Observability Of Linear Dynamical Systems Research Articles

Differential initial-value privacy and observability of linear dynamical systems

This paper studies the relationship between the differential privacy of initial values and the observability for general linear dynamical systems with Gaussian process and sensor noises, where certain initial values are privacy-sensitive and the rest is assumed to be public. First of all, necessary and sufficient conditions are established for preserving the differential privacy and unobservability of the global sensitive initial values, respectively to show their independent properties. Specifically, we show that the observability matrix reduced by the set of sensitive initial states not only characterizes the structural property of noises for achieving the differential privacy, but also affects the achievable privacy levels, while the unobservability relies on the rank of such reduced observability matrix. Next, the inherent network nature of the considered linear system is explored, where each individual state corresponds to a node and the state and output matrices induce interaction and sensing graphs, leading to a network system. Under this network perspective, the previously established results are extended for initial values of local nodes to study their differential privacy and connections with their observability. Moreover, it is shown that the qualitative property of the differential initial-value privacy is either preserved generically or lost generically, which is the same as the unobservability in the local sense, while subject to a subtle difference from the unobservability in the global sense that is either preserved fully or lost generically. Finally, a privacy-preserving consensus algorithm is revisited to illustrate the effectiveness of the established results.

Measurement Bounds for Observability of Linear Dynamical Systems Under Sparsity Constraints

In this paper, we address the problem of observability of a linear dynamical system from compressive measurements and the knowledge of its external inputs. Observability of a high-dimensional system state in general requires a correspondingly large number of measurements. We show that if the initial state vector admits a sparse representation, the number of measurements can be significantly reduced by using random projections for obtaining the measurements. Our analysis gives sufficient conditions for the restricted isometry property of the observability matrix to hold, which leads to guarantees for the observability of the system. Our results depend only on the properties of system transfer and observation matrices, and are derived using tools from probability theory and compressed sensing. Unlike the prior work in this direction, our results are applicable to systems with an arbitrary nonzero system transfer matrix. Moreover, our results are stronger than the existing results in the regime where they are comparable.

Design-Oriented Structural Controllability and Observability Analysis of Heat Exchanger Networks

The control-relevant design and analysis of Heat Exchanger Networks (HENs) is an essential issue in terms of the design and intensification of sustainable production systems. The structural controllability and observability of HENs should be studied based on their dynamical model. Recently, a maximum matching based algorithm was developed to determine the locations of the minimum number of actuators and sensors needed to ensure the controllability and observability of linear dynamical systems. In this paper, the ability of concentrated parameter state-space models of the heat exchanger units to serve as building blocks of the network of state variables in HENs, and the use of the resultant network of state variables to study the control of relevant topologies and properties of HENs is highlighted. Based on the results of the systematic analysis, the structural patterns that facilitate the control and observation of HENs with a relatively small number of actuators and sensors were determined. Two methods were proposed to define the sets of additional actuators and sensors which are required to improve the operability of the network by decreasing the order of the controlled system. The first method is based on the interpretation of the placement of the sensors and actuators as a set cover problem, while the second one uses two network science-based measures: closeness centrality and betweenness centrality. The proposed methodologies are demonstrated on a benchmark example that is well covered in the literature.

New Results on the Controllability and Observability of Fractional Dynamical Systems

In this article, we describe some new results on the controllability and observability of linear dynamical systems involving a fractional derivative of order α. We show that the input control energy required to drive the state in a given direction and the energy available at the output are related to the observability and the controllability Gramians, respectively. Our results can be considered as a generalization of the known corresponding results for the integer order case to the fractional order one, since for α 1 1, the results for the integer case are recovered.

A NOTE ON THE CONTROLLABILITY AND THE OBSERVABILITY OF FRACTIONAL DYNAMICAL SYSTEMS

In this paper, we give some new results on the controllability and the observability of linear dynamical systems with a fractional derivative of order α, where α is a non integer number. We show that the observability and the controllability Gramians, recently introduced for a fractional order system, are solutions of fractional differential Lyapunov equations, thus generalizing the classical result for the integer case (α = 1). Our results can be considered as a generalization of the known corresponding results in the integer order case to the fractional order one since for α = 1, the results for the integer case are recovered.

Qualitative Controllability and Observability of Linear Dynamical Systems

This paper considers the problem of qualitative controllability/observability of linear multivariable systems. An algorithmic criterion, based on the determination of the qualitative solution set of the system R ‘α-0, where R is the extended controllability (observability) matrix, is provided. Applications of these results to problems appearing in compartmental systems are considered and further applications in qualitative economics and sign stability problems are pointed out.

Controlled and conditioned invariant subspaces in linear system theory

The concept of invariance of a subspace under a linear transformation is strongly connected with controllability and observability of linear dynamical systems. In this paper, we definecontrolled andconditioned invariant subspaces as a generalization of the simple invariants, for the purpose of investigating some further structural properties of linear systems. Moreover, we prove some fundamental theorems on which the computation of the above-mentioned subspaces is based. Then, we give two examples of practical application of the previous concepts concerning the determination of the constant output and perfect output controllability subspaces.

Invariant Subspaces and the Controllability and Observability of Linear Dynamical Systems

The geometric mechanism of uncontrollability and unobservability for a particular class of scalar input–scalar output linear dynamical systems is characterized in terms of the invariant subspaces of the system matrix A and its transpose.

On the theory of controllability and observability of linear dynamic systems

On the theory of controllability and observability of linear dynamic systems