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 metr...

This paper studies the minimal controllability problem (MCP), i.e., the problem of, given a linear time-invariant system, finding the sparsest input vector that ensures system’s controllability. We show that the MCP can be exactly solved by (polynomially) reducing it to the minimum set covering problem, when the system dynamics matrix A is simple and the left-eigenbasis associated to A is known...

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One version of the concept of structural controllability defined for single-input systems by Lin and subsequently generalized to multi-input systems by others, states that a parameterized matrix pair (A,B) whose nonzero entries are distinct parameters, is structurally controllable if values can be assigned to the parameters which cause the resulting matrix pair to be controllable. In this paper...

In this article, we study the target controllability problem of networked dynamical systems,in which are tasked to steer a subset network nodes toward desired objective. More specifically, derive necessary and sufficient conditions for xmlns:xlink="http://www.w3.org/1999/xlink">structural targe...

Recent investigations have used diffusion-weighted imaging to reveal disturbances in the neurocircuitry that underlie cognitive-emotional control in bipolar disorder (BD) and in unaffected siblings or children at high genetic risk (HR). It has been difficult to quantify the mechanism by which structural changes disrupt the superimposed brain dynamics, leading to the emotional lability that is c...

We study the boundary controllability properties of a wave equation with structural damping ytt− yxx− 2ytxx = 0, y(0, t) = 0, y(1, t) = h(t) where 2 is a strictly positive parameter depending on the damping strength. We prove that this equation is not spectrally controllable and that the approximate controllability depends on the functional space in which the initial value Cauchy problem is stu...

Controllability of complex networks has been a hot topic in recent years. Real networks regarded as interdependent networks are always coupled together by multiple networks. The cascading process of interdependent networks including interdependent failure and overload failure will destroy the robustness of controllability for the whole network. Therefore, the optimization of the robustness of i...

This thesis introduces the concept of structural hybrid systems to address, as a particular case, the model checking problem of switching (possible large scale) linear time invariant systems. Within the proposed setup, we provide necessary conditions to ensure properties such as controllability, at each time. We show that such model checking controllability properties can be implemented using e...

This paper proves that any initial condition in the energy space for the plate equation with square root damping ζ̈ − ρ∆ζ̇ +∆2ζ = u on a smooth bounded domain, with hinged boundary conditions ζ = ∆ζ = 0, can be steered to zero by a square integrable input function u supported in arbitrarily small time interval [0, T ] and subdomain. As T tends to zero, for initial states with unit energy norm, th...