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Phasor measurement units (PMUs) are essential tools for monitoring, protection and control of power systems. The optimal PMU placement (OPP) problem refers to the determination of the minimal number of PMUs and their corresponding locations in order to achieve full network observability. This paper introduces a recursive Tabu search (RTS) method to solve the OPP problem. More specifically, the traditional Tabu search (TS) metaheuristic algorithm is executed multiple times, while in the initialisation of each TS the best solution found from all previous executions is used. The proposed RTS is found to be the best among three alternative TS initialisation schemes, in regard to the impact on the success rate of the algorithm. A numerical method is proposed for checking network observability, unlike most existing metaheuristic OPP methods, which are based on topological observability methods. The proposed RTS method is tested on the IEEE 14, 30, 57 and 118-bus test systems, on the New England 39-bus test system and on the 2383-bus power system. The obtained results are compared with other reported PMU placement methods. The simulation results show that the proposed RTS method finds the minimum number of PMUs, unlike earlier methods which may find either the same or even higher number of PMUs.

This paper presents a novel hybrid algorithm for determining the optimal Phasor Measurement Units (PMU) configuration in power networks to ensure full topological and numerical observability through a multi-phase process. In the first phase, a graph-theoretic Heuristic Node Selector (HNS) is developed to rapidly establish topological observability via Core-Tree construction and node dominance evaluation. Unlike most existing studies that implicitly assume topological observability implies numerical observability, the second phase applies a Genetic Algorithm to refine and extend the initial solution from HNS, ensuring complete numerical observability while minimizing number of PMUs. This hybrid method significantly reduces the search space and improves convergence. The HNS procedure is further extended in this work to explicitly handle Zero Injection Buses (ZIB) through rule-based topological modifications, enabling a modified version of the algorithm applicable to real networks with complex structures. Real-world implementation practices from European Transmission System Operators are considered through the adoption of a “one PMU per feeder” configuration. The proposed method is validated on standard IEEE test systems and Serbian transmission networks. Results demonstrate high scalability, adaptability to various network topologies (with and without ZIB nodes), and efficient PMU allocation. Notably, the method consistently achieves high values of the System Observability Redundancy Index, indicating strong robustness and redundancy in measurement placement.

We consider a transmission system of two nonconservative wave equations with nonconstant coefficients in the one-dimensional setting. We investigate the exact (boundary and internal) controllability of this system using a single control. To solve these exact controllability problems, we rely on the duality approach which consists in proving inverse or observability inequality for the corresponding adjoint system. To prove these observability inequalities, we establish new Carleman estimates for the corresponding uncontrolled transmission system. These Carleman estimates require the introduction of new weight functions adapted to the coefficients of the principal operators. In particular, our Carleman estimates with internal observation are new in the framework of transmission systems.

We study the linear Zakharov–Kuznetsov equation with periodic boundary conditions. Employing some tools from the nonharmonic Fourier series we obtain several internal observability theorems. Then we prove various exact controllability and rapid uniform stabilization results by applying a duality principle and a general feedback construction. The method presented here introduces a new insight into the control of dispersive equations in two-dimensional cases and may be adapted to more general equations.

In this paper we study the null controllability property for a single population model in which the population y depends on time t, space x, age a and size τ. Moreover, the diffusion coefficient k is degenerate at a point of the domain or both extremal points. Our technique is essentially based on Carleman estimates. The τ dependence requires us to modify the weight for the Carleman estimates, and accordingly the proof of the observability inequality. Thanks to this observability inequality we obtain a null controllability result for an intermediate problem and finally for the initial system through suitable cut off functions.

The primary objective of this paper is to directly establish the observability inequality for stochastic parabolic equations from measurable sets. In an immediate practical application, our focus centers on the investigation of optimal actuator placement to achieve minimum norm controls in the context of approximative controllability for stochastic parabolic equations. We introduce a comprehensive formulation of the optimization problem, encompassing both the determination of the actuator location and the corresponding minimum norm control. More precisely, we reformulate the problem into a two-player zero-sum game scenario, resulting in the derivation of four equivalent formulations. Ultimately, we substantiate the pivotal outcome that the solution to the relaxed optimization problem serves as the optimal actuator placement for the classical problem.

Accessibility and observability are two properties of dynamic models that provide insights into the structural relationships between their input, output, and state variables. They are closely related to controllability and structural local identifiability, respectively. Observability and identifiability determine, respectively, the possibility of inferring the unmeasured state variables and parameters of a model from output measurements; accessibility and controllability describe the possibility of driving its state by changing its input. Analysing these structural properties in nonlinear models of ordinary differential equations can be challenging, particularly when dealing with large systems. Two main approaches are currently used for their study: one based on differential geometry, which uses symbolic computation, and another one based on sensitivity calculations that uses numerical integration. These approaches are implemented in two MATLAB (R2024b) software tools: the differential geometry approach in STRIKE-GOLDD, and the sensitivity-based method in StrucID. These toolboxes differ significantly in their features and capabilities. Until now, their performance had not been thoroughly compared. In this paper we present a comprehensive comparative study of them, elucidating their differences in applicability, computational efficiency, and robustness against computational issues. Our core finding is that StrucID has a substantially lower computational cost than STRIKE-GOLDD; however, it may occasionally yield inconsistent results due to numerical issues.

This paper addresses the numerical resolution of controllability problems for partial differential equations (PDEs) by using physics-informed neural networks. Error estimates for the generalization error for both state and control are derived from classical observability inequalities and energy estimates for the considered PDE. These error bounds, that apply to any exact controllable linear system of PDEs and in any dimension, provide a rigorous justification for the use of neural networks in this field. Preliminary numerical simulation results for three different types of PDEs are carried out to illustrate the performance of the proposed methodology.

We will consider the use of mixed finite element method for the semi-discretization of the Schrödinger integro-differential systems. We investigate the problem of boundary observability for the semi-discrete models. We show that the semi-discretization based on a mixed finite element method with two different basis functions for the position and its differentiation with respect to time of Schrödinger type integro-differential equation, are uniformly observability as the discretization parameter h goes to zero. Some numerical results are given to illustrate our theoretical finds.

We study the null controllability for a degenerate/singular wave equation with drift in non divergence form. In particular, considering a control localized on the non degenerate boundary point, we provide some conditions for the boundary controllability via energy methods and boundary observability.