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Dual-weighted goal-oriented error estimates for a class of pointwise control constrained optimal control problems for second order elliptic partial differential equations are derived. It is demonstrated that the constraints give rise to a primal-dual weighted error term representing the mismatch in the complementarity system due to discretization. Besides a theoretical foundation, numerical results...
The problem of receding horizon control for a class of nonlinear distributed processes is investigated. The main focus of the manuscript lies in the development of a computationally efficient method to identify the optimal control action with respect to predefined performance criteria. An optimal control problem is formulated and is solved using standard, gradient-based, search algorithms. Employing...
An isolation control of SIR epidemic model are proposed and analyzed, which not only isolate infective, but also isolate susceptible. In order to calculate the optimal values of the isolate rates, it constructs a performance index that is calculated explicitly as an algebraic function of the controller parameters by solving Zubov's partial differential equation, and standard optimization techniques...
Approaching the problem of optimal adaptive control as ldquooptimal control made adaptive,rdquo namely, as a certainty equivalence combination of linear quadratic optimal control and standard parameter estimation, fails on two counts: numerical (as it requires a solution to a Riccati equation at each time step) and conceptual (as the combination actually does not possess any optimality property)....
This work focuses on optimal boundary control of highly dissipative Kuramoto-Sivashinsky equation (KSE) which describes the long-wave motions of a thin film over vertical plane. A standard transformation is initially used to reformulate the original boundary control problem as an abstract boundary control problem of the KSE partial differential equation (PDE) in an appropriate functional space setting...
Recent advances on path integral stochastic optimal control [1],[2] provide new insights in the optimal control of nonlinear stochastic systems which are linear in the controls, with state independent and time invariant control transition matrix. Under these assumptions, the Hamilton-Jacobi-Bellman (HJB) equation is formulated and linearized with the use of the logarithmic transformation of the optimal...
The problem of optimal control of an elliptic system is parametrized by a family of retracts of the boundary of the system domain, and dynamic programming is applied.
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