Dorato, P., W. Wang and C. T. Abdallah (1996). "Application of Quantifier Elimination Theory to Robust Multi-objective Feedback Design," Journal of Symbolic Computation, vol. 11, pp. 1--5.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....apply quantifier elimination techniques to problems in control theory was made by Anderson et al. 1975) However, the algorithmic techniques at that time were very complex and no computer software were available. Recently, a few papers treating control related problems have appeared (Glad 1995, Abdallah et al. 1996, Syrmos et al. 1996, Blondel and Tsitsiklis 1995) and since the seventies there has been considerable progress in the development of more effective quantifier elimination algorithms starting with Collins (1975) For an extensive bibliography see Arnon (1988) and more recent work by Hong (1992a, ....

Abdallah, C. T., Dorato, P., Yang, W., Liska, R., Steinberg, S. (1996). Applications of quantifier elimination theory to control system design. In Proc. 4th IEEE Mediterranean Symposium on Control and Automation, Crete, Greece.

.... quantifier elimination can be found in, 12, 7] For an extensive bibliography on the subject, see [3] In control theory, one of the first attempts to use quantifier elimination techniques was made by Anderson et al. 2] and recently, a few papers treating control related problems have appeared [1, 8, 9, 10, 13]. In Section 2 we formulate the curve following problem as a formula including quantified variables and show how quantifier elimination can be used to decide if the problem is solvable. Section 3 treats the question how to design a state feedback control law. Approximations of reachable sets is ....

....map is the identity. Hence we can eliminate x directly by substitution. Clearing denominators the parallel condition in formula (3) becomes s 2bs Gamma s 3 2bs 3 = 4s 1 2s 2s 3 Gamma s 4 2u 2s 4 u = 2(s 2 Gamma 1) Next follows a few lines of Mathematica code: In[1]: EliminateQuantifiers Theta 8s 9u 9 Gamma s 2 a s Gamma s 3 2 a s 3 = 4 s 1 2 s 2 s 3 Gamma s 4 2 u 2 s 4 u = 2 (s 2 Gamma 1) 0 Gamma 2 u u 2 Delta Out[1] Gamma 1 2 a 0 Gamma 4409 2548 a 790 a 2 Gamma 452 a 3 Gamma 73 a ....

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C. T. Abdallah, P. Dorato, W. Yang, R. Liska, and S. Steinberg. Applications of quantifier elimination theory to control system design. In Proc. 4th IEEE Mediterranean Symp. on Control and Automation, 1996.

....is defined and implemented in terms of algebraic algorithms. redlog has been applied successfully for solving nonacademic problems, mainly for the simulation and errordiagnosis of physical networks [17] Applications inside the scientific community include the following: ffl Control theory [1]. ffl Stability analysis for pde s [12] ffl Geometric reasoning [10] ffl Disjunctive parametric scheduling. ffl Non convex parametric linear and quadratic optimization [16] transportation problems [13] ffl Real implicitization of algebraic surfaces. ffl Computation of comprehensive ....

Abdallah, C., Dorato, P., Liska, R., Steinberg, S., and Yang, W. Applications of quantifier elimination theory to control system design. In 4th IEEE Mediterranean Symposium on Control and Automation (1996), IEEE.

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Dorato, P., Yang, W., and Abdallah, C. (1995a). Application of Quantifier Elimination Theory to Robust Multi-Objective Feedabck design. J. Symbolic Computation This issue.

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Abdallah, C., Dorato, P., Yang, W., Liska, R., and Steinberg, S. (1995). Applications of Quantifier Elimination Theory to Control System Design. Tech report # EECE95-007, EECE Department, University of New Mexico, Albuquerque, NM 87131. Also submitted: IFAC World Congress, San Fransisco, CA.

....the linear controller. Boyd, et al. 6] show that simultaneous stabilizability can be guaranteed if there exists a single solution to a set of m linear matrix inequalities. Paskota, et al. 18] simultaneously stabilize systems by solving nonlinear Li enard Chipart constraints. Dorato, et al. [10] apply a relatively new computational technique known as quantifier elimination to verify Li enard Chipart stability conditions. Finally, Chow [9] defines a multimode system controllability matrix which simultaneously describes the controllability of all m systems f(A j ; B j )g i2Im . He gives ....

....jth characteristic polynomial can be calculated with Leverrier s method (Ackermann [1] a ij (k) Gammatrf A i j a 1j A i Gamma1 j Delta Delta Delta a i Gamma1;j A j g=i where A j = A j Gamma b j k T for all i 2 I n . It turns out that a rj = 0 for all r n. Dorato, et al. [10] extend similar work by Anderson, et al. 2] They apply a relatively new computational method known as quantifier elimination 6 to the necessary and sufficient Li enard Chipart conditions. Until recently such decision theoretic problems have been essentially intractable due to computational ....

P. Dorato, W. Yang, and C. Abdallah. Application of Quantifier Elimination Theory to Robust Multi-Objective Feedback Design. Technical Report EECE 95-007, University of New Mexico Department of Electrical and Computer Engineering, Albuquerque, September 1995.

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Dorato, P., W. Wang and C. T. Abdallah (1996). "Application of Quantifier Elimination Theory to Robust Multi-objective Feedback Design," Journal of Symbolic Computation, vol. 11, pp. 1--5.

No context found.

Chaouki T. Abdallah, Peter Dorato, Wei Yang, Richard Liska, and Stanly Steinberg. Applications of quantifier elimination theory to control system design. In Proceedings of the 4th IEEE Mediterranean Symposium on Control and Automation, pages 340--345. IEEE, 1996.

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C.T. Abdallah, P. Dorato, R. Liska, S. Steinberg, and W. Yang. Applications of quantifier elimination theory to control system design. In 4th IEEE Mediterranean Symposium on Control and Automation. IEEE, 1996.

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