Nonlinear mixed H-2/H-infinity control for robust tracking design of robotic systems

A mixed H-2/H-infinity control design is proposed in this study for tracking of rigid robotic systems under parameter perturbations and external disturbances. The design objective is that under a prescribed disturbance attenuation level (H-infinity attenuation constraint), the optimal least square error (H-2 optimal tracking) must be achieved. Additionally, an explicit and global solution to this nonlinear time-varying mixed H-2/H-infinity control problem is presented by combining nonlinear minimax (Nash game) theory and LQ optimal control techniques. Moreover, by virtue of the skew symmetric property of robotic systems and adequate choice of state variable transformation, only two linear algebraic (instead of nonlinear time-varying) Riccati-like equations are required to construct the proposed mixed H-2/H-infinity tracking control law. Furthermore, these two linear algebraic equations can be solved with a very simple method so that a closed-form nonlinear mixed H-2/H-infinity tracking controller can be constructed. Finally, extensive simulations are made for mixed H-2/H-infinity tracking control of a two-link robotic manipulator. From the simulation results, the robust tracking performance of robotic systems by the proposed algorithm is remarkable.