# 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} }

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…

## 23 Citations

### A parametrization of the solutions of the finite-horizon LQ problem with general cost and boundary conditions

- MathematicsAutom.
- 2005

### Closed-form recursive formula for an optimal tracker with terminal constraints

- Mathematics
- 1984

Feedback control laws are derived for a class of optimal finite time tracking problems with terminal constraints and expressed in recursive forms so that a real-time computer implementation becomes feasible.

### A simple solution to the finite-horizon LQ problem with zero terminal state

- MathematicsKybernetika
- 2003

Closed-form expressions for the optimal state and costate trajectories of the Hamiltonian system, as well as the corresponding control law, are derived through theutions of two infinite-horizon LQ problems, thus avoiding the use of the Riccati differential equation.

### Closed-loop soft-constrained time-optimal control of flexible space structures

- Mathematics
- 1992

We propose numerically efficient solutions for the openand closed-loop time-optimal soft-constrained control of a linear system representing a large flexible space structure. The open-loop solution…

### Aparametrization of the solutions of the finite-horizonLQ problemwith general cost andboundary conditions ?

- Mathematics
- 2005

A generalization of the finite-horizon linear quadratic regulator problem is proposed for LTI continuous-time controllable systems. In particular, a formulation of the LQ problem is considered, with…

### Symplectic Transformation Based Analytical and Numerical Methods for Linear Quadratic Control with Hard Terminal Constraints

- MathematicsSIAM J. Control. Optim.
- 2012

A structure-preserving matrix recursive algorithm is derived for the computation of time-varying optimal control gains and the systems optimal trajectories and is shown to give accurate results for relative large discrete steps and keeps geometric properties of the solutions.

### Analytical neighboring optimal guidance to finite horizon linear quadratic tracking problems

- Mathematics49th IEEE Conference on Decision and Control (CDC)
- 2010

A new approach to solving finite horizon linear quadratic tracking problems is proposed based on the virtual motion camouflage concept, and pseudospectral discretization and differential inclusion techniques, which avoids several disadvantages of classic approaches.

### Saturating and time-optimal feedback controls

- Mathematics
- 1993

The open-loop solution of the soft-constrained time-optimal control problem can be efficiently computed in terms of the controllability Grammian matrix, but a closed-loop implementation was found to…

### LQ tracking controls with fixed terminal states and their application to receding horizon controls

- MathematicsSyst. Control. Lett.
- 2008

### Frequency-shaped large-angle maneuvers

- Engineering
- 1987

The paper considers the problem of maneuvering a flexible spacecraft through large angles in finite time. The basic control problem is divided into two parts. The first part consists of generating a…

## References

SHOWING 1-10 OF 10 REFERENCES

### A nonrecursive algebraic solution for the discrete Riccati equation

- Mathematics
- 1970

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

- Mathematics
- 1969

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

- Mathematics
- 1972

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

- Mathematics
- 1965

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

- Computer ScienceIEEE Transactions on Automatic Control
- 1967

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.

### Control problems with linear dynamics, quadratic criterion, and linear terminal constraints

- MathematicsIEEE Transactions on Automatic Control
- 1967

### 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