Upper Bounds of the Pursuer Control Based on a Linear-Quadratic Differential Game

Differential game formulations provide an adequate basis for a guidance law synthesis against highly maneuvering targets. This paper deals with a guidance law based on a linear-quadratic differential game formulation. This guidance law has many attractive properties: it is continuous, linear with respect to the state variables, and its gain coefficients can be precalculated offline. Nevertheless, due to the lack of hard control constraints in the formulation, the magnitude of the control can exceed the admissible level imposed by the nature of the problem. In this paper, the upper bound of the interceptor control is obtained depending on the system parameters and the penalty coefficients of the game performance index. It is shown that the interceptor can guarantee an arbitrarily small miss distance without exceeding the control constraints if it has sufficient maneuverability and if the penalty coefficients are chosen properly. By manipulating the penalty coefficients, it is possible to reduce significantly the maneuverability requirements compared to the case of zero interceptor penalty coefficient.     

Generic Well-Posedness of Constrained Variational Problems Without Convexity Assumptions

In our previous work, a generic well-posedness result (with respect to variations of the integrand of the integral functional) without the convexity condition was established for a class of optimal control problems satisfying the Cesari growth condition. In this paper, we extend this generic well-posedness result to classes of constrained variational problems in which the values at the endpoints and constraint maps are also subject to variations.     

Augmented Lagrangian Algorithms Based on the Spectral Projected Gradient Method for Solving Nonlinear Programming Problems

The spectral projected gradient method SPG is an algorithm for large-scale bound-constrained optimization introduced recently by Birgin, Martínez, and Raydan. It is based on the Raydan unconstrained generalization of the Barzilai-Borwein method for quadratics. The SPG algorithm turned out to be surprisingly effective for solving many large-scale minimization problems with box constraints. Therefore, it is natural to test its perfomance for solving the sub-problems that appear in nonlinear programming methods based on augmented Lagrangians. In this work, augmented Lagrangian methods which use SPG as the underlying convex-constraint solver are introduced (ALSPG) and the methods are tested in two sets of problems. First, a meaningful subset of large-scale nonlinearly constrained problems of the CUTE collection is solved and compared with the perfomance of LANCELOT. Second, a family of location problems in the minimax formulation is solved against the package FFSQP.     

On the Existence of Solutions to Vector Quasivariational Inequalities and Quasicomplementarity Problems with Applications Break to Traffic Network Equilibria

For vector quasivariational inequalities involving multifunctions in topological vector spaces, an existence result is obtained without a monotonicity assumption and with a convergence assumption weaker than semicontinuity. A new type of quasivariational inequality is proposed. Applications to quasicomplementarity problems and traffic network equilibria are considered. In particular, definitions of weak and strong Wardrop equilibria are introduced for the case of multivalued cost functions.     

Elliptic and parabolic problems in unbounded domains

We consider elliptic and parabolic problems in unbounded domains. We give general existence and regularity results in Besov spaces and semi‐explicit representation formulas via operator‐valued fundamental solutions which turn out to be a powerful tool to derive a series of qualitative results about the solutions. We give a sample of possible applications including asymptotic behavior in the large, singular perturbations, exact boundary conditions on artificial boundaries and validity of maximum principles. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Piecewise Deterministic Markov Control Processes with Feedback Controls and Unbounded Costs

The control of piecewise-deterministic processes is studied where only local boundedness of the data is assumed. Moreover the discount rate may be zero. The value function is shown to be solution to the Bellman equation in a weak sense; however the solution concept is strong enough to generate optimal policies. Continuity and compactness conditions are given for the existence of nonrelaxed optimal feedback controls.     

Multilevel a posteriori error analysis for reaction–convection–diffusion problems

We present a new approach to the a posteriori error analysis of stable Galerkin approximations of reaction–convection–diffusion problems. It relies upon a non-standard variational formulation of the exact problem, based on the anisotropic wavelet decomposition of the equation residual into convection-dominated scales and diffusion-dominated scales. The associated norm, which is stronger than the standard energy norm, provides a robust (i.e., uniform in the convection limit) control over the streamline derivative of the solution. We propose an upper estimator and a lower estimator of the error, in this norm, between the exact solution and any finite dimensional approximation of it. We investigate the behaviour of such estimators, both theoretically and through numerical experiments. As an output of our analysis, we find that the lower estimator is quantitatively accurate and robust.     

Boundary position feedback control of Kirchhoff's non‐linear strings

This paper is concerned with global stabilization of an undamped non‐linear string in the case where any velocity feedback is not available. The linearized system has an infinite number of poles and zeros on the imaginary axis. In the case where any velocity feedback is not available, a parallel compensator is effective. The stabilizer is constructed for the augmented system which consists of the controlled system and a parallel compensator. It is proved that the string can be stabilized by linear boundary control. Copyright © 2003 John Wiley & Sons, Ltd.     

Dynamic boundary stabilization of a Reissner–Mindlin plate with Timoshenko beam

This paper is concerned with well‐posedness results for a mathematical model for the transversal vibrations of a two‐dimensional hybrid elastic structure consisting of a rectangular Reissner–Mindlin plate with a Timoshenko beam attached to its free edge. The model incorporates linear dynamic feedback controls along the interface between the plate and the beam. Classical semigroup methods are employed to show the unique solvability of the coupled initial‐boundary‐value problem. We also show that the energy associated with the system exhibits the property of strong stability. Copyright © 2004 John Wiley & Sons, Ltd.     

Pointwise stabilization of strings with non‐linear feedback

We consider an initial and boundary value problem for a homogenous string subject to an internal pointwise control. The solution resulting from a non‐linear feedback is studied. We give various explicit decay estimates depending on the control position and the feedback non‐linearity. Copyright © 2004 John Wiley & Sons, Ltd.