Abstract
AbstractThis paper presents sufficient conditions for strong metric subregularity (SMsR) of the optimality mapping associated with the local Pontryagin maximum principle for Mayer-type optimal control problems with pointwise control constraints given by a finite number of inequalities$$G_j(u)\le 0$$Gj(u)≤0. It is assumed that all data are twice smooth, and that at each feasible point the gradients$$G_j'(u)$$Gj′(u)of the active constraints are linearly independent. The main result is that the second-order sufficient optimality condition for a weak local minimum is also sufficient for a version of the SMSR property, which involves two norms in the control space in order to deal with the so-called two-norm-discrepancy.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Control and Optimization
Reference23 articles.
1. Alt, W., Schneider, C., Seydenschwanz, M.: Regularization and implicit Euler discretization of linear-quadratic optimal control problems with bang-bang solutions. Appl. Math. Comput. 287–288, 104–124 (2016)
2. Angelov, G., Corella, A. Domínguez., Veliov, V.M.: On the accuracy of the model predictive control method. SIAM J. Control Optim. 60(4), 2469–2487 (2022)
3. Bonnans, F.J.: Local analysis of Newton-type methods for variational inequalities and nonlinear programming. Appl. Math. Optim. 29, 161–186 (1994)
4. Bonnans, F.J., Osmolovskii, N.P.: Characterization of a local quadratic growth of the Hamiltonian for control constrained optimal control problems. Dyn. Contin. Discret. Impuls. Syst. Ser. B 19, 1-2–1-16 (2012)
5. Bonnans, F.J., Shapiro, A.: Perturbation Analysis of Optimization Problems. Springer, Berlin (2000)