A feasible directions algorithm for optimal control problems with state and control constraints: Convergence analysis

SIAM Journal on Control and Optimization

Volumn 36, Issue 6, 1998, Pages 1999-2019

  Pytlak, R ^a   Vinter, R B ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Necessary optimality conditions; Numerical algorithms; Optimal control; State constrained problems

Indexed keywords

ALGORITHMS; CHEBYSHEV APPROXIMATION; CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; OPTIMIZATION;

FEASIBLE DIRECTIONS ALGORITHM; STATE CONSTRAINED PROBLEMS;

OPTIMAL CONTROL SYSTEMS;

EID: 0032206288     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012996297649     Document Type: Article

References (22)

1. W. ALT AND K. MALANOWSKI, The Lagrange-Newton method for state-constrained optimal control problems, Comput. Optim. Appl., 4 (1995), pp. 217-239.
2. J.P. AUBIN AND I. EKELAND, Applied Nonlinear Analysis, Wiley Interscience, New York, 1984.
3. T.E. BAKER AND E. POLAK, On the optimal control of systems described by evolution equations, SIAM J. Control Optim., 32 (1994), pp. 224-260.
4. R. BULIRSCH, F. MONTRONE, AND H.J. PESCH, Abort landing in the presence of windshear as a minimax optimal control problem, part 1: Necessary conditions, J. Optim. Theory Appl., 70 (1991), pp. 1-23.
5. R. BULIRSCH, F. MONTRONE, AND H.J. PESCH, Abort landing in the presence of windshear as a minimax optimal control problem, part 2: Multiple shooting and homotopy, J. Optim. Theory Appl., 70 (1991), pp. 223-254.
6. R.P. FEDORENKO, Priblizhyonnoye reshenyie zadach optimalnovo upravlenya, Nauka, Moscow, 1978.
7. A.S. DRUD, A GRG code for large sparse dynamic nonlinear optimization problems, Math. Programming, 31 (1985), pp. 153-191.
8. D.Q. MAYNE AND E. POLAK, An exact penalty function algorithm for optimal control problems with control and terminal equality constraints, part 1 and part 2, J. Optim. Theory Appl., 32 (1980), pp. 211-246; pp. 345-364.
9. D.Q. MAYNE AND E. POLAK, An exact penalty function algorithm for control problems with state and control constraints, IEEE Trans. Automat. Control, AC-32 (1987), pp. 380-387.
10. K.C.P. MACHIELSEN, Numerical Solution of Optimal Control Problems with State Constraints by Sequential Quadratic Programming in Function Space, CWI Tract 53, Centrum Wisk. Inform., Amsterdam, 1988.
11. E. POLAK, T.H. YANG, AND D.Q. MAYNE, A method of centers based on barrier functions for solving optimal control problems with continuum state and control constraints, SIAM J. Control Optim., 31 (1993), pp. 159-179.
12. E. POLAK AND L. HE, Unified steerable phasel-phaseII method of feasible directions for semi-infinite optimization, J. Optim. Theory Appl., 69 (1991), pp. 83-107.
13. R. PYTLAK, Runge-Kutta based procedure for optimal control of differential-algebraic equations, J. Optim. Theory Appl., 97 (1998), pp. 675-705.
14. R. PYTLAK AND R.B. VINTER, PH2SOL Solver: An O(N) Implementation of an Optimization Algorithm for a General Optimal Control Problem, Research Report C93-36, Centre for Process Systems Engineering, Imperial College, 1993.
15. R. PYTLAK AND R.B. VINTER, A Feasible Directions Type Algorithm for Optimal Control Problems with State and Control Constraints: Convergence Analysis, Research Report C96-24, Centre for Process Systems Engineering, Imperial College, 1996.
16. R. PYTLAK AND R.B. VINTER, A Feasible Directions Algorithm for Optimal Control Problems with State and Control Constraints: Implementation, J. Optim. Theory Appl., submitted.
17. G.I. STASSINOPOULOS AND R.B. VINTER, Conditions for convergence in the computation of optimal controls, J. Inst. Math. Appl., 22 (1978), pp. 1-14.
18. P. TANARTKIT AND L.T. BIEGLER, Stable decomposition for dynamic optimization, Indust. Engrg. Chem. Res., 34 (1995), pp. 1253-1266.
19. J. WARGA, Optimal Control of Differential and Functional Equations, Academic Press, New York, 1972.
20. J. WARGA, Iterative procedure for constrained and unilateral optimization problems, SIAM J. Control Optim., 20 (1982), pp. 360-376.
21. L.J. WILLIAMSON AND E. POLAK, Relaxed controls and the convergence of optimal control algorithms, SIAM J. Control Optim., 14 (1976), pp. 737-757.
22. S.J. WRIGHT, Structured interior point methods for optimal control, in Proc. 30th CDC, Brighton, UK, 1991, pp. 1711-1716.