38,747 research outputs found
Fast Non-Parametric Learning to Accelerate Mixed-Integer Programming for Online Hybrid Model Predictive Control
Today's fast linear algebra and numerical optimization tools have pushed the
frontier of model predictive control (MPC) forward, to the efficient control of
highly nonlinear and hybrid systems. The field of hybrid MPC has demonstrated
that exact optimal control law can be computed, e.g., by mixed-integer
programming (MIP) under piecewise-affine (PWA) system models. Despite the
elegant theory, online solving hybrid MPC is still out of reach for many
applications. We aim to speed up MIP by combining geometric insights from
hybrid MPC, a simple-yet-effective learning algorithm, and MIP warm start
techniques. Following a line of work in approximate explicit MPC, the proposed
learning-control algorithm, LNMS, gains computational advantage over MIP at
little cost and is straightforward for practitioners to implement
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
Learning an Approximate Model Predictive Controller with Guarantees
A supervised learning framework is proposed to approximate a model predictive
controller (MPC) with reduced computational complexity and guarantees on
stability and constraint satisfaction. The framework can be used for a wide
class of nonlinear systems. Any standard supervised learning technique (e.g.
neural networks) can be employed to approximate the MPC from samples. In order
to obtain closed-loop guarantees for the learned MPC, a robust MPC design is
combined with statistical learning bounds. The MPC design ensures robustness to
inaccurate inputs within given bounds, and Hoeffding's Inequality is used to
validate that the learned MPC satisfies these bounds with high confidence. The
result is a closed-loop statistical guarantee on stability and constraint
satisfaction for the learned MPC. The proposed learning-based MPC framework is
illustrated on a nonlinear benchmark problem, for which we learn a neural
network controller with guarantees.Comment: 6 pages, 3 figures, to appear in IEEE Control Systems Letter
A Real-time Nonlinear Model Predictive Controller for Yaw Motion Optimization of Distributed Drive Electric Vehicles
This paper proposes a real-time nonlinear model
predictive control (NMPC) strategy for direct yaw moment control
(DYC) of distributed drive electric vehicles (DDEVs). The NMPC
strategy is based on a control-oriented model built by integrating
a single track vehicle model with the Magic Formula (MF) tire
model. To mitigate the NMPC computational cost, the
continuation/generalized minimal residual (C/GMRES) algorithm
is employed and modified for real-time optimization. Since the
traditional C/GMRES algorithm cannot directly solve the
inequality constraint problem, the external penalty method is
introduced to transform inequality constraints into an
equivalently unconstrained optimization problem. Based on the
Pontryagin’s minimum principle (PMP), the existence and
uniqueness for solution of the proposed C/GMRES algorithm are
proven. Additionally, to achieve fast initialization in C/GMRES
algorithm, the varying predictive duration is adopted so that the
analytic expressions of optimally initial solutions in C/GMRES
algorithm can be derived and gained. A Karush-Kuhn-Tucker
(KKT) condition based control allocation method distributes the
desired traction and yaw moment among four independent
motors. Numerical simulations are carried out by combining
CarSim and Matlab/Simulink to evaluate the effectiveness of the
proposed strategy. Results demonstrate that the real-time NMPC
strategy can achieve superior vehicle stability performance,
guarantee the given safety constraints, and significantly reduce the
computational efforts
Explicit model predictive control accuracy analysis
Model Predictive Control (MPC) can efficiently control constrained systems in
real-time applications. MPC feedback law for a linear system with linear
inequality constraints can be explicitly computed off-line, which results in an
off-line partition of the state space into non-overlapped convex regions, with
affine control laws associated to each region of the partition. An actual
implementation of this explicit MPC in low cost micro-controllers requires the
data to be "quantized", i.e. represented with a small number of memory bits. An
aggressive quantization decreases the number of bits and the controller
manufacturing costs, and may increase the speed of the controller, but reduces
accuracy of the control input computation. We derive upper bounds for the
absolute error in the control depending on the number of quantization bits and
system parameters. The bounds can be used to determine how many quantization
bits are needed in order to guarantee a specific level of accuracy in the
control input.Comment: 6 pages, 7 figures. Accepted to IEEE CDC 201
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