Optimal control of linear multivariable systems with quadratic performance index, and the inverse optimal control problem

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Abstract
For a linear Nth-order time-invariant system with scalar control variable and quadratic performance index, a procedure is given for computing the optimal value of the feedback vector k. Instead of determining, as a first, step, the N(N+1)/2 elements of a symmetric matrix, the K values of k are computed directly, leading to substantial simplifications, and making the method well suited for higher-order systems. In contrast to other methods starting from the same premise, no restrictions are imposed on the form of matrix A. In addition, and based on the previous considerations, a solution of the inverse optimal control problem is also presented. The form of the weighting matrix in the performance index can be chosen arbitrarily (e.g. as diagonal). In contrast to other known procedures, the computations are straightforward, and again no restrictions are imposed on the form of the system.

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