Optimal control of delay systems with differential and algebraic dynamic constraints

ESAIM - Control, Optimisation and Calculus of Variations

Volumn 11, Issue 2, 2005, Pages 285-309

  Mordukhovich, Boris S ^a   Wang, Lianwen ^b  

^a WAYNE STATE UNIVERSITY   (United States)

^b UNIVERSITY OF CENTRAL MISSOURI   (United States)

Author keywords

Benjamin Ono equation; Dispersive equation; Exact controllability; Stabilization

Indexed keywords

APPROXIMATION THEORY; CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; FINITE DIFFERENCE METHOD; HAMILTONIANS; LINEAR ALGEBRA; LINEAR EQUATIONS; OPTIMAL CONTROL SYSTEMS; OPTIMIZATION;

DIFFERENTIAL AND ALGEBRAIC DYNAMIC CONSTRAINTS; DISCRETE APPROXIMATIONS; FUNCTIONAL-DIFFERENTIAL INCLUSIONS OF NEUTRAL TYPE; GENERALIZED DIFFERENTIATION; NECESSARY OPTIMALITY CONDITIONS; OPTIMAL CONTROL; VARIATIONAL ANALYSIS;

DELAY CONTROL SYSTEMS;

EID: 30844451024     PISSN: 12928119     EISSN: 12623377     Source Type: Journal    
DOI: 10.1051/cocv:2005008     Document Type: Article

References (20)

1. K.E. Brennan, S.L. Campbell and L.R. Pretzold, Numerical Solution of Initial Value Problems in Differential-Algebraic Equations. North-Holland, New York (1989).
2. E.N. Devdariani and Yu.S. Ledyaev, Maximum principle for implicit control systems. Appl. Math. Optim. 40 (1999) 79-103.
3. A.L. Dontchev and E.M. Farhi, Error estimates for discretized differential inclusions. Computing 41 (1989) 349-358.
4. M. Kisielewicz, Differential Inclusions and Optimal Control. Kluwer, Dordrecht (1991).
5. B.S. Mordukhovich, Maximum principle in problems of time optimal control with nonsmooth constraints. J. Appl. Math. Mech. 40 (1976) 960-969.
6. B.S. Mordukhovich, Approximation Methods in Problems of Optimization and Control. Nauka, Moscow (1988).
7. B.S. Mordukhovich, Complete characterization of openness, metric regularity, and Lipschitzian properties of multifunctions. Trans. Amer. Math. Soc. 340 (1993) 1-35.
8. B.S. Mordukhovich, Discrete approximations and refined Euler-Lagrange conditions for nonconvex differential inclusions. SIAM J. Control Optim. 33 (1995) 882-915.
9. B.S. Mordukhovich, J.S. Treiman and Q.J. Zhu, An extended extremal principle with applications to multiobjective optimization. SIAM J. Optim. 14 (2003) 359-379.
10. B.S. Mordukhovich and R. Trubnik, Stability of discrete approximation and necessary optimality conditions for delay-differential inclusions. Ann. Oper. Res. 101 (2001) 149-170.
11. B.S. Mordukhovich and L. Wang, Optimal control of constrained delay-differential inclusions with multivalued initial condition. Control Cybernet. 32 (2003) 585-609.
12. B.S. Mordukhovich and L. Wang, Optimal control of neutral functional-differential inclusions. SIAM J. Control Optim. 43(2004) 116-136.
13. B.S. Mordukhovich and L. Wang, Optimal control of differential-algebraic inclusions, in Optimal Control, Stabilization, and Nonsmooth Analysis, M. de Queiroz et al., Eds., Lectures Notes in Control and Information Sciences, Springer-Verlag, Heidelberg 301 (2004) 73-83.
14. M.D.R. de Pinho and R.B. Vinter, Necessary conditions for optimal control problems involving nonlinear differential algebraic equations. J. Math. Anal. Appl. 212 (1997) 493-516.
15. C. Pantelides, D. Gritsis, K.P. Morison and R.W.H. Sargent, The mathematical modelling of transient systems using differential-algebraic equations. Comput. Chem. Engrg. 12 (1988) 449-454.
16. R.T. Rockafellar, Equivalent subgradient versions of Hamiltonian and Euler-Lagrange conditions in variational analysis. SIAM J. Control Optim. 34 (1996) 1300-1314.
17. R.T. Rockafellar and R.J.-B. Wets, Variational Analysis. Springer-Verlag, Berlin (1998).
18. G.V. Smirnov, Introduction to the Theory of Differential Inclusions. American Mathematical Society, Providence, RI (2002).
19. R.B. Vinter, Optimal Control. Birkhauser, Boston (2000).
20. J. Warga, Optimal Control of Differential and Functional Equations. Academic Press, New York (1972).