algebraic_riccati_continuous.h

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 *  TU Dortmund - Institute of Control Theory and Systems Engineering.
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 *  Authors: Christoph Rösmann
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#ifndef SRC_NUMERICS_INCLUDE_CORBO_NUMERICS_ALGEBRAIC_RICCATI_CONTINUOUS_H_
#define SRC_NUMERICS_INCLUDE_CORBO_NUMERICS_ALGEBRAIC_RICCATI_CONTINUOUS_H_
 
#include <corbo-core/types.h>
 
#include <Eigen/Eigenvalues>
 
namespace corbo {
 
class AlgebraicRiccatiContinuous
{
 public:
    static bool solve(const Eigen::Ref<const Eigen::MatrixXd>& A, const Eigen::Ref<const Eigen::MatrixXd>& B,
                      const Eigen::Ref<const Eigen::MatrixXd>& Q, const Eigen::Ref<const Eigen::MatrixXd>& R, Eigen::MatrixXd& X,
                      Eigen::MatrixXd* G = nullptr);
 
    static bool isClosedLoopStable(const Eigen::Ref<const Eigen::MatrixXd>& A, const Eigen::Ref<const Eigen::MatrixXd>& B,
                                   const Eigen::Ref<const Eigen::MatrixXd>& G);
 
    static bool isNumericallyStable(const Eigen::Ref<const Eigen::MatrixXd>& A, const Eigen::Ref<const Eigen::MatrixXd>& B,
                                    const Eigen::Ref<const Eigen::MatrixXd>& Q, const Eigen::Ref<const Eigen::MatrixXd>& R);
 
 protected:
    static bool solveRiccatiHamiltonianSchur(const Eigen::MatrixXd& H, Eigen::MatrixXd& X);
 
    // matrix sign method, currently not in use and needs to be updated for future use
    // [1] R. Byers. "Solving the algebraic Riccati equation with the matrix sign function".
    //     Linear ALgebra and its Applications. Volume 85, 267-278, 1987.
    // static void sovleRiccatiHamiltonianMatrixSign(Eigen::MatrixXd& Z, Eigen::MatrixXd& X);
 
    static bool hasNegativeRealPart(const Eigen::Ref<const Eigen::MatrixXd>& block) { return block.eigenvalues()[0].real() < 0; }
 
    static bool hasRealPartsCloseToZero(const Eigen::Ref<const Eigen::MatrixXd>& matrix);
};
 
}  // namespace corbo
 
#endif  // SRC_NUMERICS_INCLUDE_CORBO_NUMERICS_ALGEBRAIC_RICCATI_CONTINUOUS_H_