# List of Linear-Quadratic Dynamic Optimization (LQDO) Examples

| Name | Link | Reference | Solution Type |
| ---- | ---- | ---- | ---- |
| Anderson Moore 64 | [anderson-moore-64](anderson-moore-64/) | And89 | closed-form |
| Betts Biehn Campbell 1 | [betts-biehn-campbell-1](betts-biehn-campbell-1/) | Betts02 | closed-form |
| Bryson-Denham | [bryson-denham](bryson-denham/) | Bry75 | closed-form |
| Bryson Ho 109 | [bryson-ho-109](bryson-ho-109/) | Bry75 | simple implicit |
| Bryson Ho 116 | [bryson-ho-116](bryson-ho-116/) | Bry75 | closed-form |
| Bryson Ho 153 | [bryson-ho-153](bryson-ho-153/) | Bry75 | closed-form |
| Bryson Ho 154 | [bryson-ho-154](bryson-ho-154/) | Bry75 | closed-form |
| Bryson Ho 156 | [bryson-ho-156](bryson-ho-156/) | Bry75 | closed-form |
| Bryson Ho 166 | [bryson-ho-166](bryson-ho-166/) | Bry75 | closed-form |
| Bryson Ho 248 | [bryson-ho-248](bryson-ho-248/) | Bry75 | simple implicit |
| Cart | [cart](cart/) | Ball99 | closed-form |
| DTQP Example 1 | [dt-qp-1](dt-qp-1/) | Her17 | |
| DTQP Example 2 | [dt-qp-2](dt-qp-2/) | | simple integral |
| DTQP Example 3 | [dt-qp-3](dt-qp-3/) | | closed-form |
| Gas Absorber | [gas-absorber](gas-absorber/) | Lu00 |  |
| Greenhouse Climate | [greenhouse-climate](greenhouse-climate/) | Str10 |  |
| Hager 1 | [hager-1](hager-1/) | Hag00 | closed-form |
| HDAE | [hdae](hdae/) | Betts10 |  |
| Jaddu Shimemura | [jaddu-shimemura](jaddu-shimemura/) | Jad98 | finite optimization |
| Linear Pendulum | [linear-pendulum](linear-pendulum/) | Bress11 | closed-form |
| LQR Inhomogeneous | [lqr-inhomogeneous](lqr-inhomogeneous/) | Bry75 | boundary value problem |
| LQR Scalar | [lqr-scalar](lqr-scalar/) | | closed-form |
| LQR Scalar Transfer | [lqr-scalar-transfer](lqr-scalar-transfer/) | | closed-form |
| LQR Standard | [lqr-standard](lqr-standard/) | Bry75 | boundary value problem |
| Minimum Energy Transfer | [minimum-energy-transfer](minimum-energy-transfer/) | Bry75 | matrix integral |
| Multiphase Parameter | [multiphase-parameter](multiphase-parameter/) | | finite optimization |
| Nagurka | [nagurka](nagurka/) | Lu00 |  |
| Output Tracking | [output-tracking](output-tracking/) | Bry75 | boundary value problem |
| Tavallaei Tousi 1 | [tavallaei-tousi-1](tavallaei-tousi-1/) | Tav08 | boundary value problem |
| Turner Chun Juang 1 | [turner-chun-juang-1](turner-chun-juang-1/) | Turn85 | closed-form |

### References
- [**And89**] B. D. O. Anderson and J. B. Moore, *Optimal Control: Linear Quadratic Methods*. Prentice-Hall, 1989, isbn: 0136386512
- [**Ball99**] D. H. Ballard, *An Introduction to Natural Computation*. MIT Press, 1999, isbn: 9780262522588
- [**Betts02**] J. T. Betts, N. Biehn, and S. L. Campbell, "Convergence of Nonconvergent IRK Discretizations of Optimal Control Problems with State Inequality Constraints", *SIAM Journal on Scientific Computing*, vol. 23, no. 6, pp. 1981-2007, 2002, doi: 10.1137/S1064827500383044
- [**Betts10**] J. T. Betts, *Practical Methods for Optimal Control and Estimation Using Nonlinear Programming*. SIAM, 2010, isbn: 9780898716887
- [**Bress11**]  A. Bressan, "Viscosity Solutions of Hamilton-Jacobi Equations and Optimal Control Problems", Lecture Notes, pp. 30-31, 2011
- [**Bry75**] A. E. Bryson Jr. and Y.-C. Ho, *Applied Optimal Control*. Taylor & Francis, 1975, isbn: 9780891162285
- [**Hag00**] W. W. Hager, "Runge-Kutta Methods in Optimal Control and the Transformed Adjoint System", *Numerische Mathematik*, vol. 87, no. 2, pp. 247-282, Dec. 2000, doi: 10.1007/s002110000178
- [**Her17**] D. R. Herber, *Advances in Combined Architecture, Plant, and Control Design.* PhD Dissertation, University of Illinois at Urbana-Champaign, Urbana, IL, USA, Dec. 2017
- [**Jad98**] H. Jaddu and E. Shimemura, "Solution of Constrained Linear Quadratic Optimal Control Problem Using State Parameterization," *Trans. of the Society of Instrument and Control Engineers*, vol. 34, no. 9, pp. 1164-1169, 1998, doi: 10.9746/sicetr1965.34.1164
- [**Lu00**] R. Luus, *Iterative Dynamic Programming*. CRC Press, 2000, isbn: 1584881488
- [**Str10**] G. van Straten, G. van Willigenburg, E. van Henten, and R. van Ooteghem, Optimal Control of Greenhouse Cultivation. CRC Press, 2010 [Online]. Available: http://dx.doi.org/10.1201/b10321
- [**Tav08**] M. A. Tavallaei and B. Tousi, "Closed Form Solution to an Optimal Control Problem by Orthogonal Polynomial Expansion," *American J. of Engineering and Applied Sciences*, vol. 1, no. 2, pp. 104-109, 2008. doi: 10.3844/ajeassp.2008.104.109
- [**Turn85**] J. D. Turner, H. M. Chun, J. N. Juang, "Closed-Form Solutions for a Class of Optimal Quadratic Tracking Problems", Journal of Optimization Theory and Applications, vol. 47, no. 4, pp. 465-481, Dec. 1985, doi: 10.1007/BF00942192

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