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Control system defined by some integral operator

Majewski M.

Opuscula Mathematica

2017

Vol. 37, no. 2

313--325

In the paper we consider a nonlinear control system governed by the Volterra integral operator. Using a version of the global implicit function theorem we prove that the control system under consideration is well-posed and robust, i.e. for any admissible control u there exists a uniquely defined trajectory xu which continuously depends on control u and the operator [formula] is continuously differentiable. The novelty of this paper is, among others, the application of the Bielecki norm in the space of solutions which allows us to weaken standard assumptions.

Local quadratic convergence of SQP for elliptic optimal control problems with mixed control-state constraints

Griesse R., Metla N., Rosch A.

Control and Cybernetics

2010

Vol. 39, no 3

717-738

Semilinear elliptic optimal control problems with pointwise control and mixed control-state constraints are considered. Necessary and sufficient optimality conditions are given. The equivalence of the SQP method and Newton's method for a generalized equation is discussed. Local quadratic convergence of the SQP method is proved.

Application of the classical implicit function theorem in sensitivity analysis of parametric optimal control

Malanowski K.

Control and Cybernetics

1998

Vol. 27, no 3

335-352

A family {(O[sub h])} of parametric optimal control problems for nonlinear ODEs is considered. The problems are subject to pointwise inequality type state constraints. It is assumed that the reference solution is regular. The original problems (O[sub h]) are substituted by problems [...] subject to equality type constraints with the sets of activity depending on the parameter. Using the classical implicit function theorem, conditions are derived under which stationary points of [...] are Frechet differentiable functions of the parameter. It is shown that, under additional conditions, the stationary points of [...] correspond to the solutions and Lagrange multipliers of (O[sub h]9).