Robust Control of Non-Minimum Phase Non-Linear Systems

ECS-9707891 Isidori 在过去的几年里，新的强大的思想和概念，促进了一些系统的方法的发展，为全球分析和设计的非线性反馈系统。 这些研究工作的一个共同目标是在存在结构化不确定性（例如参数变化）和/或非结构化不确定性（例如具有未建模动态）的情况下，合成反馈控制器，从而产生所选择的外源命令（干扰）的渐近稳定性（具有规定的吸引区域）和/或渐近跟踪（拒绝）。 这些鲁棒设计方法必须实现的实际设置是，只有一组变量（而不是完整的状态）可用于反馈。 在这种情况下，整个设计问题当然变得更加苛刻，鉴于需要包括;在反馈架构中的某种“状态观测器”。 这个问题在跟踪的情况下尤其明显，因为最现实的情况确实是只有“跟踪误差”（而不是整个参考轨迹）可用于控制目的。 正如任何涉及选择特定输出映射的设计方案所发生的那样，实现上述反馈设计方法的可能性深受系统所谓的“零动态”（当输入和初始状态限制输出为零时，系统内部出现的动态）的渐近性质的影响。 更确切地说，这些反馈设计方法的一致数量要求零动态是渐近稳定的：具有此属性的系统是-在类比术语流行的线性系统称为“最小相位系统”。 特别是，如果一个系统是最小相位，它是可能实现任意小的干扰和输出之间的衰减水平，具有明显的积极后果的解决问题的能力鲁棒镇定的情况下，未建模动态。 然而，许多物理系统表现出非最小相位行为。 由于能够鲁棒控制非最小相位非线性系统的重要性，以及在这一领域的可用结果的稀缺性，本研究将集中在两个方向。 第一个是研究非最小相位非线性系统在存在未建模动态时的鲁棒镇定问题。 对于这种不确定性的鲁棒性通常是通过观察受控系统的两个子系统的反馈互连来处理的，其中只有一个子系统是精确建模的，然后寻找一个控制律，该控制律尽可能地降低互连建模/未建模组件的某些适当定义的“增益”。 在这种设置中，研究将解决的问题，发现，为各种类别的非最小相位系统，估计的最低可实现的“增益”（以减少保守性的设计）。 另一个方向是研究存在参数不确定性的鲁棒跟踪问题。 不像线性系统的情况下，不稳定的零动态的存在下，一般不是一个障碍，以渐近跟踪规定的家庭的轨迹，在非最小相位非线性系统的情况下，没有方法是可用的，但实现渐近跟踪，在存在大的参数不确定性和任意大的初始条件。 这部分的研究是针对系统的方法产生半鲁棒跟踪非线性系统具有不稳定的零动态的发展。

ECS-9707891 Isidori In the last few years, new powerful ideas and concepts have contributed to the development of a number of systematic methods for global analysis and design of nonlinear feedback systems. A common goal of these research efforts has been the synthesis of feedback controllers yielding asymptotic stability (with prescribed region of attraction) and/or asymptotic tracking (rejection) of selected exogenous commands (disturbances), in the presence of structured uncertainties, such as parameter variations, and/or unstructured uncertainties, such has unmodeled dynamics. The actual setup in which these robust design methods have to be implemented is that in which only a set of variables (and not the full state) is available for feedback. In this case the entire design problem becomes of course more demanding, in view of the need of including; some kind of "state observer" in the feedback architecture. This problem is particularly felt in the case of tracking, when the most realistic situation is indeed the one in which only the "tracking error" (and not the entire reference trajectory) would be available for control purposes. As it happens for any design scheme dealing with the selection of specific output maps, the possibility of implementing the above-mentioned methods for feedback design is deeply influenced by the asymptotic properties of the so-called "zero dynamics" of the system (the dynamics which arise internally in a system when input and initial state are such as to constrain the output to be identically zero). More precisely, a consistent number of these methods for feedback design require the zero dynamics to be asymptotically stable: systems having this property are - in analogy with a terminology en vogue for linear systems called "minimum phase systems". In particular, if a system is minimum phase it is possible to achieve an arbitrarily small level of attenuation between disturbances and output, with obvious positive consequences on the ability of solving pr oblems of robust stabilization in the case of unmodeled dynamics. However, many physical systems exhibit a non-minimum phase behavior. Motivated by the importance of being able to robustly control also non-minimum phase nonlinear systems and by the scarcity of available results in this area, this research will focus on two directions. The first one deals with problems of robust stabilization of non-minimum phase nonlinear systems, in the presence of unmodeled dynamics. Robustness with respect to this kind of uncertainty is usually dealt with by looking at the controlled system as to the feedback interconnection of two subsystems, only one of which is accurately modeled, and then seeking a control law which lowers, as much as possible, some suitably defined "gain" of the interconnection modeled/unmodeled component. In this setup, the research will address the problem of finding, for various classes of non-minimum phase systems, estimates of the lowest achievable "gains" (so as to reduce the conservativeness of the design). The other direction is to study problems of robust tracking in the presence of parametric uncertainties. Unlike the case of linear systems, where the presence of unstable zero dynamics is generally not an obstruction to asymptotic tracking of prescribed families of trajectories, in the case of non-minimum phase nonlinear system no method is available yet to achieve asymptotic tracking, in the presence of large parameter uncertainties and for arbitrarily large initial conditions. This part of the proposed research is directed toward the development of systematic methods yielding semiglobal robust tracking for nonlinear systems having unstable zero dynamics.