Textbooks
There are many, and these are the ones on my shelf. All pretty much have the same content, but each author focuses on different aspects with slightly different notation. Particularly useful ones are preceded by (*) mark.
Bertsekas, Dimitri P. Nonlinear Programming. Belmont, MA: Athena Scientific, 1999. ISBN: 1886529000.
Bryson, Arthur E. Dynamic Optimization. Upper Saddle River, NJ: Pearson Education, 1998. ISBN: 0201361876.
Scales, L. E. Introduction to Non-Linear Optimization. New York, NY: Springer, 1985. ISBN: 0387912525.
Gill, Philip E., Walter Murray, and Margaret Wright. Practical Optimization. Burlington, MA: Academic Press, 1981. ISBN: 0122839528.
*Bryson, Arthur E., and Yu-Chi Ho. Applied Optimal Control: Optimization, Estimation, and Control. New York, NY: Routledge, 1975. ISBN: 0891162283.
Bryson, Arthur E. Applied Linear Optimal Control: Examples and Algorithms. Cambridge, UK: Cambridge University Press, 2002. ISBN: 0521012317.
*Stengel, R. F. Stochastic Optimal Control. New York, NY: Wiley-Interscience, 1986. ISBN: 0471864625.
Athans, Michael, and Peter Falb. Optimal Control. New York, NY: McGraw Hill, 1966. ISBN: 0070024138.
*Kirk, Donald E. Optimal Control Theory: An Introduction. New York, NY: Dover, 2004. ISBN: 0486434842.
Anderson, Brian, and John Moore. Linear Optimal Control. New York, NY: Prentice Hall, 1971. ISBN: 0135368707.
———. Optimal Control: Linear Quadratic Methods. New York, NY: Prentice Hall, 1990. ISBN: 0136385605.
Luenberger, D. Optimization by Vector Space Methods. New York, NY: John Wiley & Sons, Inc, 1969. ISBN: 047155359X.
Dorato, Peter, Chaouki Abdallah, and Vito Cerone. Linear-Quadratic Control: An Introduction. New York, NY: Prentice Hall, 1998. ISBN: 0023299622.
Burl, Jeffrey B. Linear Optimal Control. New York, NY: Prentice Hall, 1998. ISBN: 0201808684.
Bellman, Richard. Dynamic Programming. New York, NY: Dover, 2003. ISBN: 0486428095.
Bertsekas, D. P. Dynamic Programming and Optimal Control. Vols. 1 and 2. Belmont, MA: Athena Scientific, 2001. ISBN: 1886529086.
Kwakernaak, H., and R. Sivan. Linear Optimal Control Systems. New York, NY: Wiley-Interscience, 1972. (PDF)
Additional Readings
Bryson, Arthur, Jr. "Optimal Control - 1950 to 1985." IEEE Control Systems Magazine 16, no. 3 (June 1996): 26-33.
Larson, Robert E. "A Survey of Dynamic Programming Computational Procedures." IEEE Transactions on Automatic Control Survey Papers (December 1967): 767-774.
Betts, John T. "Survey of Numerical Methods for Trajectory Optimization." Journal of Guidance, Control, and Dynamics 21, no. 2 (March-April 1998): 193-207.
Kwakernaak, H., and R. Sivan. "Response to White Noise." Section 1.11 in Linear Optimal Control Systems. New York, NY: Wiley-Interscience, 1972, pp. 97-113. (PDF - 1.7 MB)
Shampine, L., J. Kierzenka, and M. Reichelt. "Solving boundary value problems for ordinary differential equations in MATLAB® with bvp4c."