Kalman-Filter-Based Unconstrained and Constrained Extremum-Seeking Guidance on SO(3)

Abstract

Extremum-seeking guidance endeavors to drive the output of a system to the extremum of an unknown objective function. This paper proposes an extremum-seeking guidance algorithm on SO3 for cases with and without inclusion and exclusion zones. The gradient of the unknown objective function is estimated via a Kalman filter so that the extremum of the objective function can be approximated. To satisfy inclusion and exclusion zone constraints, two different constrained Kalman filters are proposed. The first Kalman filter is a gain-projected Kalman filter, and the second is a novel linear matrix inequality based Kalman filter that is able to accommodate a larger class of constraints. The proposed extremum-seeking guidance algorithm is demonstrated using a performance objective that relates a spacecraft's attitude to received power of an unknown radiation source using a patch antenna.

Extremum Seeking Control for a Class of Nonholonomic Systems

“…R is globally asymptotically stable for (25). Using that r 3 is positive, one can also show that the compact subset Θ := S 1 × {0} of T S 1 is input-to-state stable for (26) with (27) as "inputs". We refer to [21] for a definition of input-to-state stability with respect to compact sets.…”

“…On the other hand, measurements of the system state are not assumed to be available. Research on this type of optimization problem is motivated by various applications, such as spacecraft attitude optimization [27], optimal alignment of solar panels [20], and environmental source seeking [14].…”

Model Predictive Control of a Tandem-Rotor Helicopter With a Nonuniformly Spaced Prediction Horizon

“…where Q = Q T ≥ 0 is the state penalty matrix, R = R T > 0 is the control input penalty matrix, and P = P T ≥ 0 is the terminal state penalty matrix. Writing (15) in matrix form, the constrained optimization problem is expressed as a QP min…”

“…The MPC formulation features control input and state constraints. The second contribution is the inclusion of an attitude keep-in zone [15] and an 1 -norm [16] constraint on the attitude error, which together enforce attitude constraint satisfaction.…”

Attitude optimization by extremum seeking for rigid bodies actuated by internal rotors only

“…Many different stabilizing control laws have been proposed and analyzed over the past decades. The problem of stabilizing relative equilibria (i.e., motions with constant velocity) is investigated, for example, in, 39‐41 and the problem of stabilizing states with zero velocity is investigated, for example, in References 42‐45. Implementations of the existing methods to stabilize relative equilibria require measurements of the velocity, and methods to stabilize states with zero velocity require measurements of the entire system state and knowledge of the desired configuration.…”