一种针对不确定机械系统的新型Lyapunov鲁棒控制方法

设计了一种针对不确定机械系统的鲁棒控制器.首先分析了质量矩阵的奇异性及上边界性质，展示了质量矩阵可能会因为模型的过度简化而变为半正定.而且，进一步研究了质量矩阵上边界的一致性.在质量矩阵正定及上边界的假设条件下，提出了一种新型鲁棒控制器以抑制机械系统中的不确定性效果.从理论上证明了设计的鲁棒控制器的一致有界性及最终一致有界性.最终趋近边界球的尺寸大小可由设计者决定.最后展示了仿真结果并作了讨论.

A New Lyapunov Based Robust Control for Uncertain Mechanical Systems

We design a new robust controller for uncertain mechanical systems. The inertia matrix s singularity and upper bound property are first analyzed. It is shown that the inertia matrix may be positive semi-definite due to over-simplified model. Furthermore, the inertia matrix s being uniformly bounded above is also limited. A robust controller is proposed to suppress the effect of uncertainty in mechanical systems with the assumption of uniform positive definiteness and upper bound of the inertia matrix. We theoretically prove that the robust control renders uniform boundedness and uniform ultimate boundedness. The size of the ultimate boundedness ball can be made arbitrarily small by the designer. Simulation results are presented and discussed.