All of the texts below have pretty much the same content, but each author focuses on different aspects with slightly different notation. Particularly useful ones are in bold.
Suggested Textbooks
Bertsekas, Dimitri. Nonlinear Programming. Nashua, NH: Athena Scientific, 1999. ISBN: 9781886529007.
Bryson, Arthur. Dynamic Optimization. Upper Saddle River, NJ: Pearson Education, 1998. ISBN: 9780201361872.
Scales, L. E. Introduction to Non-Linear Optimization. New York, NY: Springer, 1985. ISBN: 9780387912523.
Gill, Philip, Walter Murray, and Margaret Wright. Practical Optimization. Burlington, MA: Academic Press, 1982. ISBN: 9780122839528.
Bryson, Arthur, and Yu-Chi Ho. Applied Optimal Control: Optimization, Estimation, and Control. Abingdon, UK: Taylor & Francis, 1975. ISBN: 9780891162285.
Bryson, Arthur. Applied Linear Optimal Control: Examples and Algorithms. Cambridge, UK: Cambridge University Press, 2002. ISBN: 9780521012317.
Stengel, Robert. Stochastic Optimal Control. New York, NY: Wiley, 1986. ISBN: 9780471864622.
Athans, Michael, and Peter Falb. Optimal Controls. New York, NY: McGraw-Hill, 1966. ISBN: 9780070024137.
Kirk, Donald. Optimal Control Theory: An Introduction. New York, NY: Dover, 2004. ISBN: 9780486434841.
Anderson, Brian, and John Moore. Linear Optimal Control. Upper Saddle River, NJ: Prentice Hall, 1971. ISBN: 9780135368701.
———. Optimal Control: Linear Quadratic Methods. New York, NY: Dover, 2007. ISBN: 9780486457666.
Luenberger, David. Optimization by Vector Space Methods. New York, NY: Wiley, 1997. ISBN: 9780471181170.
Vincent, Thomas, and Walter Grantham. Nonlinear and Optimal Control Systems. New York, NY: Wiley, 1997. ISBN: 9780471042358.
Burl, Jeffrey. Linear Optimal Control. Upper Saddle River, NJ: Prentice Hall, 1999. ISBN: 9780201808681.
Bellman, Richard. Dynamic Programming. New York, NY: Dover, 2003. ISBN: 9780486428093.
Bertsekas, Dimitri. Dynamic Programming and Optimal Control. Vol. 1 and 2. Nashua, NH: Athena Scientific, 2007. ISBN: 9781886529083.
Kwakernaak, Huibert, and Raphael Sivan. 
Linear Optimal Control Systems (PDF). New York, NY: Wiley, 1972. ISBN: 9780471511106.