Simultaneous state and unknown input set‐valued observers for quadratically constrained nonlinear dynamical systems
Simultaneous state and unknown input set‐valued observers for quadratically constrained nonlinear dynamical systems
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DOI：
10.1002/rnc.6163
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发表时间：
2020-01
影响因子：
3.9
通讯作者：
Mohammad Khajenejad;Sze Zheng Yong
中科院分区：
文献类型：
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作者：
Mohammad Khajenejad;Sze Zheng Yong
在这篇文章中，我们提出了几类具有未知输入信号的二次约束非线性动力系统的固定阶集值（以202 $ {\ell}_2 $$-范数超球的形式）观测器，同时/联合找到包含真实状态和输入的状态和未知输入的有界超球。针对（λ，γ$ \mathcal{M}，\gamma $$）-二次约束（（λ，γ $\mathcal {M}，\gamma $$）-QC）系统，以线性矩阵不等式（LMI）的形式给出了观测器稳定（二次稳定）的充分必要条件，其中包括几类非线性系统：（I）Lipschitz连续系统，（II）（λ，γ）-QC* 系统和（III）线性变参数（LPV）系统.这种新的二次约束性质至少是一般的增量二次约束性质的非线性系统，并证明在文件中体现了广泛的非线性。此外，在满足二次稳定性条件的观测器中，我们设计了最优的H ∞$ {\mathscr{H}}_{\infty } $$观测器，并证明了设计结果具有一致有界输入有界状态（UBIBS）估计半径/误差动态和估计半径的一致有界序列.此外，我们提供了封闭形式的上限序列的估计半径和充分条件，其收敛到稳定状态。最后，所提出的集值观测器的有效性证明了通过说明性的例子，在那里我们比较我们的观测器与一些现有的观测器的性能。
In this article, we propose fixed‐order set‐valued (in the form of ℓ2$$ {\ell}_2 $$ ‐norm hyperballs) observers for several classes of quadratically constrained nonlinear dynamical systems with unknown input signals that simultaneously/jointly find bounded hyperballs of states and unknown inputs that include the true states and inputs. Necessary and sufficient conditions in the form of linear matrix inequalities (LMIs) for the stability (in the sense of quadratic stability) of the proposed observers are derived for ( ℳ,γ$$ \mathcal{M},\gamma $$ )‐quadratically constrained (( ℳ,γ$$ \mathcal{M},\gamma $$ )‐QC) systems, which includes several classes of nonlinear systems: (I) Lipschitz continuous, (II) ( 𝒜,γ )‐QC* and (III) linear parameter‐varying (LPV) systems. This new quadratic constraint property is at least as general as the incremental quadratic constraint property for nonlinear systems and is proven in the paper to embody a broad range of nonlinearities. In addition, we design the optimal ℋ∞$$ {\mathscr{H}}_{\infty } $$ observer among those that satisfy the quadratic stability conditions and show that the design results in uniformly bounded‐input bounded‐state (UBIBS) estimate radii/error dynamics and uniformly bounded sequences of the estimate radii. Furthermore, we provide closed‐form upper bound sequences for the estimate radii and sufficient conditions for their convergence to steady state. Finally, the effectiveness of the proposed set‐valued observers is demonstrated through illustrative examples, where we compare the performance of our observers with some existing observers.