43 research outputs found
Explicit Reference Governor for Continuous Time Nonlinear Systems Subject to Convex Constraints
This paper introduces a novel closed-form strategy that dynamically modifies
the reference of a pre-compensated nonlinear system to ensure the satisfaction
of a set of convex constraints. The main idea consists of translating
constraints in the state space into constraints on the Lyapunov function and
then modulating the reference velocity so as to limit the value of the Lyapunov
function. The theory is introduced for general nonlinear systems subject to
convex constraints. In the case of polyhedric constraints, an explicit solution
is provided for the large and highly relevant class of nonlinear systems whose
Lyapunov function is lower-bounded by a quadratic form. In view of improving
performances, further specializations are provided for the relevant cases of
linear systems and robotic manipulators.Comment: Submitted to: IEEE Transactions on Automatic Contro
How to solve Quantum Optimal Control Problems using Projection Operator-based Newton Steps
The Quantum PRojection Operator-based Newton method for Trajectory
Optimization, a.k.a. Q-PRONTO, is a numerical method for solving quantum
optimal control problems. This paper significantly improves prior versions of
the quantum projection operator by introducing a regulator that stabilizes the
solution estimate at every iteration. This modification is shown to not only
improve the convergence rate of the algorithm, but also steer the solver
towards better local minima compared to the un-regulated case. Numerical
examples showcase Q-PRONTO can be used to solve multi-input quantum optimal
control problems featuring time-varying costs and undesirable populations that
ought to be avoided during the transient.Comment: 10 pages, 9 figure
Attitude Trajectory Optimization and Momentum Conservation with Control Moment Gyroscopes
In this work, we develop a numerically tractable trajectory optimization
problem for rest-to-rest attitude transfers with CMG-driven spacecraft. First,
we adapt a specialized dynamical model which avoids many of the numerical
challenges (singularities) introduced by common dynamical approximations. To
formulate and solve our specialized trajectory optimization problem, we design
a locally stabilizing Linear Quadratic (LQ) regulator on the system's
configuration manifold then lift it into the ambient state space to produce
suitable terminal and running LQ cost functionals. Finally, we examine the
performance benefits and drawbacks of solutions to this optimization problem
via the PRONTO solver and find significant improvements in maneuver time,
terminal state accuracy, and total control effort. This analysis also
highlights a critical shortcoming for objective functions which penalize only
the norm of the control input rather than electrical power usage.Comment: 8 pages, 6 figures, IFAC 2023 conference submissio
A Feasibility Governor for Enlarging the Region of Attraction of Linear Model Predictive Controllers
This paper proposes a method for enlarging the region of attraction of Linear
Model Predictive Controllers (MPC) when tracking piecewise-constant references
in the presence of pointwise-in-time constraints. It consists of an add-on
unit, the Feasibility Governor (FG), that manipulates the reference command so
as to ensure that the optimal control problem that underlies the MPC feedback
law remains feasible. Offline polyhedral projection algorithms based on
multi-objective linear programming are employed to compute the set of feasible
states and reference commands. Online, the action of the FG is computed by
solving a convex quadratic program. The closed-loop system is shown to satisfy
constraints, be asymptotically stable, exhibit zero-offset tracking, and
display finite-time convergence of the reference
A Machine-Designed Optical Lattice Atom Interferometer
Performing interferometry in an optical lattice formed by standing waves of
light offers potential advantages over its free-space equivalents since the
atoms can be confined and manipulated by the optical potential. We demonstrate
such an interferometer in a one dimensional lattice and show the ability to
control the atoms by imaging and reconstructing the wavefunction at many stages
during its cycle. An acceleration signal is applied and the resulting
performance is seen to be close to the optimum possible for the time-space area
enclosed according to quantum theory. Our methodology of machine design enables
the sensor to be reconfigurable on the fly, and when scaled up, offers the
potential to make state-of-the art inertial and gravitational sensors that will
have a wide range of potential applications
Invariant Set Distributed Explicit Reference Governors for Provably Safe On-Board Control of Nano-Quadrotor Swarms
This article provides a theory for provably safe and computationally efficient distributed constrained control, and describes an application to a swarm of nano-quadrotors with limited on-board hardware and subject to multiple state and input constraints. We provide a formal extension of the explicit reference governor framework to address the case of distributed systems. The efficacy, robustness, and scalability of the proposed theory is demonstrated by an extensive experimental validation campaign and a comparative simulation study on single and multiple nano-quadrotors. The control strategy is implemented in real-time on-board palm-sized unmanned erial vehicles, and achieves safe swarm coordination without relying on any offline trajectory computations