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Abstract
A solution to the control of switching linear systems with input constraints was given in Benmerzouga (1997) for both the conventional enumeration approach and the new approach. The solution given there turned out to be not unique. The main objective in this work is to determine the optimal control sequences {Ui(k) , i = 1,..., M ; k = 0, 1, ..., N -1} which transfer the system from a given initial state X0 to a specific target state XT (or to be as close as possible) by using the same discrete time solution obtained in Benmerzouga (1997) and minimizing a running cost-to-go function. By using the dynamic programming technique, the optimal solution is found for both approaches given in Benmerzouga (1997). The computational complexity of the modified algorithm is also given.
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References
- ASLANIS, J.T. 1983. Analysis of Switched Linear Systems in the Plane, M.Sc. Thesis, Department of Systems Engineering, Case Western Reserve University, Cleveland, USA.
- BENMERZOUGA, A. 1985. The Control of Switched Linear Systems, M.Sc. Thesis, Department of Systems Engineering, Case Western Reserve University, Cleveland, USA.
- BENMERZOUGA, A. 1997. Using Switching Linear Systems to Reach a Pre-specified Target. Sultan Qaboos University Journal for Scientific Research -Science and Technology, 2: 69-76.
- BROCKETT, R.W. 1970. Finite-Dimensional Linear Systems, Wiley, New York.
- DREYFUS, S.E. and LAW, A.M. 1977. The Art and Theory of Dynamic Programming, Academic Press, New York.
- GERALA, C.F. and WHEATLEY, P.O., 1994. Applied Numerical Analysis. Addison-Wesley, New York.
- GOKA, T., TARN, T.J. and ZABORSZKY, J. 1973. On the Controllability of a Class of Discrete Bilinear Systems, Automatica, Vol. 9, pp. 615-622. Pergamon Press.
- KAILATH, T. 1980. Linear Systems, Prentice Hall, New Jersey.
- SANDELL, N.R. and ATHANS, M. 1974. Modern Control Theory, Massachusetts Institute of Technology.
- TARN, T.J., ELLIOTT, D.L. and GOKA, T. 1973. Controllability of Discrete Bilinear Systems with Bounded Control, IEEE Transaction on Automatic Control, AC-18: 298-301.
- WISMER, D.A. and CHATTERGY, R. 1978. Introduction to Nonlinear Optimization, Elsevier Science Publishing Co. Inc.
References
ASLANIS, J.T. 1983. Analysis of Switched Linear Systems in the Plane, M.Sc. Thesis, Department of Systems Engineering, Case Western Reserve University, Cleveland, USA.
BENMERZOUGA, A. 1985. The Control of Switched Linear Systems, M.Sc. Thesis, Department of Systems Engineering, Case Western Reserve University, Cleveland, USA.
BENMERZOUGA, A. 1997. Using Switching Linear Systems to Reach a Pre-specified Target. Sultan Qaboos University Journal for Scientific Research -Science and Technology, 2: 69-76.
BROCKETT, R.W. 1970. Finite-Dimensional Linear Systems, Wiley, New York.
DREYFUS, S.E. and LAW, A.M. 1977. The Art and Theory of Dynamic Programming, Academic Press, New York.
GERALA, C.F. and WHEATLEY, P.O., 1994. Applied Numerical Analysis. Addison-Wesley, New York.
GOKA, T., TARN, T.J. and ZABORSZKY, J. 1973. On the Controllability of a Class of Discrete Bilinear Systems, Automatica, Vol. 9, pp. 615-622. Pergamon Press.
KAILATH, T. 1980. Linear Systems, Prentice Hall, New Jersey.
SANDELL, N.R. and ATHANS, M. 1974. Modern Control Theory, Massachusetts Institute of Technology.
TARN, T.J., ELLIOTT, D.L. and GOKA, T. 1973. Controllability of Discrete Bilinear Systems with Bounded Control, IEEE Transaction on Automatic Control, AC-18: 298-301.
WISMER, D.A. and CHATTERGY, R. 1978. Introduction to Nonlinear Optimization, Elsevier Science Publishing Co. Inc.