A mixed H 2 /H 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 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 control problem is presented by combining nonlinear minimax (Nash game) theory and L Q 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 timevarying) Riccati-like equations are required to construct the proposed mixed H 2 /H 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 tracking controller can be constructed. Finally, extensive simulations are made for mixed H 2 /H 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.
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