Uma Abordagem Evolutiva para o Problema de Custo Médio a Longo Prazo com Saltos Não-Observados
DOI:
https://doi.org/10.5540/tema.2012.013.02.0155Abstract
Neste artigo propomos uma adaptação de um algoritmo baseado na evolução biológica para a obtenção do controle ótimo do problema do custo médio a longo prazo para sistemas lineares com saltos markovianos. Não há na literaturaum método que forneça, comprovadamente, o controle ótimo do problema, nem estudos comparativos de diferentes métodos. O algoritmo empregado diferencia-se dos algoritmos genéticos básicos por substituir os operadores evolutivos por um sorteio de acordo com uma distribuição probabilística. Comparamos o algoritmo proposto com um método bastante utilizado para esta classe de problema, levando em consideração a relação entre os custos obtidos, o tempo de CPU e a quantidadede problemas em que o critério de parada estabelecido foi atingido.References
L. Blackmore, M. Ono, A. Bektassov, B.C. Williams, A probabilistic particle control approximation of chance-constrained stochastic predictive control. IEEE Transactions on Robotics, 26, No. 3 (2010), 502-517.
O.L.V. Costa e M.V. Araújo, A generalized multi-period mean-variance portfolio optimization with Markov switching parameters. Automatica, 44, No. 10 (2008), 2487-2497.
O.L.V. Costa, J.B.R. do Val, Jump LQ-optimal control for discrete-time markovian systems with stochastic inputs. Stochastic Analysis and Applications, 16, No. 5 (1998), 843-858.
O.L.V. Costa, M.D. Fragoso, R.P. Marques, “Discrete-Time Markovian Jump Linear Systems”, Springer-Verlag, New York, 2005.
E.F. Costa, A.N. Vargas, J.B.R. do Val, Quadratic costs and second moments of jump linear systems with general Markov chain, Mathematics of Control, Signals and Systems, 23, No. 1 (2011), 141-157.
J.B.R. do Val, T. Basar, Receding horizon control of jump linear systems and a macroeconomic policy problem, Journal of Economic Dynamics & Control, 23 (1999), 1099-1131.
Z. Gajic, R. Losada, Solution of the state-dependent noise optimal control problem in terms of Lyapunov iterations, Automatica, 35, No. 5 (1999) 951-954.
D.E. Goldberg, “Genetic Algorithms in Search, Optimization and Machine Learning”, 1st ed., Addison Wesley, 1989.
M.N.Magalhães, A.C.P. Lima,“Noções de Probabilidade e Estatística”, Editora da Universidade de São Paulo, 2002.
H. Muhlenbeing, The equation for response to selection and its use for prediction, Evolutionary Computation, 5, No. 3 (1997), 303-346.
M. Scheffer, J.M. Baveco, D.L. De Angelis, K.A. Rose, E.H. van Nes, Superindividuals a simple solution for modelling large populations on an individual basis, Ecological modelling, 80 No. 2-3 (1995), 161-170.
C.A. Silva, E.F. Costa, An algorithm for the long run average cost problem for linear systems with non-observed Markov jump parameters, “American Control Conference”, pp. 4434-4439, St. Louis, USA, 2009.
A.A.G. Siqueira, M.H. Terra, T.B.R. Francisco, Controle robusto de robôs móveis em formação sujeitos a falhas, Sba Controle & Automação, 21, No. 1 (2010), 29-42.
C.E. de Souza, M.D. Fragoso, H∞ filtering for discrete-time linear systems with Markovian jumping parameters, International Journal of Robust and Nonlinear Control, 13 (2003) 1299-1316.
P. Stoica, I. Yaesh, Jump Markovian-based control of wing deployment for an uncrewed aircraft, Journal of Guidance, Control, and Dynamics, 25, No. 2 (2002), 407–411.
M.G. Todorov, M.D. Fragoso, On the stability radii of continuous-time infinite Markov jump linear systems, Mathematics of control, Signals, and Systems, 22, No. 1 (2010), 23-38.
A.N. Vargas, J.B.R. do Val, E.F. Costa, Controle de horizonte retrocedente de sistemas lineares com saltos Markovianos para o problema de rastreamento com alvos dinâmicos, SBA Controle & Automação, 16, No. 4 (2006), 435-448.
A.N. Vargas, “Estabilidade e Controle com Critério de Custo Médio a Longo Prazo em Sistemas Lineares Estocásticos”, Tese de Doutorado, FEEC, Unicamp, Campinas, SP, 2009.
A.N. Vargas, J.B.R. do Val, E.F. Costa, Receding horizon control of Markov jump linear system subject to noise and unobserved state chain, “IEEE Conference on Decision and Control”, pp. 4381–4386, Atlantis, Bahamas, 2004.
Downloads
Additional Files
Published
How to Cite
Issue
Section
License
Copyright
Authors of articles published in the journal Trends in Computational and Applied Mathematics retain the copyright of their work. The journal uses Creative Commons Attribution (CC-BY) in published articles. The authors grant the TCAM journal the right to first publish the article.
Intellectual Property and Terms of Use
The content of the articles is the exclusive responsibility of the authors. The journal uses Creative Commons Attribution (CC-BY) in published articles. This license allows published articles to be reused without permission for any purpose as long as the original work is correctly cited.
The journal encourages Authors to self-archive their accepted manuscripts, publishing them on personal blogs, institutional repositories, and social media, as long as the full citation is included in the journal's website version.
