Optimal PMU Placement for Power System Dynamic State Estimation by Using Empirical Observability Gramian

In this paper the empirical observability Gramian calculated around the operating region of a power system is used to quantify the degree of observability of the system states under specific phasor measurement unit (PMU) placement. An optimal PMU placement method for power system dynamic state estimation is further formulated as an optimization problem which maximizes the determinant of the empirical observability Gramian and is efficiently solved by the NOMAD solver, which implements the Mesh Adaptive Direct Search (MADS) algorithm. The implementation, validation, and also the robustness to load fluctuations and contingencies of the proposed method are carefully discussed. The proposed method is tested on WSCC 3-machine 9-bus system and NPCC 48-machine 140-bus system by performing dynamic state estimation with square-root unscented Kalman filter. The simulation results show that the determined optimal PMU placements by the proposed method can guarantee good observability of the system states, which further leads to smaller estimation errors and larger number of convergent states for dynamic state estimation compared with random PMU placements. Under optimal PMU placements an obvious observability transition can be observed. The proposed method is also validated to be very robust to both load fluctuations and contingencies.Comment: Accepted by IEEE Transactions on Power System

State-Robust Observability Measures for Sensor Selection in Nonlinear Dynamic Systems

This paper explores the problem of selecting sensor nodes for a general class of nonlinear dynamical networks. In particular, we study the problem by utilizing altered definitions of observability and open-loop lifted observers. The approach is performed by discretizing the system's dynamics using the implicit Runge-Kutta method and by introducing a state-averaged observability measure. The observability measure is computed for a number of perturbed initial states in the vicinity of the system's true initial state. The sensor node selection problem is revealed to retain the submodular and modular properties of the original problem. This allows the problem to be solved efficiently using a greedy algorithm with a guaranteed performance bound while showing an augmented robustness to unknown or uncertain initial conditions. The validity of this approach is numerically demonstrated on a $H_{2}/O_{2}$ combustion reaction network.Comment: To Appear in the 62$^{\text{nd}}$ IEEE Conference on Decision and Control (CDC'2023), Singapore, Decemeber 202

On Submodularity and Controllability in Complex Dynamical Networks

Controllability and observability have long been recognized as fundamental structural properties of dynamical systems, but have recently seen renewed interest in the context of large, complex networks of dynamical systems. A basic problem is sensor and actuator placement: choose a subset from a finite set of possible placements to optimize some real-valued controllability and observability metrics of the network. Surprisingly little is known about the structure of such combinatorial optimization problems. In this paper, we show that several important classes of metrics based on the controllability and observability Gramians have a strong structural property that allows for either efficient global optimization or an approximation guarantee by using a simple greedy heuristic for their maximization. In particular, the mapping from possible placements to several scalar functions of the associated Gramian is either a modular or submodular set function. The results are illustrated on randomly generated systems and on a problem of power electronic actuator placement in a model of the European power grid.Comment: Original arXiv version of IEEE Transactions on Control of Network Systems paper (Volume 3, Issue 1), with a addendum (located in the ancillary documents) that explains an error in a proof of the original paper and provides a counterexample to the corresponding resul

Motion Planning for Optimal Information Gathering in Opportunistic Navigation Systems

Motion planning for optimal information gathering in an opportunistic navigation (OpNav) environment is considered. An OpNav environment can be thought of as a radio frequency signal landscape within which a receiver locates itself in space and time by extracting information from ambient signals of opportunity (SOPs). The receiver is assumed to draw only pseudorange-type observations from the SOPs, and such observations are fused through an estimator to produce an estimate of the receiver’s own states. Since not all SOP states in the OpNav environment may be known a priori, the receiver must estimate the unknown SOP states of interest simultaneously with its own states. In this work, the following problem is studied. A receiver with no a priori knowledge about its own states is dropped in an unknown, yet observable, OpNav environment. Assuming that the receiver can prescribe its own trajectory, what motion planning strategy should the receiver adopt in order to build a high-fidelity map of the OpNav signal landscape, while simultaneously localizing itself within this map in space and time? To answer this question, first, the minimum conditions under which the OpNav environment is fully observable are established, and the need for receiver maneuvering to achieve full observability is highlighted. Then, motivated by the fact that not all trajectories a receiver may take in the environment are equally beneficial from an information gathering point of view, a strategy for planning the motion of the receiver is proposed. The strategy is formulated in a coupled estimation and optimal control framework of a gradually identified system, where optimality is defined through various information-theoretic measures. Simulation results are presented to illustrate the improvements gained from adopting the proposed strategy over random and pre-defined receiver trajectories.Aerospace Engineering and Engineering Mechanic

Sequential Detection with Mutual Information Stopping Cost

This paper formulates and solves a sequential detection problem that involves the mutual information (stochastic observability) of a Gaussian process observed in noise with missing measurements. The main result is that the optimal decision is characterized by a monotone policy on the partially ordered set of positive definite covariance matrices. This monotone structure implies that numerically efficient algorithms can be designed to estimate and implement monotone parametrized decision policies.The sequential detection problem is motivated by applications in radar scheduling where the aim is to maintain the mutual information of all targets within a specified bound. We illustrate the problem formulation and performance of monotone parametrized policies via numerical examples in fly-by and persistent-surveillance applications involving a GMTI (Ground Moving Target Indicator) radar

Where Should Traffic Sensors Be Placed on Highways?

This paper investigates the practical engineering problem of traffic sensors placement on stretched highways with ramps. Since it is virtually impossible to install bulky traffic sensors on each highway segment, it is crucial to find placements that result in optimized network-wide, traffic observability. Consequently, this results in accurate traffic density estimates on segments where sensors are not installed. The substantial contribution of this paper is the utilization of control-theoretic observability analysis -- jointly with integer programming -- to determine traffic sensor locations based on the nonlinear dynamics and parameters of traffic networks. In particular, the celebrated asymmetric cell transmission model is used to guide the placement strategy jointly with observability analysis of nonlinear dynamic systems through Gramians. Thorough numerical case studies are presented to corroborate the proposed theoretical methods and various computational research questions are posed and addressed. The presented approach can also be extended to other models of traffic dynamics

Analysis and synthesis of collaborative opportunistic navigation systems

textNavigation is an invisible utility that is often taken for granted with considerable societal and economic impacts. Not only is navigation essential to our modern life, but the more it advances, the more possibilities are created. Navigation is at the heart of three emerging fields: autonomous vehicles, location-based services, and intelligent transportation systems. Global navigation satellite systems (GNSS) are insufficient for reliable anytime, anywhere navigation, particularly indoors, in deep urban canyons, and in environments under malicious attacks (e.g., jamming and spoofing). The conventional approach to overcome the limitations of GNSS-based navigation is to couple GNSS receivers with dead reckoning sensors. A new paradigm, termed opportunistic navigation (OpNav), is emerging. OpNav is analogous to how living creatures naturally navigate: by learning their environment. OpNav aims to exploit the plenitude of ambient radio frequency signals of opportunity (SOPs) in the environment. OpNav radio receivers, which may be handheld or vehicle-mounted, continuously search for opportune signals from which to draw position and timing information, employing on-the-fly signal characterization as necessary. In collaborative opportunistic navigation (COpNav), multiple receivers share information to construct and continuously refine a global signal landscape. For the sake of motivation, consider the following problem. A number of receivers with no a priori knowledge about their own states are dropped in an environment comprising multiple unknown terrestrial SOPs. The receivers draw pseudorange observations from the SOPs. The receivers' objective is to build a high-fidelity signal landscape map of the environment within which they localize themselves in space and time. We then ask: (i) Under what conditions is the environment fully observable? (ii) In cases where the environment is not fully observable, what are the observable states? (iii) How would receiver-controlled maneuvers affect observability? (iv) What is the degree of observability of the various states in the environment? (v) What motion planning strategy should the receivers employ for optimal information gathering? (vi) How effective are receding horizon strategies over greedy for receiver trajectory optimization, and what are their limitations? (vii) What level of collaboration between the receivers achieves a minimal price of anarchy? This dissertation addresses these fundamental questions and validates the theoretical conclusions numerically and experimentally.Electrical and Computer Engineerin