Unified approach to H₂ and H_∞ optimal control of a hypersonic vehicle

Recently, there has been resurrection in hypersonics and SCRamjet technology to provide an easy and inexpensive `access to space' and other space-related missions including military applications such as interceptor, tactical and strategic reconnaissance, high-speed transport and orbital transport. Compared to other types of air vehicles, the hypersonic vehicles (HSVs) have many desirable features such as large increase in speed, altitude and range and at the same time pose tremendous challenges to engineering community in terms of integration of aerodynamics and air-breathing propulsion, thermal management and absence of ground-based testing facilities at the hypersonic speeds. In this paper, a unified approach which alleviates the difficulties of `over crowding' of the roots inside the unit circle and the corresponding numerical difficulties in working with the traditional z-transform domain, is applied to design controllers for hypersonic vehicles. A modification to unified approach to problems with quadratic performance index involving output is carried out. The unified approach has a very attractive feature of its applicability to both continuous-time and discrete-time domains simultaneously. In particular, some simple H₂- and H_∞-based optimal controllers are designed for a linearized model of a typical hypersonic vehicle.