Optimal output tracking control for bilinear systems

Abstract

We consider the optimal output tracking control (OOTC) problem for a class of bilinear systems with a quadratic performance index. Using a successive approximation approach (SAA), the original non-linear optimal problem is transformed into a sequence of linear non-homogeneous two-point boundary value (TPBV) problems. An adjoint vector sequence can be obtained from the iterative solution of the sequence of TPBV problems. The OOTC law obtained consists of accurate linear feedback and feedforward terms and a non-linear compensation term which is the limit of the adjoint vector sequence. A reference input observer is constructed to make the approximate OOTC law physically realizable. A numerical simulation is provided to illustrate the effectiveness of the proposed method.

Keywords

bilinear systems optimal control successive approximation approach tracking control

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References

Aganovic, Z. and Gajic, Z. 1994: Successive approximation procedure for finite-time optimal control of bilinear systems . IEEE Transactions on Automatic Control 39, 1932-1935 .

Aganovic, Z. and Gajic, Z. 1995: Successive approximation procedure for steady state optimal control of bilinear systems . Journal of Optimization Theory and Applications 84, 273-291 .

Banks, S.P. and McCaffrey, D. 1998: Lie algebras, structure of non-linear systems and chaotic motion . International Journal of Bifurcation and Chaos 8, 1437-1462 .

Cebuhar, W.A. and Costanza, V. 1984: Approximate procedures for the optimal control of bilinear and non-linear systems . Journal of Optimization Theory and Applications 43, 615-627 .

Cimen, T. and Banks, S.P. 2004a: Global optimal feedback control for general nonlinear systems with nonquadratic performance criteria . Systems and Control Letters 53, 327-346 .

Cimen, T. and Banks, S.P. 2004b: Non-linear optimal tracking control with application to super-tankers for autopilot design . Automatica 40, 1845-1863 .

Hemami, A. , Mehrabi, M. G. and Cheng, R.M.H. 1992: Synthesis of an optimal control law for path tracking in mobile robots . Automatica 28, 383-387 .

Hofer, E. and Tibken, B. 1988: An iterative method for the finite-time bilinear quadratic control problem . Journal of Optimization Theory and Applications 57, 411-427 .

Lancaster, P. , Lerer, L. and Tismenetsky, M. 1984: Factored forms for solutions of AX / XB / C and X / AXB / C in companion matrices . Linear Algebra and Its Applications 62, 19-49 .

10.

McLain, T.W. , Bailey, C.A. and Beard, R.W. 1999: Synthesis and experimental testing of a non-linear optimal tracking controller , Proceedings of the American Control Conference, San Diego, 2847-2851 .

11.

Mohler, R.R. 1991: Non-linear systems. Volume 2, Applications to bilinear control. Prentice Hall.

12.

Nagy, E. 2002: Non-linear control through optimized trajectory tracking , Proceedings of the American Control Conference, Anchorage, 3980-3985 .

13.

Samaras, N.S. and Simaan, M.A. 2004: Optimized trajectory tracking control with disturbance attenuation of dynamic multistage metal-cooling processes . IEEE Transactions on Industry Applications 40, 926-931 .

14.

Soueres, P. , Balluchi, A. and Bicchi, A. 2001: Optimal feedback control for route tracking with a bounded-curvature vehicle . International Journal of Control 74, 1009-1019 .

15.

Tang, G.-Y. 2005: Suboptimal control for nonlinear systems: a successive approximation approach . Systems and Control Letters 54, 429-434 .

16.

Tang, G.-Y. and Wang, H.-H. 2005: Successive approximation approach of optimal control for non-linear discrete-time systems . International Journal of Systems Science 36, 153-161 .

17.

Tang, G.-Y. , Ma, H. and Zhang, B.-L. 2005: Successive approximation approach of optimal control for bilinear discrete-time systems . IEE Proceedings of Control Theory and Applications 152, 639-644 .