Geometric algorithms for input constrained systems with application to flight control.
In this thesis novel numerical algorithms are developed to solve some problems of analysis and control design for unstable linear dynamical systems having their input constrained by maximum amplitude and rate of the control signals. Although the results obtained are of a general nature, all the problems considered are induced by flight control applications. Moreover, all these problems are stated in terms of geometry, and because of this their solution in the thesis was effectively achieved by geometrically-oriented methods. The problems considered are mainly connected with the notions of the controllable and stability regions. The controllable region is defined as the set of states of an unstable dynamical system that can be stabilized by some realizable control action. This region is bounded due to input constraints and its size can serve as a controllability measure for the control design problem. A numerical algorithm for the computation of two-dimensional slices of the region is proposed. Moreover, the stability region design is also considered. The stability region of the closed-loop system is the set of states that can be stabilized by a particular controller. This region generally utilizes only a part of the controllable region. Therefore, the controller design objective may be formulated as maximizing this region. A controller that is optimal in this sense is proposed for the case of one and two exponentially unstable open-loop eigenvalues. In the final part of the thesis a linear control allocation problem is considered for overactuated systems and its real-time solution is suggested. Using the control allocation, the actuator selection task is separated from the regulation task in the control design. All fault detection and reconfiguration capabilities are concentrated in one special unit called the control allocator, while a general control algorithm, which produces 'virtual' input for the system, remains intact. In the case of an actuator fault, only the control allocation unit needs to be reconfigured and in many cases it can generate the same 'virtual' input using a different set of control effectors. A novel control allocation algorithm, which is proposed in the thesis, is based on multidimensional interval bisection techniques.
- PhD