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On the Iterative Solution to H Control Problems

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DOI: 10.4236/am.2015.68119    2,872 Downloads   3,260 Views   Citations

ABSTRACT

This paper addresses the problem for solving a Continuous-time Riccati equation with an indefinite sign of the quadratic term. Such an equation is closely related to the so called full information H control of linear time-invariant system with external disturbance. Recently, a simultaneous policy update algorithm (SPUA) for solving H control problems is proposed by Wu and Luo (Simultaneous policy update algorithms for learning the solution of linear continuous-time H state feedback control, Information Sciences, 222, 472-485, 2013). However, the crucial point of their method is to find an initial point, which ensuring the convergence of the method. We will show one example where Wu and Luo’s method is not effective and it converges to an indefinite solution. Three effective methods for computing the stabilizing solution to the considered equation are investigated. Computer realizations of the presented methods are numerically compared on the computational platforms MATLAB and SCILAB.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Ivanov, I. , Ivanov, I. and Netov, N. (2015) On the Iterative Solution to H Control Problems. Applied Mathematics, 6, 1263-1270. doi: 10.4236/am.2015.68119.

References

[1] Lanzon, A., Feng, Y., Anderson, B. and Rotkowitz, M. (2008) Computing the Positive Stabilizing Solution to Algebraic Riccati Equations with an Indefinite Quadratic Term via a Recursive Method. IEEE Transactions on Automatic Control, 53, 2280-2291.
http://dx.doi.org/10.1109/TAC.2008.2006108
[2] Praveen, P. and Bhasin, S. (2013) Online Partially Model-Free Solution of Two-Player Zero Sum Differential Games, Preprints of the 10th IFAC International Symposium on Dynamics and Control of Process Systems. The International Federation of Automatic Control.
[3] Vrabie, D. and Lewis, F. (2011) Adaptive Dynamic Programming for Online Solution of a Zero-Sum Differential Game. Journal of Control Theory and Applications, 9, 353-360.
http://dx.doi.org/10.1007/s11768-011-0166-4
[4] Dragan, V., Freiling, G., Morozan, T. and Stoica, A.-M. (2008) Iterative Algorithms for Stabilizing Solutions of Game Theoretic Riccati Equations of Stochastic Control. Proceedings of the 18th International Symposium on Mathematical Theory of Networks & Systems.
http://scholar.lib.vt.edu/MTNS/Papers/078.pdf
[5] Dragan, V. and Ivanov, I. (2011) Computation of the Stabilizing Solution of Game Theoretic Riccati Equation Arising in Stochastic H∞ Control Problems. Numerical Algorithms, 57, 357-375.
http://dx.doi.org/10.1007/s11075-010-9432-7
[6] Feng, Y.T. and Anderson, B.D.O. (2010) An Iterative Algorithm to Solve State-Perturbed Stochastic Algebraic Riccati Equations in LQ Zero-Sum Games. Systems & Control Letters, 59, 50-56.
http://dx.doi.org/10.1016/j.sysconle.2009.11.006
[7] Zhu, H.-N., Zhang, C.-K. and Bin, N. (2012) Infinite Horizon LQ Zero-Sum Stochastic Differential Games with Markovian Jumps. Applied Mathematics, 3, 1321-1326.
http://dx.doi.org/10.4236/am.2012.330188
[8] Wu, H.-N. and Luo, B. (2013) Simultaneous Policy Update Algorithms for Learning the Solution of Linear Continuous-Time H∞ State Feedback Control. Information Sciences, 222, 472-485.
http://dx.doi.org/10.1016/j.ins.2012.08.012
[9] Basar, T. and Bernhard, P. (1995) H∞ Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach. Systems & Control: Foundations and Applications Series, Birkhauser, Boston, 1995.
[10] Lancaster, P. and Rodman, L. (1995) Algebraic Riccati Equations. Clarendon Press, Oxford.

  
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