The authors present an approach for constructing optimal feedback control laws for regulation of a rotating rigid spacecraft. They 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. The authors give a characterization of (nonlinear) stability margins achieved with the inverse optimal control law.

In this paper we present some recent results on the description and control of the attitude motion of rotating rigid bodies We derive a new class of globally asymptotically stabilizing feedback control laws for the complete i e dynamics and kinematics attitude motion We show that the use of a Lyapunov function which involves the sum of a quadratic term in the angular velocities and a logarithmic term in the kinematic parameters leads to the design of linear controllers We also show that the feedback control laws for the kinematics minimize a quadratic cost in the state and control variables for all initial conditions For the complete system we construct a family of exponentially stabilizing control laws and we investigate their optimality characteristics The proposed control laws are given in terms of the classical Cayley Rodrigues parameters and the Modi ed Rodrigues parameters

This letter addresses the optimal covariance control problem for stochastic discrete-time linear systems subject to chance constraints. To the best of our knowledge, covariance steering problems with probabilistic chance constraints have not been discussed previously in the literature, although their treatment seems to be a natural extension. In this letter, we first show that, unlike the case with no chance constraints, the covariance steering problem with chance constraints cannot be decoupled to mean and covariance steering sub-problems. We then propose an approach to solve the covariance steering problem with chance constraints by converting it to a convex programming problem. The proposed algorithm is verified using a numerical example.

This work addresses the problem of vehicle path planning in the presence of obstacles and uncertainties, a fundamental robotics problem. While several path planning algorithms have been proposed over the years, many of them have dealt with only deterministic environments or with only open-loop uncertainty, i.e., the uncertainty of the system state is not controlled and, typically, increases with time due to exogenous disturbances. This may lead to potentially conservative nominal paths. The typical approach to deal with disturbances and reduce uncertainty is to use a lower-level feedback controller. We advocate the premise that, if a path planner can consider the closed-loop evolution of the system uncertainty, it can lead to less conservative, but still feasible, paths. To this end, in this work we develop an approach that is based on optimal covariance steering, which explicitly steers the state covariance for stochastic linear systems.We verify the proposed framework using extensive numerical simulations.