The present paper studies an optimal control problem governed by measure driven differential systems and in presence of state constraints. The first result shows that using the graph completion of the measure, the optimal solutions can be obtained by solving a reparametrized control problem of absolutely continuous trajectories but with time-dependent state-constraints. The second result shows ...

Hypertree decomposition has been shown to be the most general CSP decomposition method. However, so far the exact methods are not able to find optimal hypertree decompositions of realistic instances. We present a backtracking procedure which, along with isomorphic component detection, results in optimal hypertree decompositions. We also make the procedure generic; variations of which results in...

We consider the problems of designing a linear, time-varying filter with a specified " time-frequency (TF) pass region " and of constructing an orthonormal basis for the parsimonious expansion of signals located in a given TF support region. These problems of TF filtering and TF signal expunsion are reduced to the problem of designing a " TF subspace, " i.e., a linear signal space comprising al...

A boundary optimal control problem for a nonlinear nonstationary heat transfer model is considered. The model describes coupled conduction and radiation within the P1 approximation. The control parameter is related to the emissivity of the boundary and varies with time. The optimal control problem is to minimize or maximize a cost functional which is assumed to be monotonic. Sufficient conditio...

We consider the discretization of an optimal boundary control problem with distributed observation by the boundary concentrated finite element method. With an H(Ω) regular elliptic PDE on two-dimensional domains as constraint, we prove that the discretization error ‖u∗ − uh‖L2(Γ) decreases like N −δ, where N denotes the total number of unknowns. For the case δ = 1 in convex polygonal domains, t...

In this paper, we investigate the superconvergence property of the numerical solution of a quadratic convex optimal control problem by using rectangular mixed finite element methods. The state and co-state variables are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. Some realistic regularity a...

This note addresses the problem of local stabilization of linear systems subject to control amplitude and rate saturation. Considering the actuator represented by a first-order system subject to input and state saturation, a condition for the stabilization of an a priori given set of admissible initial states is formulated from certain saturation nonlinearities representation and quadratic stab...

Research on multigrid methods for optimization problems is reviewed. Optimization problems include shape design, parameter optimization, and optimal control problems governed by partial differential equations of elliptic, parabolic, and hyperbolic type.

Problems of optimal control are considered in the neoclassical Bolza format, which centers on states and velocities and relies on nonsmooth analysis. Subgradient versions of the EulerLagrange equation and the Hamiltonian equation are shown to be necessary for the optimality of a trajectory, moreover in a newly sharpened form that makes these conditions equivalent to each other. At the same time...