riccati.hpp

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// toolboxes/control/include/nk/control/riccati/riccati.hpp
//
// Algebraic Riccati equation solvers.
//
//   care: continuous-time ARE   AᵀX + XA − XBR⁻¹BᵀX + Q = 0
//   dare: discrete-time   ARE   AᵀXA − X − AᵀXB(R + BᵀXB)⁻¹BᵀXA + Q = 0
//
// Both are solved by the matrix sign-function method (no Schur
// ordering): a Newton iteration drives an embedding matrix to its
// sign, whose stable invariant subspace yields X via a small
// least-squares solve. care embeds the Hamiltonian directly; dare
// embeds the symplectic matrix through a Cayley transform that maps the
// unit disk onto the left half-plane so the same sign machinery applies.
//
// Practical for the state dims that show up in textbook control
// problems (n ≲ 32). dare requires a nonsingular A (the explicit
// symplectic form needs A⁻¹); the singular-A pencil path would need a
// QZ solver we do not have yet.
 
#pragma once
 
#include <memory_resource>
#include <nk/value/value.hpp>
 
namespace nk::control {

 

struct RiccatiResult {
    Value X;   
    Value L;   
    Value G;   
};

RiccatiResult care(const Value &A, const Value &B, const Value &Q,
                   const Value &R, std::pmr::memory_resource *mr = nullptr);

RiccatiResult dare(const Value &A, const Value &B, const Value &Q,
                   const Value &R, std::pmr::memory_resource *mr = nullptr);
 

} // namespace nk::control