Milman, Mark H. Approximating the linear quadratic optimal control law for hereditary systems with delays in the control. (English) Zbl 0651.93025 SIAM J. Control Optimization 26, No. 2, 291-320 (1988). For the problem \[ \dot x(t)=\int^{0}_{-r}d_{\theta}\eta (t,\theta)x(t+\theta)+\sum^{k}_{i=0}B_ i(t)u(t-r_ i)+\int^{t}_{t-r}B(t,\theta)u(\theta)d\theta,\quad x(t)=\phi (t),\quad t\in [-r,0], \]\[ (1)\quad \int^{T}_{- r}<x(s),Q(s)x(s)>d\mu +\int^{T}_{-r}| u(s)|^ 2ds\to \min \] an appropriate perturbed problem is considered where the functional (1) is approximated by \[ \int^{T}_{- r}<x(s),Q(s)x(s)>d\mu_{\pi}(s)+\int^{T}_{-r}| u(s)|^ 2ds,\quad \mu_{\pi}\to \mu. \] In the case \(\mu =\lambda +\delta_ T\), where \(\lambda\) denotes the Lebesgue measure and \(\delta_ T\) is the Dirac measure with support on \(\{\) \(T\}\), convergence of optimal controls and optimal trajectories is shown. For \(\mu =\sum^{n}_{i=1}a_ i\delta_{s_ i}\), \(s_ i\in [-r,T]\), \(S_ n=T\), the performance of an optimal feedback kernel is studied on the basis of which an algorithm is proposed. A numerical example is considered. Reviewer: T.Tadumadze Cited in 3 Documents MSC: 93B40 Computational methods in systems theory (MSC2010) 34K35 Control problems for functional-differential equations 93C05 Linear systems in control theory 49M99 Numerical methods in optimal control 65K10 Numerical optimization and variational techniques Keywords:hereditary systems; approximation; linear quadratic optimal control; convergence of optimal controls and optimal trajectories; algorithm PDFBibTeX XMLCite \textit{M. H. Milman}, SIAM J. Control Optim. 26, No. 2, 291--320 (1988; Zbl 0651.93025) Full Text: DOI Link