Jason L. Speyer

The performance of a process - for example, how an aircraft consumes fuel - can be enhanced when the most effective controls and operating points for the process are determined. This holds true for many physical, economic, biomedical, manufacturing, and engineering processes whose behavior can often be influenced by altering certain parameters or controls to optimize some desired property or output. Primer on Optimal Control Theory:* Provides a rigorous introduction to analyzing these processes and finding the best modes of control and operation for them.* Makes optimal control theory accessible to a large class of engineers and scientists who are not mathematicians but have a basic mathematical background and need to understand the sophisticated material associated with optimal control theory.* Presents the important concepts of weak and strong control variations leading to local necessary conditions, as well as global sufficiency of Hamilton-Jacobi-Bellman theory.* Gives the second variation for local optimality where the associated Riccati equation is derived from the transition matrix of the Hamiltonian system, ideas that lead naturally to the development of H2 and H? synthesis algorithms.

Uncertainty and risk are integral to engineering because real systems have inherent ambiguities that arise naturally or due to our inability to model complex physics. The authors discuss probability theory, stochastic processes, estimation, and stochastic control strategies and show how probability can be used to model uncertainty in control and estimation problems. The material is practical and rich in research opportunities. The authors provide a comprehensive treatment of stochastic systems from the foundations of probability to stochastic optimal control. The book covers discrete- and continuous-time stochastic dynamic systems leading to the derivation of the Kalman filter, its properties, and its relation to the frequency domain Wiener filter as well as the dynamic programming derivation of the linear quadratic Gaussian (LQG) and the linear exponential Gaussian (LEG) controllers and their relation to H2 and H-inf controllers and system robustness. Stochastic Processes, Estimation, and Control is divided into three related sections.First, the authors present the concepts of probability theory, random variables, and stochastic processes, which lead to the topics of expectation, conditional expectation, and discrete-time estimation and the Kalman filter. After establishing this foundation, stochastic calculus and continuous-time estimation are introduced. Finally, dynamic programming for both discrete-time and continuous-time systems leads to the solution of optimal stochastic control problems, resulting in controllers with significant practical application.