Executive Summary : | Mathematical control theory is a branch of control theory that focuses on application-oriented mathematics. Optimal Control Theory is one of the most multidisciplinary fields of science today, combining Engineering and Mathematics in a way that is both beautiful and useful. Optimal control theory is a 385-year-old result of the calculus of variations, but it was only with the introduction of the computer that interest in it exploded, sparked by the remarkable results of optimal trajectory prediction in aerospace applications in the early 1960s. So, in an optimal control problem, at least two items, namely the dynamics and the functional to be reduced, make the situation interesting. Modern finite dimensional optimal control theory is defined by three milestones: the Kalman optimal linear regulator theory, the Bellman dynamic programming approach, and the Pontryagin maximum principle. The objective of the research is to obtain optimality conditions for the following nonlinear systems. 1.Optimal control for integer order nonlinear systems 2. Optimal control for fractional order nonlinear control system 3. Optimal control for population dynamics 4. Optimal control for third order dispersion equation 5. Optimal control for third order thermoelastic system The optimal control problem for nonlinear control systems can be studied by different methods, which can be classified as follows: 1. Minimizing Sequence Method 2. Pontryagin Maximum Principle 3. Increment Approach Optimal Control Theory plays a major role in many disciplines of science and technology today, and it poses exciting problems. We'll go through a few of the fields where these problems are evident such as Biomedical research, Hydrology, Control of computer aided systems, etc. |