Fractional control systems with the Caputo derivative are considered. The modified controllability Gramian and the minimum energy optimal control problem are investigated. Construction of minimizing steering controls for the modified energy functional are proposed.

We proposed a weighted l minimization: min , ‖x‖ + λ‖f‖ s.t.Ax+ f= b to recover a sparse vector x and the corrupted noise vector f from a linear measurement b = Ax + f when the sensing matrix A is an m × n row i.i.d subgaussian matrix. Our first result shows that the recovery is possible when the fraction of corrupted noise is smaller than a positive constant, provided that ‖x‖ ≤ O(n/ln (n/‖x ∗...

Maximum hands-off control aims to maximize the length of time over which zero actuator values are applied to a system when executing specified control tasks. To tackle such problems, recent literature has investigated optimal control problems which penalize the size of the support of the control function and thereby lead to desired sparsity properties. This article gives the exact set of necess...

An approximation procedure for time optimal control problems for the linear wave equation is analyzed. Its asymptotic behavior is investigated and an optimality system including the maximum principle and the transversality conditions for the regularized and unregularized problems are derived.

this paper presents a rational haar wavelet operational method for solving the inverse laplace transform problemand improves inherent errors from irrational haar wavelet. the approach is thus straightforward, rather simple andsuitable for computer programming. we define that $p$ is the operational matrix for integration of the orthogonalhaar wavelet. simultaneously, simplify the formulaes of li...

Lower bounds on the condition number minκp(V ) of a Vandermonde matrix V are established in terms of the dimension n or n and the largest absolute value among all nodes that define the Vandermonde matrix. Many bounds here are asymptotically sharp, and compare favorably to those of the same kind due to Gautschi and Inglese (Numer. Math., 52 (1988), 241–250) who considered either all positive nod...

In mixed effect models the variability of the regression parameters has substantial influence on the choice of the optimal design. If less observations per individual are possible than parameters are to be estimated, the optimality results of single-group designs no longer hold.