Designing an adaptive LQR controller...

I would like to know if anyone knows any software (of the kind of Maple

> or Matlab) that allows you to solve symbolically AREs (Algebraic Riccati > Equations). So that given a certain Optimal Control Problem with a > couple of parameters a general expression of the Gain matrix of the > controller could be computed depending on those two parameters without > having to solve all the time the new ARE.

I know that it's hard to solve symbolically AREs or in general quadratic matrix equations, some considerations on the symbolic solution of matrix equation AX^2+BX+C=0 can be found in Higham & Kim, "Numerical analysis of a quadratic matrix equation" IMA j. numer. anal. 20 (2000), no. 4, 499--519. You can use computer algebra systems to solve polynomial equations.

In alternative you could consider numerical solution, there are quick solvers for particular Riccati equation and they need only matrix multiplication and inversion. It depends on the dimension of matrix. Please send your equation in the form XDX+A'X+XA-C=0.

Bye Bruno Iannazzo

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Bruno I.
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