Closed-form solutions for a class of optimal quadratic regulator problems with terminal constraints

@article{Juang1984ClosedformSF,
  title={Closed-form solutions for a class of optimal quadratic regulator problems with terminal constraints},
  author={Jer-Nan Juang and James D. Turner and Hon M. Chun},
  journal={Journal of Dynamic Systems Measurement and Control-transactions of The Asme},
  year={1984},
  volume={108},
  pages={44-48}
}
  • J. Juang, J. Turner, H. M. Chun
  • Published 14 May 1984
  • Mathematics
  • Journal of Dynamic Systems Measurement and Control-transactions of The Asme
Closed-form solutions are derived for coupled Riccati-like matrix differential equations describing the solution of a class of optimal finite time quadratic regulator problems with terminal constraints. Analytical solutions are obtained for the feedback gains and the closed-loop response trajectory. A computational procedure is presented which introduces new variables for efficient computation of the terminal control law. Two examples are given to illustrate the validity and usefulness of the… 

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References Juang, J. M, Turner, J. D., and Chun, H.M., "Closed-Form Solutions for a Class of Optimal Quadratic Regulator Problems with Terminal Constraints," ASME Journal on Dynamics, Measurement,
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References

SHOWING 1-10 OF 10 REFERENCES
A nonrecursive algebraic solution for the discrete Riccati equation
Equations for the optimal linear control and filter gains for linear discrete systems with quadratic performance criteria are widely documented. A nonrecursive algebraic solution for the Riccati
On the applicability of the sweep method to optimal control problems
Two types of linear quadratic problems are investigated. The first is associated with problems in which the final time is specified and the second with problems in which the final time is given
Linear Optimal Control Systems
TLDR
An excellent introduction to feedback control system design, this book offers a theoretical approach that captures the essential issues and can be applied to a wide range of practical problems.
The algebraic eigenvalue problem
Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices of
On solutions of the Riccati equation in optimization problems
  • B. Friedland
  • Computer Science
    IEEE Transactions on Automatic Control
  • 1967
TLDR
The relations can be used to compare the solution of the Riccati equation with its asymptotic solution and to evaluate M(t) for optimization problems in which M(T) does not exist.
ORACLS—A Design System for Linear Multivariate Control, Marcel Dekker, Inc
  • New York,
  • 1980
A Negative Solution for the Matrix Riccati Equation,
  • IEEE Trans. Automatic Control,
  • 1969
A Users Manual for the Automatic Synthesis Program,
  • NASA Rept
  • 1966
Optimal Feedback Control of a Flexible Spacecraft During a Large-Angle Rotational Maneuver," Paper No. 82-1589-CP
  • Presented at the AIAA Guidance and Control Conference,
  • 1982