Model Predictive Regulation

We show how optimal nonlinear regulation can be achieved in a model predictive control fashion

Generalized splines in ℝn and optimal control

We give a new time-dependent definition of spline curves in ℝn, which extends a recent definition of vector-valued splines introduced by Rodrigues and Silva Leite for the time-independent case. Previous results are based on a variational approach, with lengthy arguments, which do not cover the non-autonomous situation. We show that the previous results are a consequence of the Pontryagin maximum principle, and are easily generalized using the methods of optimal control. Main result asserts that vector-valued splines are related to the Pontryagin extremals of a non-autonomous linear-quadratic optimal control problem

The extended symplectic pencil and the finite-horizon LQ problem with two-sided boundary conditions

This note introduces a new analytic approach to the solution of a very general class of finite-horizon optimal control problems formulated for discrete-time systems. This approach provides a parametric expression for the optimal control sequences, as well as the corresponding optimal state trajectories, by exploiting a new decomposition of the so-called extended symplectic pencil. Importantly, the results established in this paper hold under assumptions that are weaker than the ones considered in the literature so far. Indeed, this approach does not require neither the regularity of the symplectic pencil, nor the modulus controllability of the underlying system. In the development of the approach presented in this paper, several ancillary results of independent interest on generalised Riccati equations and on the eigenstructure of the extended symplectic pencil will also be presented

Generation of dynamic motion for anthropomorphic systems under prioritized equality and inequality constraints

In this paper, we propose a solution to compute full-dynamic motions for a humanoid robot, accounting for various kinds of constraints such as dynamic balance or joint limits. As a first step, we propose a unification of task-based control schemes, in inverse kinematics or inverse dynamics. Based on this unification, we generalize the cascade of quadratic programs that were developed for inverse kinematics only. Then, we apply the solution to generate, in simulation, wholebody motions for a humanoid robot in unilateral contact with the ground, while ensuring the dynamic balance on a non horizontal surface