- Volume 37 Issue 4
NECESSARY AND SUFFICIENT OPTIMALITY CONDITIONS FOR CONTROL SYSTEMS DESCRIBED BY INTEGRAL EQUATIONS WITH DELAY
- Elangar, Gamal-N. (Department of Mathematics University of South Carolina at Spartanburg Spartanburg) ;
- Mohammad a Kazemi (Department of Mathematics University of North Crolina at Charlotte) ;
- Kim, Hoon-Joo (Department of Computer Science Daebul University)
- Published : 2000.07.01
In this paper we formulate an optimal control problem governed by time-delay Volterra integral equations; the problem includes control constraints as well as terminal equality and inequality constraints on the terminal state variables. First, using a special type of state and control variations, we represent a relatively simple and self-contained method for deriving new necessary conditions in the form of Pontryagin minimum principle. We show that these results immediately yield classical Pontryagin necessary conditions for control processes governed by ordinary differential equations (with or without delay). Next, imposing suitable convexity conditions on the functions involved, we derive Mangasarian-type and Arrow-type sufficient optimality conditions.
optimal control;time-delay;Volterra integral equation;necessary condition;Pontryagin minimum principle;Mangasarian-type;Arrow type;sufficient optimality condition
- Analysis and synthesis of time delay systems Giorecki, H.
- Public Investment, the Rate of Return, and Optimal Fiscal Policy Arrow, K. J.;Kurz, M.
- J. Optimiz. Theory and Applics. v.19 On the optimal control of systems governed by nonlinear integral equations Angell, T. S.
- J. Optimiz. Theory and Applics. v.13 A maximum principle for an optimal control problem with integral constraints Bakke, V. L.
- SIAM J. Control and Optim. v.34 Causal feedback optimal control for Volterra integral equations Pritchard, A. J.;You, Y.
- Optimization: a theory of necessary conditions Neustadt, L. W.
- J. Optimiz. Theory and Applics. Optimal control of time-delay systems with distributed parameters. Sadek, L. S.
- SIAM J. Control v.4 Sucient conditions for the optimal control of nonlinear systems Mangasarian, O. L.
- J. Differential equations v.13 An attainable sets approach to optimal control of functional dierential equations with function space conditions Bank, H. T.;Jacobs, M.
- J. Optimiz. Theory and Applics. v.54 An elementary proof of the maximum principle for optimal control problems governed by a Volterra integral equation Carlson, D. A.
- IMA J. Math. Control Info. v.7 Optimal control of distributed parabolic systems involving time lags Kowalewski, A.
- Optimization-Theory and applications, problems with ordinary differential equations Cesari, L.
- Rendiconti Del Circolo Matematico Di Palermo Serie II, Tomo v.34 Optimization of systems governed by hyperbolic partial dierential equation with equality and inequality constraints
- J. Austral. Math. Soc. v.B37 Necessary conditions for constrained distributed parameter systems with deviating argument Kazemi, M. A.
- SIAM J. Control and Optim. v.13 Optimal control of parabolic systems with boundary conditions having time delays Wong, P. K. C.
- Integral equations and applications Corduneanu, C.
- Transl. AMS. American Mathematical Society Qualitative methods of mathematical analysis El'sgol'c, L.E.
- Convex analysis Rockafellar, R. T.
- J. Optimiz. Theory and Applics. v.43 Optimal control on a class of systems with continuous lags: a dynamic programming approach and economic interpretations Hartl, R. F.;Sethi, S. P.
- IMA J. Math. Control Info. v.15 Optimal control of a system governed by nonlinear Volterra integral equations with delay Burnap, C.;Kazemi, M. A.