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

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Page 4

Constraining the structure of the feedback gains to be

linear regulator problem effectively becomes an optimization problem over the

parameters which describe the feedback control; in particular, the constant gain ...

Constraining the structure of the feedback gains to be

**piecewise constant**, thelinear regulator problem effectively becomes an optimization problem over the

parameters which describe the feedback control; in particular, the constant gain ...

Page 66

S. USE OF GAIN MATRICES FOR DESIRED TRANSFER FUNCTION

CHARACTERISTICS -- AN EXAMPLE As previously mentioned, one advantage

of constraining the feedback control to have

optimizing ...

S. USE OF GAIN MATRICES FOR DESIRED TRANSFER FUNCTION

CHARACTERISTICS -- AN EXAMPLE As previously mentioned, one advantage

of constraining the feedback control to have

**piecewise**-**constant**gains and thenoptimizing ...

Page 69

CONCLUSION It has been shown that by restricting the structure of the feedback

gain matrix for the linear regulator problem to be

optimality can be traded for ease of implementation, and the loss of optimality ...

CONCLUSION It has been shown that by restricting the structure of the feedback

gain matrix for the linear regulator problem to be

**piecewise**-**constant**, a degree ofoptimality can be traded for ease of implementation, and the loss of optimality ...

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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