## On the design of a piecewise-constant feedback control for the linear regulator problem |

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### Contents

Surface Modeling Algorithms | 5 |

Structure of the Suboptimal Feedback Control | 13 |

Structure of the State Transition Matrix | 19 |

8 other sections not shown

### Common terms and phrases

accuracy approximation bound building blocks computed Consider constant gain matrices constraint algorithm contraction mapping cost index cubically convergent define a convergent denote determine eigenvalues equation example feedback control feedback gain matrix finite Gauss-Legendre quadrature gradient and Hessian Hess Hessian matrix Hessian p.d. Hessian implementation integral interpolation iterations to solution K!WK linear regulator problem matrix norm method modified Hessian nonsingular null space number of evaluations number of iterations number of switches OSV algorithm p.d. Hessian p.d. partial derivatives performance index piecewise-constant point quadrature polynomial positive definite positive definite matrix positive semidefinite Proof Q+K'WK QR algorithm quadratic R(tQ rate of convergence respect Riccati feedback gain Riccati solution satisfy scalar spectral norm structure suboptimal gain sufficient condition surface model symmetric Table Taylor expansion tensor tf;T Theorem A-2 thesis third-variation algorithm tion TjTi TjTk Tk Tj transition matrix U(KR variation algorithm vector