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The problem of robustifying linear quadratic regulators(LQRs) for a class of uncertain affine nonlinear systems is considered.First,the exact linearization technique is used to transform an uncertain nonlinear system into a linear one and an optimal LQR is designed for the corresponding nominal system.Then,based on the integral sliding mode,a design approach to robustifying the optimal regulator is studied.As a result,the system exhibits global robustness to uncertainties and the ideal sliding mode dynamics is the same as that of the optimal LQR for the nominal system.A global robust optimal sliding mode control(GROSMC) is realized.Finally,a numerical simulation is demonstrated to show the effectiveness and superiority of the proposed algorithm compared with the conventional optimal LQR.
The problem of robustifying linear quadratic regulators (LQRs) for a class of uncertain affine nonlinear systems is considered. First, the exact linearization technique is used to transform an uncertain nonlinear system into a linear one and an optimal LQR is designed for the corresponding nominal system .Then, based on the integral sliding mode, a design approach to robustifying the optimal regulator is studied. As a result, the system exhibits global robustness to uncertainties and the ideal sliding mode dynamics is the same as that of the optimal LQR for the nominal system.A global robust optimal sliding mode control (GROSMC) is realized. Finally, a numerical simulation is demonstrated to show the effectiveness and superiority of the proposed algorithm compared with the conventional optimal LQR.