Set-valued state estimation of nonlinear discrete-time systems with nonlinear invariants based on constrained zonotopes
Set-valued state estimation of nonlinear discrete-time systems with nonlinear invariants based on constrained zonotopes
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DOI：
10.1016/j.automatica.2021.109638
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发表时间：
2021-07
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影响因子：
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通讯作者：
B. S. Rego;Joseph K. Scott;D. Raimondo;G. Raffo
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文献类型：
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作者：
B. S. Rego;Joseph K. Scott;D. Raimondo;G. Raffo
本文提出了离散时间非线性系统的集值状态估计的新方法，这些系统的轨迹已知满足非线性等式约束，称为不变量（例如，守恒定律）。集值估计的目的是在每个时间步计算可能的系统状态的紧外壳未知，但有界的不确定性。大多数现有的方法采用标准的预测更新框架，基于集合的预测和更新步骤基于各种集合表示和技术。然而，实现非线性系统的精确外壳仍然是一个重大的挑战。本文提出了新的方法的基础上约束zonotopes，改进了标准的预测更新框架的系统不变量，通过增加协调步骤。这一新步骤使用不变量来减少保守性，并通过基于非线性约束的约束zonotopes的新算法来实现。本文还提出了显着的改进，现有的预测和更新步骤的约束zonotopes。具体而言，新的更新算法的开发，允许非线性测量方程的第一次，和现有的预测方法的基础上保守近似技术进行修改，以允许更灵活的选择的近似点，这可能会导致更严格的外壳。数值结果表明，由此产生的方法可以提供显着更紧密的外壳比现有的基于zonotope-based方法，同时保持相当的效率。
This paper presents new methods for set-valued state estimation of discrete-time nonlinear systems whose trajectories are known to satisfy nonlinear equality constraints, calledinvariants(e.g., conservation laws). Set-valued estimation aims to compute tight enclosures of the possible system states in each time step subject to unknown-but-bounded uncertainties. Most existing methods employ a standard prediction-update framework with set-based prediction and update steps based on various set representations and techniques. However, achieving accurate enclosures for nonlinear systems remains a significant challenge. This paper presents new methods based on constrained zonotopes that improve the standard prediction-update framework for systems with invariants by adding aconsistency step. This new step uses invariants to reduce conservatism and is enabled by new algorithms for refining constrained zonotopes based on nonlinear constraints. This paper also presents significant improvements to existing prediction and update steps for constrained zonotopes. Specifically, new update algorithms are developed that allow nonlinear measurement equations for the first time, and existing prediction methods based on conservative approximation techniques are modified to allow a more flexible choice of the approximation point, which can lead to tighter enclosures. Numerical results demonstrate that the resulting methods can provide significantly tighter enclosures than existing zonotope-based methods while maintaining comparable efficiency.