Abstract
Given a body subject to quadratic drag forces so that the position y(t) and the applied control thrust u(t) are related by \ddot{y}(t)+a\dot{y}(t)|\dot{y}(t)| = u(t), |u(t)| \leq 1 , the control u(t) is found which forces the body to a desired position, and stops it there, and which minimizes the cost J=\int\liminf{0} \limsup{T}\{k + |u(t)|\}dt . The response time T is not fixed, k > 0 , and |u(t)| is proportional to the rate of flow of fuel. Repeated use of the necessary conditions provided by the Maximum Principle results in the optimum feedback system. It is shown that if k\leq 1 , then singular controls exist and they are optimal; if k > 1 , then singular controls are not optimal. Techniques for the construction of the various switch curves are given, and extensions of the results to other nonlinear systems are discussed.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
