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**Contents:**

Secondly, for an optimal birth control problem of a McKendrick type age-structured population dynamics, we establish the optimal feedback control laws by the dynamic programming viscosity solution DPVS approach.

Finally, for a well-adapted upwind finite-difference numerical scheme for the HJB equation arising in optimal control, we prove its convergence and show that the solution from this finite-difference scheme converges to the value function of the associated optimal control problem.

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In this chapter, we wish to show that dynamic programming applied to the calculus of variations leads to various classes of partial differential equations. Purchase Dynamic Programming and Partial Differential Equations, Volume 88 - 1st Edition. Print Book & E-Book. ISBN ,

Springer Professional "Technik" Online-Abonnement. Sussmann, H. Ho, Y. IEEE Trans. Fattorini, H.

Encyclopedia of Mathematics and Its Applications. Cambridge University Press, Cambridge Guo, B. Science Press, Beijing Rubio, J. Bryson Jr. Teo, K. Rehbock, V. B 40 , — CrossRef. Jennings, L.

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Discrete Continuous Dyn. Augustin, D. Liu, Y. Theory Appl. Malanowski, K. Maurer, H. SIAM J. Control Optim. Crandall, M. In: Capuzzo-Dolcetta, I. Viscosity Solutions and Applications. Lecture Notes in Mathematics, vol.

Springer, Berlin Bardi, M. Maurizio Falcone and Pierpaolo Soravia. Barron, E. Cannarsa, P. Gozzi, F. Kalman filter: there is no control in the state equation. Use Raccati recursion to update the covariance matrix of the state-estimation error. To find a lower bound of a constrained optimization problem, tighten the constraints work on sufficient conditions ; to find a upper bound of a constrained optimization problem, loosen the constraints work on the necessary conditions.

Model Predictive Control MPC has been widely adopted in industry as an effective means to deal with large multivariable constrained control problems.

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In MPC the control action is chosen by solving an optimal control problem on line. The optimization aims at minimizing a performance criterion over a future small horizon, possibly subject to constraints on the manipulated inputs and outputs. MPC is different from conventional optimal control in the following aspects:.

Although MPC has long been recognized as the preferred alternative for constrained systems, its applicability has been limited to slow systems such as chemical processes, where large sampling times make it possible to solve large optimization problems each time new measurements are collected from the plant.

Quenez , Backward stochastic differential equation in finance. Finance 7 Fuhrman and G. Tessitore , Nonlinear Kolmogorov equation in infinite dimensional spaces : the backward stochastic differential equations approach and applications to optimal control.

Fuhrman , F. Masiero and G. SIAM J.

matronics.in Control Optim. Larssen , Dynamic programming in stochastic control of systems with delay. Larssen and N. Risebro , When are HJB equations for control problems with stochastic delay equations finite dimensional? Zbl The Geido Workshop ; Progress in Probability.

Birkhauser Peng , A generalized dynamic programming principle and Hamilton-Jacobi-Bellmen equation.

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