Selecting appropriate weighting matrices for desired Linear Quadratic Regulator (LQR) controller design using evolutionary algorithms is presented in this paper. Obviously, it is not easy to determine the appropriate weighting matrices for an optimal control system and a suitable systematic method is not presented for this goal. In other words, there isn’t direct relationship between weighting matrices and control system characteristics and selecting these matrices is done using by trial and error based on designer’s experience. In this paper we use the Particle Swarm Optimization (PSO) method which is inspired by the social behavior of fish and birds in finding food sources to determine these matrices. Stable convergence characteristics and high calculation speed are advantages of the proposed method. Simulation results demonstrate that in comparison with Genetic Algorithms (GAs), the PSO method is very efficient and robust in designing of optimal LQR controller.
Introduction
In designing of many systems and solving the problems, we need to choose an answer between some possible answers as an optimal response. But because of the wide range of answers, all of them cannot be tested and then this test should be performed stochastically. On the other hand, this stochastic procedure should lead to the best answer [1].
Because of its simple implementation in engineering problems, it has been paid special attention on linear quadratic optimal control theory. Linear quadratic optimal control is significant for modern control theory and it can be implemented easily for engineering applications and it is the basic theory of other control techniques. However, in a special case which the cost function is a linear quadratic function, the o...
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...o. 5, pp: 1322- 1325, 2011.
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[13] X. Xiong and Z. Wan , "The simulation of double inverted pendulum control based on particle swarm optimization LQR algorithm," IEEE International Conference on Software Engineering and Service Sciences (ICSESS), pp. 253- 256, 2010.
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Today, engineers rely on damping systems to counteract nature's forces. There are many types of damping systems that engineers can now use for structures, automobiles, and even tennis rackets! This site focuses on damping systems in structures, mainly architectural variations of the tuned mass damper.
One of the researchers was Shu that he presented the differential quadrature method (DQ) for the first time [71]. To solve the computational mechanic problems, Bert and Malik [72] applied the DQM and they reported that the DQM was the most efficient method and they reported that the DQM solved the differential equations with fewer grid points and high accuracy. To this end, to date, the researchers have used the DQM to solve many mechanical engineering problems [73-80]. It is caused to gain accurate results in the lowest time. As noted, supplying the results which have the lowest grid point and deriving in the fast way are two important advantages of DQ method. In the recent years, to obtain the mechanical properties of the nanostructures the DQM is used and this is caused to produce the mechanical property of these structures accurately. The stability behavior of the rectangular nanoplate is investigated by Mohammadi et al. [77]. In that research, the DQM is used to obtain the shear in-plane buckling loads of the rectangular nanoplate. The stability analysis of the rectangular nanoplate subjected to linear load is investigated by Farajpour et al.
A complex adaptive system is entity of networks and connections. It can “learn and adapt to change over time” which can change the “structure of the system” (Clancy, Effken, Pesut, 2008). It contains twelve elements: autopoesis or self-regenerization, open exchange, participation in networks, fractals, phase transition between order and chaos, search for fitness peaks, nonlinear dynamics, sensitive dependence, attractors that limit growth, strange attractors of emergence...
Genetic Algorithms provide a holistic search process based on principles of natural genetics and survivals of the fittest……
Below I will analyse the most important components of an evolutionary computation algorithm and explain how it works.
Many methods have been developed to simplify the decision making process. In this paper, the rational model of decision making will be discussed first. Then, some of the factors that cause deviation in the rational model will be clarified.
... in Wireless Sensor Networks: Current proposal and Future Development, IEEE Xplore, Hong Kong, Oct- 2007.
Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be apportioned to different sources of uncertainty in its inputs. A related practice is uncertainty analysis, which has a greater focus on uncertainty quantification and its propagation. Ideally, uncertainty and sensitivity analysis should be run in tandem. As the optimization method provides the best set of inputs for optimum output, the input parameters are different at all the times and a superlative situation may not be rewarded. Some of the input factors may have sparing effect on the output on the contrary others have dominating effect. Though this situation is not prevalent in ideal situation, it is strongly recommended to check the most dominating input parameter which will have impact on output. This will strengthen the understanding of the manufacturing firm regarding where control is required. To cater this need sensitivity analysis is carried out using MS frontline solver 12.5 for regression and dimensional analysis.
Fogel, D. (2009) Artificial intelligence through simulated evolution. Wiley-IEEE Press. Available at: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5311738 (Accessed: February 09, 2014).
...ithms can be integrated with neural networks to solve the complex problems in machine learning, such systems are called hybrid intelligent systems. Neural networks are very powerful tools for Intelligence Systems. Although there are some limitations in terms of the complexity of the neural circuit and the lack of representation in very complex systems, there is an ongoing research to improve performance and capabilities of neural networks.
Barbara Mowat and Paul Warstine. New York: Washington Press, 1992. Slethaug, Gordon. A. See "Lecture Notes" for ENGL1007.
Linear programming helps the Mini factory in optimum operation of numerous standing factors in production, w...
2) Fundamentals of Physics Extended: Fifth Edition. David Hanley, Robert Resnick, Jearl Walker. Published by John Wiley & Sons, Inc, New York, Chichester, Brisbane, Toronto, Singapore. 1997.
Genetic Algorithm is a sequential procedure developed from the science involved in genetic behaviour organisms for optimization purpose. Working Principle of GA includes the simulation of evolution theory in which, the initial set of “population” is selected in random, and then successive "generations" of solutions are reproduced till the optimal convergence. Existence of the fittest individual and natural selection operators is the main agenda of GA process. Philosophically one can say that GAs are based on Darwin’ theory of survival of the fittest. Genetic algorithm is a method for solving optimization problems that is based on natural selection, the process that drives biological evolution. Being analogous to genetics, it is a long complex thread of DNAs and RNAs containing the hereditary data, by which a traits of each individual can be determined, as chromosomes. Each trait in living organisms is being coded with some combination of DNAs like A (Adenine), C (Cytosine), T (Thymine) and G (Guanine).
The field of neural networks involves a new approach to computing that uses mathematical structures with the ability to learn (Zsolutions). These methods were inspired by investigations into modeling nervous system learning (Zsolutions). For example, neurons in the human brain are used to transmit data back and forth to each other. Artificial neural networks use this same technique to process various kinds of information (Fu, p 4).