Spectral theory of linear control and estimation problems
| Autor: | E. A. Jonckheere, L. M. Silverman |
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| Rok vydání: | 2005 |
| Předmět: | |
| Zdroj: | International Symposium on Systems Optimization and Analysis ISBN: 3540094474 International Symposium on Systems Optimization and Analysis ISBN: 9783662389669 |
| Popis: | Consider the finite-dimensional discrete-time linear system $$x\left( {k + 1} \right) = A\;x\left( k \right) + B\;u\left( k \right),\;x\left( i \right) = \xi $$ (1) where x(k) e R and u(k) ϵ Rr; A and B are time-invariant matrices of compatible size. The pair (A, B) is assumed to be controllable and A is asymptotically stable (by feedback invariance [4], this restriction does not introduce any loss of generality here). Together with (1), define the quadratic cost $$J\left[ {\xi ,U\left( {i,t} \right)} \right] = \sum\limits_{k = 1}^{t - 1} {\left[ {x'\left( k \right)Qx\left( k \right) + 2x'\left( k \right)Su\left( k \right) + u'\left( k \right)Ru\left( k \right)} \right]} $$ (2) where U(i, t) = [u’(i) u’(i + 1) ... u’(t-1)]’ and ξ = x(i) . The overall weighting matrix\(W = \left[ {\begin{array}{*{20}{c}} Q \\ {S'} \\ \end{array} \quad \begin{array}{*{20}{c}} S \\ R \\ \end{array} } \right]\) is symmetric, but not necessarily positive semi-definite. |
| Databáze: | OpenAIRE |
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