TY - GEN
T1 - State estimation of dynamical systems with unknown inputs
T2 - 21st International Conference on Hybrid Systems: Computation and Control, HSCC 2018
AU - Sibai, Hussein
AU - Mitra, Sayan
N1 - Funding Information:
We thank Daniel Liberzon for providing detailed and insightful comments on an earlier draft of this paper. This work is in part supported by research grants AFOSR FA9550-17-1-0236 and NSF 1739966.
Publisher Copyright:
© 2018 Association for Computing Machinery.
PY - 2018/4/11
Y1 - 2018/4/11
N2 - Finding the minimal bit rate needed for state estimation of a dynamical system is a fundamental problem in control theory. In this paper, we present a notion of topological entropy, to lower bound the bit rate needed to estimate the state of a nonlinear dynamical system, with unknown bounded inputs, up to a constant error ϵ. Since the actual value of this entropy is hard to compute in general, we compute an upper bound. We show that as the bound on the input decreases, we recover a previously known bound on estimation entropy - a similar notion of entropy - for nonlinear systems without inputs [10]. For the sake of computing the bound, we present an algorithm that, given sampled and quantized measurements from a trajectory and an input signal up to a time bound T > 0, constructs a function that approximates the trajectory up to an ϵ error up to time T. We show that this algorithm can also be used for state estimation if the input signal can indeed be sensed in addition to the state. Finally, we present an improved bound on entropy for systems with linear inputs.
AB - Finding the minimal bit rate needed for state estimation of a dynamical system is a fundamental problem in control theory. In this paper, we present a notion of topological entropy, to lower bound the bit rate needed to estimate the state of a nonlinear dynamical system, with unknown bounded inputs, up to a constant error ϵ. Since the actual value of this entropy is hard to compute in general, we compute an upper bound. We show that as the bound on the input decreases, we recover a previously known bound on estimation entropy - a similar notion of entropy - for nonlinear systems without inputs [10]. For the sake of computing the bound, we present an algorithm that, given sampled and quantized measurements from a trajectory and an input signal up to a time bound T > 0, constructs a function that approximates the trajectory up to an ϵ error up to time T. We show that this algorithm can also be used for state estimation if the input signal can indeed be sensed in addition to the state. Finally, we present an improved bound on entropy for systems with linear inputs.
KW - Bit rates
KW - Discrepancy functions
KW - Entropy
KW - Nonlinear systems
KW - State estimation
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U2 - 10.1145/3178126.3178150
DO - 10.1145/3178126.3178150
M3 - Conference contribution
AN - SCOPUS:85049455454
T3 - HSCC 2018 - Proceedings of the 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week)
SP - 217
EP - 226
BT - HSCC 2018 - Proceedings of the 21st International Conference on Hybrid Systems
PB - Association for Computing Machinery, Inc
Y2 - 11 April 2018 through 13 April 2018
ER -