Generalized solutions of optimal control problems
Keywords:optimal control, mathematical modeling, processes with concentrated parameters, processes with distributed parameters
The problems of optimal control of systems of algebraic-integro-differential equations and partial differential equations are considered, which describe controlled processes with concentrated and distributed parameters. Generalized optimal solutions that exist for a wide range of optimal control applications are identified. Methods for constructing approximate generalized solutions are considered.
M.Z. Zgurovsky and N.D. Pankratova, System analysis: problems, methodology, applications. Kiev: Publishing house of Nauk.dumka, 2011, 728 p.
Eugene A. Feinberg, Pavlo O. Kasyanov, and Michael Z. Zgurovsky, “Partially Observable Total-Cost Markov Decision Processes with Weakly Continuous Transition Probabilities”, Mathematics of Operations Research 41(2), pp. 656–681, 2016.
I. Beyko, P. Zinko, and A. Nakonechny, Problems, methods and algorithms of optimization. Kyiv: Kyiv University Publishing and Printing Center, 2012, 799 p.
F. Troltzsch, Optimal Control of Partial Differential Equations: Theory, Methods and Applications. Amer Mathematical Society, 2010.
E. Polak, Optimization: Algorithms and Consistent Approximations. Heidelberg, Germany: Springer-Verlag, 1997.
R. Becker and M. Braack, “A Finite Element Pressure Gradient Stabilization for the StokesEquations Based on Local Projections”, Calcolo, 38(4), pp. 173–199, 2001.
W.W. Hager, “Runge-Kutta Methods in Optimal Control and the Transformed Adjoint Systems”, Numerishe Mathematik, vol. 87, pp. 247–282, 2000.
I. Beyko and M. Beyko, “On the numerical construction of optimal controls”, Modeling of nonstationary processes. Kiev: IM AN UkrSSR, 1977, pp. 173–190.
F. Fahroo and I.M. Ross, “Pseudospectral Methods for Infinite-Horizon Nonlinear Optimal Control Problems”, Journal of Guidance, Control, and Dynamics, vol. 31, no.4, pp. 927–936, 2008.
I. Beyko, “Development of methods of solving and asymptotically-solving operators for construction of optimal and asymptotically-optimal mathematical models”, Visnyk of Kyiv National University. Series: Cybernetics, vol. 3, pp. 10–15, 2002.
M. Ulbrich, Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems. SIAM Philadelphia, 2011.