Adaptive optimal observer design via approximate dynamic programming

J. Na, G. Herrmann, K. Vamvoudakis
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引用次数: 12

Abstract

This paper presents an optimal observer design framework using a recently emerging method, approximate dynamic programming (ADP), to minimize a predefined cost function. We first exploit the duality between the linear optimal observer and the linear quadratic tracking (LQT) control. We show that the optimal observer design can be formulated as an optimal control problem subject to a specific cost function, and thus the solution can be obtained by solving an algebraic Riccati equation (ARE). For nonlinear systems, we further introduce an optimal observer design formulation and suggest a modified policy iteration method. Finally, to solve the problem online we propose a framework based on ADP and specifically on an approximator structure. Namely, a critic approximator is used to estimate the optimal value function, and a newly developed tuning law is proposed to find the parameters online. The stability and the performance are guaranteed with rigorous proofs. Numerical simulations are given to validate the theoretical studies.
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基于近似动态规划的自适应最优观测器设计
本文提出了一种最优观测器设计框架,使用一种新出现的方法,近似动态规划(ADP),以最小化预定义的代价函数。我们首先利用线性最优观测器和线性二次跟踪(LQT)控制之间的对偶性。我们证明了最优观测器设计可以被表述为一个受特定成本函数约束的最优控制问题,因此可以通过求解代数Riccati方程(ARE)得到其解。对于非线性系统,我们进一步引入了最优观测器设计公式,并提出了一种改进的策略迭代方法。最后,为了在线解决这个问题,我们提出了一个基于ADP的框架,特别是一个近似器结构。即,使用一个临界逼近器来估计最优值函数,并提出了一种新的调谐律来在线查找参数。稳定性和性能有严格的证明保证。通过数值模拟验证了理论研究的正确性。
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