Gain-Scheduled Inverse Optimal Satellite Attitude Control

Abstract

Despite the theoretical advances in optimal control, satellite attitude control is still predominantly performed by standard controllers, such as PD laws, which are easier to implement. A switched controller is proposed, based on inverse optimal control theory, which circumvents the complex task of numerically solving online the Hamilton Jacobi Bellman (HJB) partial differential equation of the global nonlinear optimal control problem. The inverse optimization problem consists of minimizing the norm of the control torque subject to a constraint on the convergence rate of a parameterized Lyapunov function, under the effect of the benchmark controller, which is chosen to be a PD law without loss of generality. The controller is then modified by gain scheduling to achieve a tradeoff enhancement compared to the benchmark controller, while maintaining torque saturation limits. The extent to which performance can be enhanced is shown to be dependent on the controller parameters. A controller tuning analysis shows how a design settling time limit can be achieved, within the problem's constraints on the maximum torque and the total integrated torque. The proposed optimization approach is globally stabilizing and presents low implementation complexity, which is highly desirable given the limited resources onboard satellites.

Output Feedback Control of Switched Nonlinear Systems: A Gain Scheduling Approach

“…Here, the proof is repeated only in basic steps. Substituting (22), (23) and (27) to Lemma 1 one obtains inequalities (28), which proves the sufficient conditions of Theorem 2.…”

“…Consider a stable closed-loop switched system (11) with N modes. If there is a control law u(t) (10) and a positive scalar J * such that the closed-loop cost function (13) or (14) …”

“…There are only some results in the field of switched (gain scheduled) controller design for continuous-time systems [10,19,23,25] and stabilization of switched continuous time linear systems [3,6], where in [19] the switching gain scheduled control technique is used to control the flexible ball-screw drive servo with a wide range of operating conditions. The framework of [25] is based on the linear matrix inequalities (LMI) formulation with parameter dependent Lyapunov functions.…”

“…The results of the proposed synthesis is a gain scheduled controller that guarantees stability even for a nonlinear plant. In [23] a switched controller is proposed based on the inverse optimal theory. The obtained controller is then modified by gain scheduling to achieve the quality of the closed-loop system performance.…”

“…In [6] the authors introduce the notion of the dwelltime T d (minimal time interval between switching) into the switched controller design procedure. In the stability analysis condition of switched systems the dwell-time is included to the term e AcT d (A c -closed-loop matrix (11)). In such a way the proposed design procedure for stability analysis and switching controller design for the real switching time interval T > T d becomes conservative.…”