Abstract
This paper proposes a new set-membership technique to implement polytopic set computation for nonlinear discrete-time systems indirectly. The proposed set-membership technique is applied to solve the guaranteed state estimation problem for nonlinear discrete-time systems with a bounded description of noises and parameters. A common practice for this problem in the literature is to search an optimal zonotope to bound the intersection of the evolved uncertain state trajectory and the region of the state space consistent with the observed output at each observation update. The new approach keeps the polytopic set resulting from the intersection intact and computes the evolution of this intact polytopic set for the next time step through representing the polytopic set exactly by the intersection of zonotopes. Such an approach avoids the overapproximation bounding process at each observation update, and thus, a more accurate state estimation can be obtained. An illustrative example is provided to demonstrate the effectiveness of the proposed guaranteed state estimation via indirectly implemented polytopic set computation.
Highlights
State estimation is formulated as the problem of estimating the real state of the system given the mathematical model of the system and noise-corrupted measurements of the system output [1]
The most notable stochastic approach for state estimation is the Kalman filter, which is an efficient and recursive procedure to estimate the system state in a way that minimizes the mean of the squared estimation error [2]
A common practice within these zonotope-based state estimation approaches for nonlinear discrete-time systems is to search an optimal zonotope to bound the intersection of the evolved uncertain state trajectory and the region of the state space consistent with the observed output at each observation update
Summary
State estimation is formulated as the problem of estimating the real state of the system given the mathematical model of the system and noise-corrupted measurements of the system output [1]. A common practice within these zonotope-based state estimation approaches for nonlinear discrete-time systems is to search an optimal zonotope to bound the intersection of the evolved uncertain state trajectory and the region of the state space consistent with the observed output at each observation update. Since there is no direct method to implement polytopic set computation for nonlinear discrete-time systems, an indirectly implemented polytopic set computation technique is to be proposed for the first time
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