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.

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

UR - http://www.scopus.com/inward/record.url?scp=85049455454&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85049455454&partnerID=8YFLogxK

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 -