ISSN:
1573-2878
Keywords:
Time-delay systems
;
bounded state problems
;
maximum principle
;
retarded control problems
;
state variable constraints
;
optimal control problems
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract A maximum principle is obtained for control problems involving a constant time lag τ in both the control and state variables. The problem considered is that of minimizing $$I(x) = \int_{t^0 }^{t^1 } {L (t,x(t), x(t - \tau ), u(t), u(t - \tau )) dt} $$ subject to the constraints 1 $$\begin{gathered} \dot x(t) = f(t,x(t),x(t - \tau ),u(t),u(t - \tau )), \hfill \\ x(t) = \phi (t), u(t) = \eta (t), t^0 - \tau \leqslant t \leqslant t^0 , \hfill \\ \end{gathered} $$ 1 $$\psi _\alpha (t,x(t),x(t - \tau )) \leqslant 0,\alpha = 1, \ldots ,m,$$ 1 $$x^i (t^1 ) = X^i ,i = 1, \ldots ,n$$ . The results are obtained using the method of Hestenes.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01268174
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