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THE LINEAR PROGRAMMING APPROACH TO DETERMINISTIC OPTIMAL CONTROL PROBLEMS
"... Abstract. Given a deterministic optimal control problem (OCP) with value function, say J∗, we introduce a linear program (P) and its dual (P ∗) whose values satisfy sup(P ∗) ≤ inf(P) ≤ J∗(t, x). Then we give conditions under which (i) there is no duality gap, i.e. sup(P ∗) = inf(P), and (ii) (P) ..."
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Abstract. Given a deterministic optimal control problem (OCP) with value function, say J∗, we introduce a linear program (P) and its dual (P ∗) whose values satisfy sup(P ∗) ≤ inf(P) ≤ J∗(t, x). Then we give conditions under which (i) there is no duality gap, i.e. sup(P ∗) = inf(P), and (ii) (P
Idempotent Analogue of Resolvent Kernels for a Deterministic Optimal Control Problem
"... Introduction In several places, the use of the semiring (R; min; +) appears to be fundamental in order to apply constructions developed for linear operators to non linear ones. It is well known that the discrete Bellman equation can be treated as linear over appropriate idempotent semirings, and in ..."
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Cited by 1 (1 self)
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by means of resolvent kernels. Indeed our method is neither the most general w.r.t idempotent analysis neither conditions which permits to point out this connection are widely assumed in the theory of optimal control, but these permit us to show, that it is possible to apply also in a wider way the analogy
A maxplus finite element method for solving finite horizon deterministic optimal control problems
 in "Proceedings of MTNS’04, Louvain, Belgique", Also arXiv:math.OC/0404184, 2004, http://hal.inria.fr/inria00071426. Maxplus 31
"... Abstract. We introduce a maxplus analogue of the PetrovGalerkin finite element method, to solve finite horizon deterministic optimal control problems. The method relies on a maxplus variational formulation, and exploits the properties of projectors on maxplus semimodules. We obtain a nonlinear d ..."
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Cited by 12 (3 self)
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Abstract. We introduce a maxplus analogue of the PetrovGalerkin finite element method, to solve finite horizon deterministic optimal control problems. The method relies on a maxplus variational formulation, and exploits the properties of projectors on maxplus semimodules. We obtain a nonlinear
The maxplus finite element method for solving deterministic optimal control problems: basic properties and convergence analysis, in "SIAM J. Control and Opt.", to appear
, 2007
"... Abstract. We introduce a maxplus analogue of the PetrovGalerkin finite element method to solve finite horizon deterministic optimal control problems. The method relies on a maxplus variational formulation. We show that the error in the sup norm can be bounded from the difference between the value ..."
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Cited by 25 (4 self)
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Abstract. We introduce a maxplus analogue of the PetrovGalerkin finite element method to solve finite horizon deterministic optimal control problems. The method relies on a maxplus variational formulation. We show that the error in the sup norm can be bounded from the difference between
Original Russian Text Copyright c○2001 by Loreti, Pedicini The Idempotent Analog of Resolvent Kernels for a Deterministic Optimal Control Problem
, 1998
"... Abstract—A solution of a discrete Hamilton–Jacobi–Bellman equation is represented in terms of idempotent analysis as a convergent series of integral operators. Key words: idempotent analysis, optimal control problem, Hamilton–Jacobi–Bellman equation, Volterra equation, correspondence principle, reso ..."
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Abstract—A solution of a discrete Hamilton–Jacobi–Bellman equation is represented in terms of idempotent analysis as a convergent series of integral operators. Key words: idempotent analysis, optimal control problem, Hamilton–Jacobi–Bellman equation, Volterra equation, correspondence principle
Constrained model predictive control: Stability and optimality
 AUTOMATICA
, 2000
"... Model predictive control is a form of control in which the current control action is obtained by solving, at each sampling instant, a finite horizon openloop optimal control problem, using the current state of the plant as the initial state; the optimization yields an optimal control sequence and t ..."
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Cited by 738 (16 self)
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Model predictive control is a form of control in which the current control action is obtained by solving, at each sampling instant, a finite horizon openloop optimal control problem, using the current state of the plant as the initial state; the optimization yields an optimal control sequence
Optimization Flow Control, I: Basic Algorithm and Convergence
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 1999
"... We propose an optimization approach to flow control where the objective is to maximize the aggregate source utility over their transmission rates. We view network links and sources as processors of a distributed computation system to solve the dual problem using gradient projection algorithm. In thi ..."
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Cited by 694 (64 self)
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We propose an optimization approach to flow control where the objective is to maximize the aggregate source utility over their transmission rates. We view network links and sources as processors of a distributed computation system to solve the dual problem using gradient projection algorithm
Topology Control of Multihop Wireless Networks using Transmit Power Adjustment
, 2000
"... We consider the problem of adjusting the transmit powers of nodes in a multihop wireless network (also called an ad hoc network) to create a desired topology. We formulate it as a constrained optimization problem with two constraints connectivity and biconnectivity, and one optimization objective ..."
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Cited by 688 (3 self)
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We consider the problem of adjusting the transmit powers of nodes in a multihop wireless network (also called an ad hoc network) to create a desired topology. We formulate it as a constrained optimization problem with two constraints connectivity and biconnectivity, and one optimization objective
New results in linear filtering and prediction theory
 TRANS. ASME, SER. D, J. BASIC ENG
, 1961
"... A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary sta ..."
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Cited by 607 (0 self)
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in this field. The Duality Principle relating stochastic estimation and deterministic control problems plays an important role in the proof of theoretical results. In several examples, the estimation problem and its dual are discussed sidebyside. Properties of the variance equation are of great interest
Results 1  10
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