Global optimal trajectory in Chaos and NP-Hardness
- Authors: Latorre, Vittorio , Gao, David
- Date: 2016
- Type: Text , Journal article
- Relation: International Journal of Bifurcation and Chaos Vol. 26, no. 8 (2016), p. 1-14
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- Description: This paper presents an unconventional theory and method for solving general nonlinear dynamical systems. Instead of the direct iterative methods, the discretized nonlinear system is first formulated as a global optimization problem via the least squares method. A newly developed canonical duality theory shows that this nonconvex minimization problem can be solved deterministically in polynomial time if a global optimality condition is satisfied. The so-called pseudo-chaos produced by linear iterative methods are mainly due to the intrinsic numerical error accumulations. Otherwise, the global optimization problem could be NP-hard and the nonlinear system can be really chaotic. A conjecture is proposed, which reveals the connection between chaos in nonlinear dynamics and NP-hardness in computer science. The methodology and the conjecture are verified by applications to the well-known logistic equation, a forced memristive circuit and the Lorenz system. Computational results show that the canonical duality theory can be used to identify chaotic systems and to obtain realistic global optimal solutions in nonlinear dynamical systems. The method and results presented in this paper should bring some new insights into nonlinear dynamical systems and NP-hardness in computational complexity theory. © 2016 World Scientific Publishing Company.
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
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- 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.
Extraction and processing of real time strain of embedded FBG sensors using a fixed filter FBG circuit and an artificial neural network
- Authors: Kahandawa, Gayan , Epaarachchi, Jayantha , Wang, Hao , Canning, John , Lau, Alan
- Date: 2013
- Type: Text , Journal article
- Relation: Measurement: Journal of the International Measurement Confederation Vol. 46, no. 10 (2013), p. 4045-4051
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- Description: Fibre Bragg Grating (FBG) sensors have been used in the development of structural health monitoring (SHM) and damage detection systems for advanced composite structures over several decades. Unfortunately, to date only a handful of appropriate configurations and algorithm sare available for using in SHM systems have been developed. This paper reveals a novel configuration of FBG sensors to acquire strain reading and an integrated statistical approach to analyse data in real time. The proposed configuration has proven its capability to overcome practical constraints and the engineering challenges associated with FBG-based SHM systems. A fixed filter decoding system and an integrated artificial neural network algorithm for extracting strain from embedded FBG sensor were proposed and experimentally proved. Furthermore, the laboratory level experimental data was used to verify the accuracy of the system and it was found that the error levels were less than 0.3% in predictions. The developed SMH system using this technology has been submitted to US patent office and will be available for use of aerospace applications in due course. © 2013 Elsevier Ltd. All rights reserved.