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Optimal control of differential-algebraic inclusions. (English) Zbl 1160.49024

de Queiroz, Marcio (ed.) et al., Optimal control, stabilization and nonsmooth analysis. Papers from the Louisiana conference on mathematical control theory (MCT’03), Louisiana State University, Baton Rouge, LA, USA, April 10–13, 2003. Berlin: Springer (ISBN 3-540-21330-9/pbk). Lecture Notes in Control and Information Sciences 301, 73-83 (2004).
The authors consider the optimization problem \[ J[x,z] := \varphi(x(a),x(b)) + \int_a^b f(x(t),x(t-\Delta),\dot{z}(t),t)dt \longrightarrow \min \] for the system governed by the following relations \[ \begin{aligned} &\dot{z}(t) \in F(x(t),x(t-\Delta),t) \,\,{\text a.e.}\,\,t \in [a,b]; \\ &z(t) = x(t) + A x(t - \Delta),\,\,\,t\in [a,b];\\ &x(t) = c(t),\,\,\,t\in [a - \Delta,a);\\ &(x(a),x(b)) \in \Omega \subset \mathbb{R}^{2n}, \end{aligned} \] where \(\Delta > 0,\) \(c\) is a given function, \(F\) is a closed multimap, and \(A\) is an \(n \times n\) matrix. By application of the method of discrete approximations developed by the first author in [SIAM J. Control Optimization 33, No. 3, 882–915 (1995; Zbl 0844.49017)] the necessary optimality conditions for the above problem are obtained.
For the entire collection see [Zbl 1051.49001].

MSC:

49K24 Optimal control problems with differential inclusions (nec./ suff.) (MSC2000)
34A60 Ordinary differential inclusions
49K25 Optimal control problems with equations with ret.arguments (nec.) (MSC2000)

Citations:

Zbl 0844.49017
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