Turnpike theory : Stability of optimal trajectories
- Authors: Mammadov, Musa
- Date: 2009
- Type: Text , Book chapter
- Relation: Encyclopedia of Optimization Chapter p. 3948-3955
- Full Text: false
A turnpike theorem for continuous-time control systems when the optimal stationary point is not unique
- Authors: Mammadov, Musa
- Date: 2003
- Type: Text , Journal article
- Relation: Abstract and Applied Analysis Vol. 2003, no. 11 (2003), p. 631-650
- Full Text: false
- Reviewed:
- Description: We study the turnpike property for the nonconvex optimal control problems described by the differential inclusion x˙∈a(x). We study the infinite horizon problem of maximizing the functional ∫0Tu(x(t))dt as T grows to infinity. The turnpike theorem is proved for the case when a turnpike set consists of several optimal stationary points.
- Description: C1
- Description: 2003000343
Asymptotical stability of optimal paths in nonconvex problems
- Authors: Mammadov, Musa
- Date: 2009
- Type: Text , Book chapter
- Relation: Optimization Chapter 5 p. 95-134
- Full Text: false
- Reviewed:
- Description: In this chapter we study the turnpike property for the nonconvex optimal control problems described by the differential inclusion . We study the infinite horizon problem of maximizing the functional as T grows to infinity. The purpose of this chapter is to avoid the convexity conditions usually assumed in turnpike theory. A turnpike theorem is proved in which the main conditions are imposed on the mapping a and the function u. It is shown that these conditions may hold for mappings a with nonconvex images and for nonconcave functions u.
- Description: 2003007899
Turnpike theorem for an infinite horizon optimal control problem with time delay
- Authors: Mammadov, Musa
- Date: 2014
- Type: Text , Journal article
- Relation: SIAM Journal on Control and Optimization Vol. 52, no. 1 (2014), p. 420-438
- Full Text:
- Reviewed:
- Description: An optimal control problem for systems described by a special class of nonlinear differential equations with time delay is considered. The cost functional adopted could be considered as an analogue of the terminal functional defined over an infinite time horizon. The existence of optimal solutions as well as the asymptotic stability of optimal trajectories (that is, the turnpike property) are established under some quite mild restrictions on the nonlinearities of the functions involved in the description of the problem. Such mild restrictions on the nonlinearities allowed us to apply these results to a blood cell production model. © 2014 Society for Industrial and Applied Mathematics.