Abstract
The infinite horizon optimal control problem is solved for 2D systems described by the Fornasini-Marchesini model. An ℓ2-approach permits us to reduce the optimal control problem to a norm minimization one in Hilbert spaces. Both necessary and sufficient conditions for solvability and the structure of the solution are established. Moreover, a comparison with known results is presented, and the singularities of the 2D Riccati equation are examined in order to characterize suboptimal control laws that apply whenever the solvability conditions are not satisfied.
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References
M. Bisiacco, “State and output feedback stabilizability of 2-D systems,”IEEE Trans. on Circuits and Systems vol. CAS-32, pp. 1246–1254, 1985.
P. Rocha and J. C. Willems, “Controllability of 2-D systems,”IEEE Trans. on Automatic Control Vol. 36, pp. 413–423, 1991.
E. Fornasini and G. Marchesini, “Non interacting control of 2-D systems,”IEEE Trans. on Automatic Control vol. 36, pp. 90–95, 1991.
C. Li and M. S. Fadali, “Optimal control of 2-D systems,”IEEE Trans. on Automatic Control vol. 36, pp. 223–228, 1991.
M. Bisiacco and E. Fornasini, “Optimal control of two-dimensional systems,”SIAM Journal on Control and Optimization vol. 28, pp. 582–601, 1990.
M. Bisiacco, “Optimal control of linear systems: an l2-approach,” submitted for publication.
E. Fornasini and G. Marchesini, “Stability analysis of 2D systems,”IEEE Trans. on Circuits and Systems vol. CAS-27, pp. 1210–1217, 1980.
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Bisiacco, M. New results in 2D optimal control theory. Multidim Syst Sign Process 6, 189–222 (1995). https://doi.org/10.1007/BF00981083
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DOI: https://doi.org/10.1007/BF00981083