Results 1  10
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125
InputOutputtoState Stability
 SIAM J. Control Optim
, 1999
"... This work explores Lyapunov characterizations of the inputoutputtostate stability (oss) property for nonlinear systems. The notion of IOSS is a natural generalization of the standard zerodetectability property used in the linear case. The main contribution of this work is to establish a compl ..."
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Cited by 49 (17 self)
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This work explores Lyapunov characterizations of the inputoutputtostate stability (oss) property for nonlinear systems. The notion of IOSS is a natural generalization of the standard zerodetectability property used in the linear case. The main contribution of this work is to establish a complete equivalence between the inputoutputtostate stability property and the existence of a certain type of smooth Lyapunov function. As corollaries, one shows the existence of "normestimators", and obtains characterizations of nonlinear detectability in terms of relative stability and of finiteenergy estimates.
Navier–Stokes equations: Controllability by means of low modes forcing
 J. Math. Fluid Mech
"... We study controllability issues for 2D and 3D NavierStokes (NS) systems with periodic boundary conditions. The systems are controlled by a degenerate (applied to few low modes) forcing. Methods of differential geometric/Lie algebraic control theory are used to establish global controllability of ..."
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Cited by 42 (8 self)
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We study controllability issues for 2D and 3D NavierStokes (NS) systems with periodic boundary conditions. The systems are controlled by a degenerate (applied to few low modes) forcing. Methods of differential geometric/Lie algebraic control theory are used to establish global controllability of finitedimensional Galerkin approximations of 2D and 3D NS and Euler systems, global controllability in finitedimensional projection of 2D NS system and L2approximate controllability for 2D NS system. Beyond these main goals we obtain results on boundedness and continuous dependence of trajectories of 2D NS system on degenerate forcing, when the space of forcings is endowed with so called relaxation metric.
Suboptimization of singularly perturbed control systems
 SIAM J. Control Optim
, 1992
"... Abstract. An averaging technique for nonlinear multiscale singularly perturbed control systems is developed. Issues concerning the existence and structure of limit occupational measures sets generated by such systems are discussed. General results are illustrated with special cases. Key words. multi ..."
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Cited by 36 (14 self)
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Abstract. An averaging technique for nonlinear multiscale singularly perturbed control systems is developed. Issues concerning the existence and structure of limit occupational measures sets generated by such systems are discussed. General results are illustrated with special cases. Key words. multiscale singularly perturbed control systems, occupational measures, averaging method, limit occupational measures sets, nonlinear control, approximation of slow motions
Linear programming approach to deterministic infinite horizon optimal control problems with discounting
 SIAM J. Control Optim
, 2009
"... Abstract. We establish that deterministic long run average problems of optimal control are “asymptotically equivalent ” to infinitedimensional linear programming problems (LPPs) and we establish that these LPPs can be approximated by finitedimensional LPPs, the solutions of which can be used for c ..."
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Cited by 26 (5 self)
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Abstract. We establish that deterministic long run average problems of optimal control are “asymptotically equivalent ” to infinitedimensional linear programming problems (LPPs) and we establish that these LPPs can be approximated by finitedimensional LPPs, the solutions of which can be used for construction of the optimal controls. General results are illustrated with numerical examples.
Limit occupational measures set for a control system and averaging of singularly perturbed control systems
 J. Math. Anal. Appl
, 1999
"... Abstract. A representation of the limit occupational measures set of a control system in terms of the vector function defining the system’s dynamics is established. Applications in averaging of singularly perturbed control systems are demonstrated. Key words. singularly perturbed control systems, oc ..."
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Cited by 16 (8 self)
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Abstract. A representation of the limit occupational measures set of a control system in terms of the vector function defining the system’s dynamics is established. Applications in averaging of singularly perturbed control systems are demonstrated. Key words. singularly perturbed control systems, occupational measures, averaging method, limit occupational measures sets, approximation of slow motions
On Prohorov's theorem for transition probabilities
 Travaux S'em. Anal. Convexe Montpellier
, 1989
"... In this paper we settle the open problem of proving Prohorov’s theorem for transition probabilities (alias Young measures) in its most general form, viz. in the case where the transition probabilities act into a completely regular Suslin space. Among others, the present author ..."
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Cited by 15 (9 self)
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In this paper we settle the open problem of proving Prohorov’s theorem for transition probabilities (alias Young measures) in its most general form, viz. in the case where the transition probabilities act into a completely regular Suslin space. Among others, the present author
Timedependent systems of generalized Young measures
 Netw. Heterog. Media
"... Abstract. In this paper some new tools for the study of evolution problems in the framework of Young measures are introduced. A suitable notion of timedependent system of generalized Young measures is defined, which allows to extend the classical notions of total variation and absolute continuity w ..."
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Cited by 14 (2 self)
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Abstract. In this paper some new tools for the study of evolution problems in the framework of Young measures are introduced. A suitable notion of timedependent system of generalized Young measures is defined, which allows to extend the classical notions of total variation and absolute continuity with respect to time, as well as the notion of time derivative. The main results are a Helly type theorem for sequences of systems of generalized Young measures and a theorem about the existence of the time derivative for systems with bounded variation with respect to time. 1. Introduction. The notion of Young measure was introduced by L.C. Young in [29] to describe generalized solutions to minimum problems in the calculus of variations. Since then it has been applied to several problems in the calculus of variations, in control theory, in partial differential equations, and in mathematical
Sensitivity of dynamical system to Banach space parameters
 J. Math. Analysis and Applications
, 2005
"... We consider general nonlinear dynamical systems in a Banach space with dependence on parameters in a second Banach space. An abstract theoretical framework for sensitivity equations is developed. An application to measure dependent delay differential systems arising in a class of HIV models is prese ..."
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Cited by 14 (10 self)
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We consider general nonlinear dynamical systems in a Banach space with dependence on parameters in a second Banach space. An abstract theoretical framework for sensitivity equations is developed. An application to measure dependent delay differential systems arising in a class of HIV models is presented.
Boundedfrombelow solutions of the HamiltonJacobi equation for optimal control problems with exit times: Vanishing Lagrangians, eikonal equations, and shapefromshading.” submitted
"... We study the HamiltonJacobi equation for undiscounted exit time control problems with general nonnegative Lagrangians using the dynamic programming approach. We prove theorems characterizing the value function as the unique boundedfrombelow viscosity solution of the HamiltonJacobi equation which ..."
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Cited by 11 (5 self)
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We study the HamiltonJacobi equation for undiscounted exit time control problems with general nonnegative Lagrangians using the dynamic programming approach. We prove theorems characterizing the value function as the unique boundedfrombelow viscosity solution of the HamiltonJacobi equation which is null on the target. The result applies to problems with the property that all trajectories satisfying a certain integral condition must stay in a bounded set. We allow problems for which the Lagrangian is not uniformly bounded below by positive constants, in which the hypotheses of the known uniqueness results for HamiltonJacobi equations are not satisfied. We apply our theorems to eikonal equations from geometric optics, shapefromshading equations from image processing, and variants of the Fuller Problem.