Article Outline
Introduction
Formulation
Methods
Taylor Models
Verifying Solver for Parametric ODEs
Deterministic Global Optimization Method
Cases
Catalytic Cracking of Gas Oil
Singular Control Problem
Conclusions
References
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Adjiman CS, Androulakis IP, Floudas CA, Neumaier A (1998) A global optimization method, αBB, for general twice-differentiable NLPs–I. Theoretical advances. Comput Chem Eng 22:1137–1158
Adjiman CS, Dallwig S, Floudas CA, Neumaier A (1998) A global optimization method, αBB, for general twice-differentiable NLPs–II. Implementation and computational results. Comput Chem Eng 22:1159–1179
Brusch R, Schappelle R (1973) Solution of highly constrained optimal control problems using nonlinear programming. AIAA J 11:135–136
Chachuat B, Latifi MA (2004) A new approach in deteterministic global optimisation of problems with ordinary differential equations. In: Floudas CA, Pardalos PM (eds) Frontiers in Global Optimization. Kluwer, Dordrecht
Corliss GF, Rihm R (1996) Validating an a priori enclosure using high-order Taylor series. In: Alefeld G, Frommer A (eds) Scientific Computing : Computer Arithmetic, and Validated Numerics. Akademie Verlag, Berlin
Esposito WR, Floudas CA (2000) Deterministic global optimization in nonlinear optimal control problems. J Global Optim 17:97–126
Esposito WR, Floudas CA (2000) Global optimization for the parameter estimation of differential-algebraic systems. Ind Eng Chem Res 39:1291–1310
Lin Y, Stadtherr MA (2006) Determinstic global optimization for parameter estimation of dynamic systems. Ind Eng Chem Res 45:8438–8448
Lin Y, Stadtherr MA (2007) Deterministic global optimization of nonlinear dynamic systems. AIChE J 53:866–875
Lin Y, Stadtherr MA (2007) Validated solutions of initial value problems for parametric ODEs. Appl Num Math 58:1145–1162
Luus R (1990) Optimal control by dynamic programming using systematic reduction in grid size. Int J Control 51:995–1013
Luus R, Cormack DE (1972) Multiplicity of solutions resulting from the use of variational methods in optimal control problems. Can J Chem Eng 50:309–311
Makino K, Berz M (1999) Efficient control of the dependency problem based on Taylor model methods. Reliab Comput 5:3–12
Makino K, Berz M (2003) Taylor models and other validated functional inclusion methods. Int J Pure Appl Math 4:379–456
Makino K, Berz M (2005) Verified global optimization with Taylor model-based range bounders. Trans Comput 11:1611–1618
Moore RE (1966) Interval Analysis. Prentice-Hall, Englewood Cliffs
Nedialkov NS, Jackson KR, Corliss GF (1999) Validated solutions of initial value problems for ordinary differential equations. Appl Math Comput 105:21–68
Nedialkov NS, Jackson KR, Pryce JD (2001) An effective high-order interval method for validating existence and uniqueness of the solution of an IVP for an ODE. Reliab Comput 7:449–465
Neumaier A (2003) Taylor forms – Use and limits. Reliab Comput 9:43–79
Neuman C, Sen A (1973) A suboptimal control algorithm for constraint problems using cubic splines. Automatica 9:601–613
Papamichail I, Adjiman CS (2002) A rigorous global optimization algorithm for problems with ordinary differential equations. J Global Optim 24:1–33
Papamichail I, Adjiman CS (2004) Global optimization of dynamic systems. Comput Chem Eng 28:403–415
Singer AB (2006) Personal communication
Singer AB, Barton PI (2006) Bounding the solutions of parameter dependent nonlinear ordinary differential equations. SIAM J Sci Comput 27:2167–2182
Singer AB, Barton PI (2006) Global optimization with nonlinear ordinary differential equations. J Global Optim 34:159–190
Teo K, Goh G, Wong K (1991) A unified computational approach to optimal control problems. Pitman Monographs and Surveys in Pure and Applied Mathematics, vol 55. Wiley, New York
Tjoa TB, Biegler LT (1991) Simultaneous solution and optimization strategies for parameter estimation of differential-algebraic equation systems. Ind Eng Chem Res 30:376
Tsang TH, Himmerlblau DM, Edgar TF (1975) Optimal control via collocation and nonlinear programming. Int J Control 21:763–768
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag
About this entry
Cite this entry
Lin, Y., Stadtherr, M.A. (2008). Interval Analysis for Optimization of Dynamical Systems . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_298
Download citation
DOI: https://doi.org/10.1007/978-0-387-74759-0_298
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-74758-3
Online ISBN: 978-0-387-74759-0
eBook Packages: Mathematics and StatisticsReference Module Computer Science and Engineering