Title: Input Redundancy under Input and State Constraints (Extended version of the submission accepted to Automatica) Show Chinese title

Title: 输入冗余在输入和状态约束下的研究（提交至Automatica的扩展版本）

Abstract: For a given unconstrained dynamical system, input redundancy has been recently redefined as the existence of distinct inputs producing identical output for the same initial state. By directly referring to signals, this definition readily applies to any input-to-output mapping. As an illustration of this potentiality, this paper tackles the case where input and state constraints are imposed on the system. This context is indeed of foremost importance since input redundancy has been historically regarded as a way to deal with input saturations. An example illustrating how constraints can challenge redundancy is offered right at the outset. A more complex phenomenology is highlighted. This motivates the enrichment of the existing framework on redundancy. Then, a sufficient condition for redundancy to be preserved when imposing constraints is offered in the most general context of arbitrary constraints. It is shown that redundancy can be destroyed only when input and state trajectories lie on the border of the set of constraints almost all the time. Finally, those results are specialized and expanded under the assumption that input and state constraints are linear. Show Chinese abstract

Abstract: 对于给定的无约束动力系统，输入冗余最近被重新定义为存在不同的输入在相同初始状态下产生相同的输出。 通过直接参考信号，这个定义可以很容易地应用于任何输入到输出的映射。 作为这种潜力的一个例子，本文处理了对系统施加输入和状态约束的情况。 这种情况确实非常重要，因为历史上输入冗余被视为处理输入饱和的一种方法。 在一开始就提供了一个说明约束如何挑战冗余的例子。 强调了更复杂的现象学。 这促使对现有的冗余框架进行丰富。 然后，在任意约束的最一般背景下，提出了在施加约束时保持冗余的充分条件。 结果表明，只有当输入和状态轨迹几乎一直在约束集的边界上时，冗余才会被破坏。 最后，在假设输入和状态约束是线性的情况下，对这些结果进行了专门化和扩展。