To obtain approximate-exact solutions to nonlocal initial-boundary value problems (IBVPs) of linear and nonlinear parabolic hyperbolic partial differential equations (PDEs) subject initial boundary conditions integral type, the homotopy perturbation method (HPM) is utilized in this study. The HPM used solve specified IBVPs, which are then transformed into local Dirichlet IBVPs. Some examples de...

This paper considers the optimal control problem of minimizing control effort subject to multiple performance constraints on output covariance matrices Yi of the form Yi ≤ Y i, where Y i is given. The contributions of this paper are a set of conditions that characterize global optimality, and an iterative algorithm for finding a solution to the optimality conditions. This iterative algorithm is...

We develop necessary conditions of broad applicability for optimal control problems in which the state and control are subject to mixed constraints. We unify, subsume and significantly extend most of the results on this subject, notably in the three special cases that comprise the bulk of the literature: calculus of variations, differential-algebraic systems, and mixed constraints specified by ...

Idiographic methods focus on time-dependent variation within a single individual (intra-subject variability) in contrast to group-level relationships (inter-subject variability) that may yield different results. Equivalent results occur only if two, probably unrealistic, conditions specified by Ergodic Theorems are met: (1) Each trajectory follows the same dynamic laws, and (2) Each trajectory ...