## Primer on Optimal Control TheoryThe performance of a process, such as aircraft fuel consumption, can be enhanced when its most effective controls and operating points are determined. Primer on Optimal Control Theory provides an introduction to the theory behind analysing these processes and finding the best controls, which provides a sound basis for those wishing to tackle more advanced literature. The book presents the important concepts of weak and strong control variations leading to local necessary conditions, and also global sufficiency of Hamilton-Jacobi-Bellman theory. It also gives the second variation for local optimality where the associated Riccati equation is derived from the transition matrix of the Hamiltonian system. These ideas lead naturally to the development of H2 and H synthesis algorithms. This book will enable applied mathematicians, engineers, scientists, biomedical researchers, and economists to understand and implement optimal control theory at a level of sufficient generality and applicability for most practical purposes. |

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assumed Assumption boundary conditions Calculus of Variations conditions for optimality continuous function continuously differentiable control function converges cost criterion defined derivative determined disturbance attenuation eigenvalues example exists first-order necessary conditions G(tf given gradient H-J-B equation Hamiltonian system Implicit Function Theorem implies integral Lagrange multiplier linear dynamic system LQ problem method Minimize the performance minimum necessary and sufficient nonlinear nonnegative norm Note obtain once continuously differentiable open set optimal control problem optimal value function optimization problem p-vector P(to parameter performance index perturbation piecewise continuous Pontryagin’s Principle positive definite Proof Riccati differential equation Riccati equation S(tf t;S f satisfies scalar second variation Section solution solved ſto strongly positive sufficient condition Suppose symmetric symmetric matrix symplectic terminal constraints Theorem tion trajectory transition matrix unconstrained uo(t variable vector zero