Using interval arithmetic for robust state feedback design. (English) Zbl 1031.93087
A problem of modal P-regulator synthesis for a linear multivariable dynamical system with uncertain (interval) parameters in the state space is considered. The designed regulator has to place all coefficients of the system characteristic polynomial within assigned intervals. We develop the approach proposed earlier by I. V. Dugarova and E. M. Smagina [Avtomat. Telemekh. 11, 176-181 (1990)] and prove a direct correlation between interval system controllability and the existence of a robust modal P-regulator.
MSC:
| 93B55 | Pole and zero placement problems |
| 65G40 | General methods in interval analysis |
| 93B35 | Sensitivity (robustness) |
| 93B50 | Synthesis problems |
Keywords:
interval parameters; robust modal regulator; Robust control; Stability; pole placement; regulator synthesis; interval system controllabilityReferences:
| [1] | Alefeld, G.; Herzberg, J., Introduction to Interval Computations (1983), Academic Press: Academic Press New York · Zbl 0552.65041 |
| [2] | B.S. Dobronets, V.V. Shaidurov, Two-sided Numerical Methods, Nauka (Siberian Department), Novosoborsk, 1990 (in Russian).; B.S. Dobronets, V.V. Shaidurov, Two-sided Numerical Methods, Nauka (Siberian Department), Novosoborsk, 1990 (in Russian). · Zbl 0714.65001 |
| [3] | I.V. Dugarova, A method for computing intervals including the coefficients of the characteristic polynomial, Moscow, No. 1187-B88, VINITI 11 February 1988.; I.V. Dugarova, A method for computing intervals including the coefficients of the characteristic polynomial, Moscow, No. 1187-B88, VINITI 11 February 1988. |
| [4] | I.V. Dugarova, Application of interval analysis for the design of the control systems with uncertain parameters, Ph.D. Thesis, Tomsk State University, Russia, 1989.; I.V. Dugarova, Application of interval analysis for the design of the control systems with uncertain parameters, Ph.D. Thesis, Tomsk State University, Russia, 1989. |
| [5] | Dugarova, I. V.; M. Smagina, Ye., Ensuring the stability of a system with uncertain parameters, Avtomat. i Telemech., 11, 176-181 (1990) |
| [6] | Kharitonov, V. L., Asymptotic stability of an equilibrium position of a family of systems of linear differential equations, Differential Equations, 14, 1483-1485 (1979) · Zbl 0409.34043 |
| [7] | N.A. Khlebalin, An analytical method for the synthesis of regulators under conditions of uncertainly in the plant’s parameters, in: A.G. Alexandrov (Ed.), Analytical Methods for the Synthesis of Regulators, Saratov Polyt. Inst. Press, Saratov, Russia, 1981, pp. 107-123 (in Russian).; N.A. Khlebalin, An analytical method for the synthesis of regulators under conditions of uncertainly in the plant’s parameters, in: A.G. Alexandrov (Ed.), Analytical Methods for the Synthesis of Regulators, Saratov Polyt. Inst. Press, Saratov, Russia, 1981, pp. 107-123 (in Russian). |
| [8] | Malan, S.; Milanese, M.; Taragna, M., Robust analysis and design of control systems using interval arithmetic, Automatica, 33, 1363-1372 (1997) · Zbl 0890.93034 |
| [9] | S.M. Markov, Extended interval arithmetic, C.R. Acad. Bulgare Sci. 30 (1977) 1239-1242.; S.M. Markov, Extended interval arithmetic, C.R. Acad. Bulgare Sci. 30 (1977) 1239-1242. · Zbl 0407.65018 |
| [10] | Moore, R. E., Methods and Applications of Interval Analysis (1979), SIAM: SIAM Philadelphia · Zbl 0417.65022 |
| [11] | Owens, D. H., Feedback and Multivariable Systems (1978), Peter Peregrinus Ltd: Peter Peregrinus Ltd England · Zbl 0446.93001 |
| [12] | Shary, S. P., Solving the linear interval tolerance problem, Math. Comput. Simulation, 39, 53-85 (1995) |
| [13] | Smagina, Ye. M., A new approach to the modal regulator synthesis for interval plant with scalar input, Reliable Comput., 3, 401-410 (1997) · Zbl 0885.65071 |
| [14] | Ye.M. Smagina, I.V. Brewer, Problem of asymptotic tracking for system with interval parameters, Proceedings of the 13th IFAC Congress, Vol. G, San-Francisco, Pergamon, USA, 1996, pp. 423-428.; Ye.M. Smagina, I.V. Brewer, Problem of asymptotic tracking for system with interval parameters, Proceedings of the 13th IFAC Congress, Vol. G, San-Francisco, Pergamon, USA, 1996, pp. 423-428. |
| [15] | Ye.M. Smagina, I.V. Brewer, Development of the modal regulator design method for a plant with interval parameters, Proceedings of the Seventh Mediterranean Conference on Control and Automation, Haifa, Israel, 1999, pp. 2087-2092.; Ye.M. Smagina, I.V. Brewer, Development of the modal regulator design method for a plant with interval parameters, Proceedings of the Seventh Mediterranean Conference on Control and Automation, Haifa, Israel, 1999, pp. 2087-2092. |
| [16] | Ye.M. Smagina, I.V. Brewer, Robust modal P and PI regulator synthesis for plant with interval parameters in the state space. Proceedings of ACC, Chicago, Illinois, USA, 2000, pp. 1317-1321.; Ye.M. Smagina, I.V. Brewer, Robust modal P and PI regulator synthesis for plant with interval parameters in the state space. Proceedings of ACC, Chicago, Illinois, USA, 2000, pp. 1317-1321. |
| [17] | Tsujino, T.; Fujii, T.; Wei, K., On the connection between controllability and stabilizibility of linear systems with structural uncertain parameters, Automatica, 29, 1, 7-12 (1993) · Zbl 0772.93070 |
| [18] | Wei, K., Stabilization of linear time-invariant interval systems via constant state feedback control, IEEE Trans. Automat. Control, 39, 22-32 (1994) · Zbl 0796.93098 |
| [19] | Wonham, W. M., Linear Multivariable Control: A Geometric Approach (1974), Springer: Springer New York · Zbl 0314.93008 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
