We present an approach for constructing optimal feedback control laws for regulation of a rotating rigid spacecraft. We employ the inverse optimal control approach which circumvents the task of solving a Hamilton-Jacobi equation and results in a controller optimal with respect to a meaningful cost functional. The inverse optimality approach requires the knowledge of a control Lyapunov function and a stabilizing control law of a particular form. For the spacecraft problem, they are both constructed using the method of integrator backstepping. We give a characterization of (nonlinear) stability margins achieved with the inverse optimal control law. Keywords--- Attitude control, stabilization, inverse optimality, stability margins, backstepping. I. Introduction Optimal control of rigid bodies has a long history stemming from interest in the control of rigid spacecraft and aircraft [1], [2], [3], [4], [5]. The main thrust of this research has been directed, however, towards the time-opti...

We present an approach for constructing optimal feedback control laws for optimal regulation of a rotating rigid spacecraft. We employ the inverse optimal control approach which circumvents the task of solving a Hamilton-Jacobi equation and results in a controller optimal with respect to a meaningful cost functional. The design reported in the paper is the first optimal control design for attitude regulation of the complete, nonlinear system, which includes a penalty on the angular velocity, orientation and the control torque. 1. Introduction Optimal control of rigid bodies has a long history stemming from interest in the control of rigid spacecraft and aircraft [1, 2, 3]. The main thrust of this research has been directed, however, towards the time-optimal and fuel-optimal control problems [4, 5, 6]. The optimal regulation problem over a finite or infinite horizon has been treated in the past mainly for the angular velocity subsystem and for special quadratic costs [7, 8, 9]. The ca...

. This paper considers the problem of controlling the rotational motion of a rigid body using three independent control torques. Given a quadratic cost we seek stabilizing state feedback controllers which guarantee that all motions starting within a specified bounded set satisfy a specified bound on a quadratic performance index or cost. For a special class of cost functions, we present explicit expressions for the optimal stabilizing controllers. For the general case, we present sufficient conditions which guarantee the existence of linear, suboptimal, stabilizing controllers. Keywords. Attitude control; quadratic cost; linear matrix inequalities. 1 INTRODUCTION In this paper we consider the problem of controlling the rotational motion of a rigid body using three independent control torques. The minimal requirement on the controller is to stabilize the body about a specified orientation. In addition, we require the controller to guarantee that a quadratic performance index or cost b...