efficacy of the proposed technique is used to design the control system for inverted pendulum, an under-actuated nonlinear mechanical system