前馈非线性系统的饱和时滞设计

Saturation and delay are the commonly encountered problems in control engineering. Assigning saturated stabilizing control laws for the systems with delay in the input, which we call the saturated delayed design, is a difficult but significant issue. Concerning the saturated delayed design for feedforward nonlinear systems that often emerge in practical applications,there exist many unsolved problems. Focusing on several classes of intractable feedforward nonlinear systems, we do the following works: 1) for the feedforward nonlinear systems whose nominal dynamics consists of both multiple integrators and multiple oscillators, we introduce a suitable normal form and deal with nonlinear terms in an effective simple manner, and therefore establish a recursive design mechanism of saturated delayed controls, which is able to compensate an arbitrarily large input delay. Then the algorithm is again extended to the setting of output feedback; 2）for the feedforward nonlinear systems that are hard to be tackled by the constant saturation technique, we assign saturation level functions according to complex nonlinear terms and compute linear gains in many ways. As a result, saturated delayed controls can be assigned under certain structure conditions; 3) for the feedforward nonlinear systems that contain a chain of power integrators, we use inequality techniques to compute delayed terms, verify the saturation reduction via the contradiction that is related to small time intervals, and thus extend the saturated design to the setting of delay in the input. The works above will help to augment the classes of systems that can be stabilized by saturated delayed controls, and also bring about profound and distinct algorithms in various circumstances. In this sense, the current study is theoretically significant and is of potential values in applications.

饱和与时滞是控制工程经常面临的问题，为存在输入时滞的系统设计饱和的镇定控制律，简称饱和时滞设计，是有着重要意义的难点课题；前馈非线性系统大量存在于现实应用中，其饱和时滞设计研究还存在诸多尚待解决的问题。项目就较难处理的前馈非线性系统开展工作：1)针对同时含多积分器多振荡器的前馈非线性系统，引入合适的规范型,采用简单有效的非线性项处理方式，建立补偿任意大输入时滞的迭代设计方法，并拓展到输出反馈的情形；2）针对难以用"常饱和技巧"处理的前馈非线性系统，根据非线性项的特性设置饱和度函数，多途径获取线性增益，给出一定结构条件下的饱和时滞控制律；3)针对含高次多积分器的前馈非线性系统，运用不等式技巧计算时滞项，用小时间长度的矛盾式反证饱和的退化，将饱和设计推进为饱和时滞设计。上述工作不仅扩展饱和时滞设计研究的系统类，还将形成不同情形下深刻独特的处理方法,具有重要理论意义及潜在的实践价值。

饱和与时滞是控制工程中比较普遍的现象，而较难处理的前馈非线性系统则大量存在于现实应用中。项目研究补偿前馈非线性系统的输入饱和与输入时滞。1)针对同时含多积分器多振荡器的前馈非线性系统，引入合适的规范型，采用简单有效的方式处理非线性项，建立起补偿输入饱和及输入时滞的迭代设计方法；2）针对难以用"常饱和技巧"处理的前馈非线性系统，根据非线性项的特性设置饱和度函数，多途径获取线性增益，给出状态依赖的饱和控制律；3)针对线性多积分器、高次多积分器，设计奇数幂的连续控制律。通过合适的坐标变换，时滞项的处理难题转化为简单的计算问题，由此将现有的饱和补偿或时滞补偿推进为饱和时滞设计。上述工作给出了饱和时滞设计在不同情形下的处理方法，并应用于典型实际模型，具有重要理论意义及潜在的实践价值。