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Full-Text Articles in Applied Mathematics
Optimal Control And Feedback Design Of State-Constrained Parabolic Systems In Uncertainty Conditions, Boris S. Mordukhovich
Optimal Control And Feedback Design Of State-Constrained Parabolic Systems In Uncertainty Conditions, Boris S. Mordukhovich
Mathematics Research Reports
The paper concerns minimax control problems for linear multidimensional parabolic systems with distributed uncertain perturbations and control functions acting in the Dirichlet boundary conditions. The underlying parabolic control system is functioning under hard/pointwise constraints on control and state variables. The main goal is to design a feedback control regulator that ensures the required state performance and robust stability under any feasible perturbations and minimize an energy-type functional under the worst perturbations from the given area. We develop a constructive approach to the minimax control design of constrained parabolic systems that is based on certain characteristic features of the parabolic dynamics …
Variational Analysis In Semi-Infinite And Infinite Programming, I: Stability Of Linear Inequality Systems Of Feasible Solutions, M J. Cánovas, M A. Lopez, Boris S. Mordukhovich, J Parra
Variational Analysis In Semi-Infinite And Infinite Programming, I: Stability Of Linear Inequality Systems Of Feasible Solutions, M J. Cánovas, M A. Lopez, Boris S. Mordukhovich, J Parra
Mathematics Research Reports
This paper concerns applications of advanced techniques of variational analysis and generalized differentiation to parametric problems of semi-infinite and infinite programming, where decision variables run over finite-dimensional and infinite-dimensional spaces, respectively. Part I is primarily devoted to the study of robust Lipschitzian stability of feasible solutions maps for such problems described by parameterized systems of infinitely many linear inequalities in Banach spaces of decision variables indexed by an arbitrary set T. The parameter space of admissible perturbations under consideration is formed by all bounded functions on T equipped with the standard supremum norm. Unless the index set is finite, this …
Second-Order Analysis Of Polyhedral Systems In Finite And Infinite Dimensions With Applications To Robust Stability Of Variational Inequalities, René Henrion, Boris S. Mordukhovich, Nguyen Mau Nam
Second-Order Analysis Of Polyhedral Systems In Finite And Infinite Dimensions With Applications To Robust Stability Of Variational Inequalities, René Henrion, Boris S. Mordukhovich, Nguyen Mau Nam
Mathematics Research Reports
This paper concerns second-order analysis for a remarkable class of variational systems in finite-dimensional and infinite-dimensional spaces, which is particularly important for the study of optimization and equilibrium problems with equilibrium constraints. Systems of this type are described via variational inequalities over polyhedral convex sets and allow us to provide a comprehensive local analysis by using appropriate generalized differentiation of the normal cone mappings for such sets. In this paper we efficiently compute the required coderivatives of the normal cone mappings exclusively via the initial data of polyhedral sets in reflexive Banach spaces. This provides the main tools of second-order …
Robust Stability And Optimality Conditions For Parametric Infinite And Semi-Infinite Programs, M J. Cánovas, M A. Lopez, Boris S. Mordukhovich, J Parra
Robust Stability And Optimality Conditions For Parametric Infinite And Semi-Infinite Programs, M J. Cánovas, M A. Lopez, Boris S. Mordukhovich, J Parra
Mathematics Research Reports
This paper primarily concerns the study of parametric problems of infinite and semi-infinite programming, where functional constraints are given by systems of infinitely many linear inequalities indexed by an arbitrary set T, where decision variables run over Banach (infinite programming) or finite-dimensional (semi-infinite case) spaces, and where objectives are generally described by nonsmooth and nonconvex cost functions. The parameter space of admissible perturbations in such problems is formed by all bounded functions on T equipped with the standard supremum norm. Unless the index set T is finite, this space is intrinsically infinite-dimensional (nonreflexive and nonseparable) of the l(infinity)-type. By using …
Suboptimal Minimax Design Of Constrained Parabolic Systems With Mixed Boundary Control, Boris S. Mordukhovich
Suboptimal Minimax Design Of Constrained Parabolic Systems With Mixed Boundary Control, Boris S. Mordukhovich
Mathematics Research Reports
The paper concerns minimax control problems for linear multidimensional parabolic systems with distributed uncertain perturbations and control functions acting in mixed (Robin) boundary conditions. The main goal is to design a feedback control regulator that ensures the required state performance and robust stability under any feasible perturbations and minimize an energy-type functional under the worst perturbations from the given area. We design and justify an easily implemented suboptimal structure of the feedback boundary regulator and compute its optimal parameters ensuring the required state performance and robust stability of the nonlinear closed-loop control system on the infinite horizon.
Suboptimal Feedback Control Design Of Constrained Parabolic Systems In Uncertainty Conditions, Boris S. Mordukhovich
Suboptimal Feedback Control Design Of Constrained Parabolic Systems In Uncertainty Conditions, Boris S. Mordukhovich
Mathematics Research Reports
The paper concerns minimax control problems forlinear multidimensional parabolic systems with distributed uncertain perturbations and control functions acting in the Dirichlet boundary conditions. The underlying parabolic control system is functioning under hard/pointwise constraints on control and state variables. The main goal is to design a feedback control regulator that ensures the required state performance and robust stability under any feasible perturbations and minimize an energy-type functional under the worst perturbations from the given area. We develop an efficient approach to the minimax control design of constrained parabolic systems that is based on certain characteristic features of the parabolic dynamics including …