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

TL;DR

This paper develops a Lyapunov-based, mixed-integer programming method for optimal sensor placement in nonlinear dynamic systems, ensuring observability and optimized estimation metrics.

Contribution

It introduces a two-phase approach combining Lyapunov theory and mixed-integer convex programming for sensor placement in specific classes of nonlinear systems, with theoretical optimality guarantees.

Findings

Sensor placements align with traffic theory expectations.

The method achieves minimal sensor configurations for observability.

Numerical tests validate the approach's effectiveness.

Abstract

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.