62,509 research outputs found
A Discrete Geometric Optimal Control Framework for Systems with Symmetries
This paper studies the optimal motion control of
mechanical systems through a discrete geometric approach. At
the core of our formulation is a discrete Lagrange-d’Alembert-
Pontryagin variational principle, from which are derived discrete
equations of motion that serve as constraints in our optimization
framework. We apply this discrete mechanical approach to
holonomic systems with symmetries and, as a result, geometric
structure and motion invariants are preserved. We illustrate our
method by computing optimal trajectories for a simple model of
an air vehicle flying through a digital terrain elevation map, and
point out some of the numerical benefits that ensue
An Improved Constraint-Tightening Approach for Stochastic MPC
The problem of achieving a good trade-off in Stochastic Model Predictive
Control between the competing goals of improving the average performance and
reducing conservativeness, while still guaranteeing recursive feasibility and
low computational complexity, is addressed. We propose a novel, less
restrictive scheme which is based on considering stability and recursive
feasibility separately. Through an explicit first step constraint we guarantee
recursive feasibility. In particular we guarantee the existence of a feasible
input trajectory at each time instant, but we only require that the input
sequence computed at time remains feasible at time for most
disturbances but not necessarily for all, which suffices for stability. To
overcome the computational complexity of probabilistic constraints, we propose
an offline constraint-tightening procedure, which can be efficiently solved via
a sampling approach to the desired accuracy. The online computational
complexity of the resulting Model Predictive Control (MPC) algorithm is similar
to that of a nominal MPC with terminal region. A numerical example, which
provides a comparison with classical, recursively feasible Stochastic MPC and
Robust MPC, shows the efficacy of the proposed approach.Comment: Paper has been submitted to ACC 201
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