Sensor Placement Strategies for Some Classes of Nonlinear Dynamic Systems via Lyapunov Theory

In this paper, the problem of placing sensors for some classes of nonlinear dynamic systems (NDS) is investigated. In conjunction with mixed-integer programming, classical Lyapunov-based arguments are used to find the minimal sensor configuration such that the NDS internal states can be observed while still optimizing some estimation metrics. The paper’s approach is based on two phases. The first phase assumes that the encompassed nonlinearities belong to one of the following function set classifications: bounded Jacobian, Lipschitz continuous, one-sided Lipschitz, or quadratically inner-bounded. To parameterize these classifications, two approaches based on stochastic point-based and interval-based optimization methods are explored. Given the parameterization, the second phase formulates the sensor placement problem for various NDS classes through mixed-integer convex programming. The theoretical optimality of the sensor placement alongside a state estimator design are then given. Numerical tests on traffic network models showcase that the proposed approach yields sensor placements that are consistent with conventional wisdom in traffic theory.

[1]  Andrey V. Savkin,et al.  A framework for optimal actuator/sensor selection in a control system , 2019, Int. J. Control.

[2]  Pushkin Kachroo,et al.  Observability and Sensor Placement Problem on Highway Segments: A Traffic Dynamics-Based Approach , 2016, IEEE Transactions on Intelligent Transportation Systems.

[3]  Deian Stefan,et al.  Low discrepancy sequences for Monte Carlo simulations on reconfigurable platforms , 2008, 2008 International Conference on Application-Specific Systems, Architectures and Processors.

[4]  Shreyas Sundaram,et al.  Sensor selection for Kalman filtering of linear dynamical systems: Complexity, limitations and greedy algorithms , 2017, Autom..

[5]  George J. Pappas,et al.  Minimal Actuator Placement With Bounds on Control Effort , 2014, IEEE Transactions on Control of Network Systems.

[6]  R. Rajamani,et al.  Observer design for Lipschitz nonlinear systems using Riccati equations , 2010, Proceedings of the 2010 American Control Conference.

[7]  Shapour Azarm,et al.  Optimal actuator placement for linear systems with limited number of actuators , 2017, 2017 American Control Conference (ACC).

[8]  Tyler H. Summers,et al.  Algorithms for Joint Sensor and Control Nodes Selection in Dynamic Networks , 2018, Autom..

[9]  Xiaobo Tan,et al.  Randomized Sensor Selection for Nonlinear Systems With Application to Target Localization , 2019, IEEE Robotics and Automation Letters.

[10]  Nikolaos Gatsis,et al.  Time-Varying Sensor and Actuator Selection for Uncertain Cyber-Physical Systems , 2017, IEEE Transactions on Control of Network Systems.

[11]  Goele Pipeleers,et al.  Combined H∞/H2 controller design and optimal selection of sensors and actuators , 2018 .

[12]  Javad Lavaei,et al.  Multiplier-based Observer Design for Large-Scale Lipschitz Systems , 2018 .

[13]  Garth P. McCormick,et al.  Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problems , 1976, Math. Program..

[14]  Kai Sun,et al.  Optimal PMU placement for power system dynamic state estimation by using empirical observability Gramian , 2015, 2015 IEEE Power & Energy Society General Meeting.

[15]  Wei Gao,et al.  Dynamic Actuator Selection and Robust State-Feedback Control of Networked Soft Actuators , 2018, 2018 IEEE International Conference on Robotics and Automation (ICRA).

[16]  J. Lofberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004, 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508).

[17]  Soummya Kar,et al.  A Framework for Structural Input/Output and Control Configuration Selection in Large-Scale Systems , 2013, IEEE Transactions on Automatic Control.

[18]  Ahmad F. Taha,et al.  On the need for sensor and actuator placement algorithms in nonlinear systems: WIP abstract , 2019, ICCPS.

[19]  Jianhui Wang,et al.  Comparing Kalman Filters and Observers for Power System Dynamic State Estimation With Model Uncertainty and Malicious Cyber Attacks , 2016, IEEE Access.

[20]  Knud D. Andersen,et al.  The Mosek Interior Point Optimizer for Linear Programming: An Implementation of the Homogeneous Algorithm , 2000 .

[21]  Aleksandar Haber,et al.  State Observation and Sensor Selection for Nonlinear Networks , 2017, IEEE Transactions on Control of Network Systems.

[22]  Jorge Cortes,et al.  Co-Optimization of Control and Actuator Selection for Cyber-Physical Systems , 2018 .

[23]  Zhi-Quan Luo,et al.  An ADMM algorithm for optimal sensor and actuator selection , 2014, 53rd IEEE Conference on Decision and Control.

[24]  Sergei S. Kucherenko,et al.  Application of Deterministic Low-Discrepancy Sequences in Global Optimization , 2005, Comput. Optim. Appl..

[25]  Christian Claudel,et al.  Traffic Density Modeling and Estimation on Stretched Highways: The Case for Lipschitz-Based Observers , 2019, 2019 American Control Conference (ACC).

[26]  Housheng Su,et al.  Full-order and reduced-order observers for one-sided Lipschitz nonlinear systems using Riccati equations , 2012 .

[27]  Junjian Qi,et al.  Characterizing the Nonlinearity of Power System Generator Models , 2019, 2019 American Control Conference (ACC).

[28]  M. A. Wolfe,et al.  Interval methods for global optimization , 1996 .