A Category of Control Systems

[1] A.A. Agrachev and Y.L. Sachkov, Control Theory from the Geometric Viewpoint, Springer-Verlag, Berlin, 2004. 10.1007/978-3-662-06404-7Search in Google Scholar

[2] R.W. Brockett, System theory on group manifolds and coset spaces, SIAM J. Control 10(2)(1972), 265-284. 10.1137/0310021Search in Google Scholar

[3] V.I. Elkin, Affine control systems: their equivalence, classification, quotient systems and subsystems, J. Math. Sci. 88(5)(1998), 675-721. 10.1007/BF02364666Search in Google Scholar

[4] V.V. Gorbatsevich, A.L. Onishchik and E.B. Vinberg, Foundations of Lie Theory and Lie Transformation Groups, Springer-Verlag, Berlin, 1997. Search in Google Scholar

[5] E. Haghverdi, P. Tabuada and G. Pappas, Bisimulation relations for dynamical and control systems, Electron. Notes Theor. Comp. Sci. 69(2003), 120-136. 10.1016/S1571-0661(04)80562-0Search in Google Scholar

[6] V. Jurdjevic, Geometric Control Theory, Cambridge University Press, Cambridge, 1997. 10.1017/CBO9780511530036Search in Google Scholar

[7] V. Jurdjevic and H.J. Sussmann, Control systems on Lie groups, J. Diff. Equations 12(1972), 313-329. 10.1016/0022-0396(72)90035-6Search in Google Scholar

[8] A.W. Knapp, Lie Groups Beyond an Introduction (Second Edition), Birkh¨auser, Boston, 2004. Search in Google Scholar

[9] A.D. Lewis, The Category of Affine Connection Control Systems, in Proc. 39th IEEE Conf. Decision & Control, Sydney, Australia, 2000, pp. 1260- 1265. Search in Google Scholar

[10] S. Mac Lane, Categories for the Working Mathematician (Second Edition), Springer-Verlag, New York, 1997. Search in Google Scholar

[11] G.J. Pappas, G. Lafferriere and S. Sastry, Hierarchically consistent control systems, IEEE Trans. Automat. Control 45(6)(2000), 1144-1160. 10.1109/9.863598Search in Google Scholar

[12] C.C. Remsing, Optimal control and Hamilton-Poisson formalism, Int. J. Pure Appl. Math. 59(1)(2010), 11-17. Search in Google Scholar

[13] Y.L. Sachkov, Control theory on Lie groups, J. Math. Sci. 156(3)(2009), 381-439. 10.1007/s10958-008-9275-0Search in Google Scholar

[14] H.J. Sussmann, Lie brackets, real analyticity and geometric control, in Differential Geometric Control Theory (R.W. Brockett, R.S. Millman, H.J. Sussmann, eds.), Birkh¨auser, 1983, pp. 1-116. Search in Google Scholar

[15] P. Tabuada, On the Factorization of Trajectory Lifting Maps, in Proc. 44th IEEE Conf. Decision & Control, Seville, Spain, 2005, pp. 4225-4230. Search in Google Scholar

[16] P. Tabuada and G.J. Pappas, Bisimilar control affine systems, Syst. Con- trol Lett. 52(1)(2004), 49-58. 10.1016/j.sysconle.2003.09.013Search in Google Scholar

[17] P. Tabuada and G.J. Pappas, Quotients of fully nonlinear control systems, SIAM J. Control Optim. 43(5)(2005), 1844-1866. 10.1137/S0363012901399027Search in Google Scholar