Derivation of Optimal Guidance and Control Problem

New tactical missile requirements are so stringent that weapon subsystem technology must be utilized at the highest possible level consistent with cost, reliability, and performance. This is particularly true with the guidance and control subsystems, which are the nerve center or backbone of a weapon. As a result of this, there is continuing requirement for more and better tools for analyzing performance, predicting requirements, determining error sources, and selecting suitable concepts. Among these concepts is the optimal guidance and control which is indispensable for advanced guidance processes where ever-increasing performance requirements are to be achieved with minimum control or actuation and minimum cost. This cost is the performance index that mathematically weights different flight variables including the time constraints, the guidance commands or actuating signals or commanded acceleration and miss distance especially near the target interception. That is, tackling such problems necessitates formulation, solution and design with synthesis which is mathematically cumbersome and boring for researchers. Therefore, this paper is devoted to formulate the problem in a systematic and concise approach with detailed and complete derivation of riccatti equations and its impact on the controller\autopilot design. Then, the theory is also derived for the regulator and servomechanism\ tracking problems. Each theory is augmented with analytical case study to clarify the impact of optimality and riccatti equation solution upon the system’s performance.