We study the problem of actuator and sensor placement in a linear advection partial differential equation (PDE). The problem is motivated by its application to actuator and sensor placement in building systems for the control and detection of a scalar quantity such as temperature and contaminants. We propose a gramian based approach to the problem of actuator and sensor placement. The special s...

In this study, time-delayed stochastic dynamical systems of linear and nonlinear equations are discussed. The existence uniqueness the semilinear time-delay system in finite dimensional space is investigated. Introducing delay Gramian matrix, we establish some sufficient necessary conditions for relative approximate controllability systems. addition, by applying Banach fixed point theorem, diff...

This paper presents a new analysis of power complementary filters using the state-space representation. Our analysis is based on the bounded-real Riccati equations that were developed in the field of control theory. Through this new state-space analysis of power complementary filters, we prove that the sum of the controllability/observability Gramians of a pair of power complementary filters is...

We give dimension-free and data-dependent bounds for linear multi-task learning where a common linear operator is chosen to preprocess data for a vector of task specific linear-thresholding classifiers. The complexity penalty of multi-task learning is bounded by a simple expression involving the margins of the task-specific classifiers, the Hilbert-Schmidt norm of the selected preprocessor and ...

We introduce the delayed sine/cosine-type matrix function and use Laplace transform method to obtain a closed form solution IVP for second-order time-delayed linear system with noncommutative matrices A ?. also delay Gramian examine relative controllability linear/semi-linear time system. have obtained necessary sufficient condition of In addition, we conditions semi-linear time-delay Finally, ...

A class of multidimensional hybrid linear systems is presented, with the time vector composed by q continuous-time real components and by r discrete-time integer ones, q, r ≥ 1. The state equation is of multidimensional partial differential-difference type. A generalized variation-of-parameters formula is provided and it is used to obtain the state and the general response of the system. The fu...

In this paper we present a generalization of empirical gramians as used for nonlinear model reduction. This approach enables us to directly use data, generated by relevant trajectories, to compute the empirical controllability gramian. The observability gramian can be derived along the trajectory while ensuring that the perturbed initial conditions remain feasible. The feasibility of the pertur...

A dyadic algorithm for diagonalizing an arbitrary positive definite band matrix, referred to as a Gramian, is obtained efficiently orthogonalize the B-splines. The can be also used fast inversion method Gramian characterized by remarkable sparsity of matrix. There are two versions algorithm: first one more efficient and applicable Toeplitz while second general, works with any but computationall...

The purpose of this letter is to provide some contributions one notion Output controllability for Linear Time Varying (LTV) systems which the Complete State Controllability (CSOC), introduced in 60s by Sarachik and Kranc. More precisely, we consider LTV with direct transmission input output establish criteria ensure CSOC finite time these systems. We also give, under assumption time, an explici...

We establish a class of nonlinear fractional differential systems with distributed time delays in the controls and impulse effects. discuss controllability criteria for both linear systems. The main results required suitable Gramian matrix defined by Mittag–Leffler function, using standard Laplace transform Schauder fixed-point techniques. Further, we provide an illustrative example supported g...