521 research outputs found
Data-driven Economic NMPC using Reinforcement Learning
Reinforcement Learning (RL) is a powerful tool to perform data-driven optimal
control without relying on a model of the system. However, RL struggles to
provide hard guarantees on the behavior of the resulting control scheme. In
contrast, Nonlinear Model Predictive Control (NMPC) and Economic NMPC (ENMPC)
are standard tools for the closed-loop optimal control of complex systems with
constraints and limitations, and benefit from a rich theory to assess their
closed-loop behavior. Unfortunately, the performance of (E)NMPC hinges on the
quality of the model underlying the control scheme. In this paper, we show that
an (E)NMPC scheme can be tuned to deliver the optimal policy of the real system
even when using a wrong model. This result also holds for real systems having
stochastic dynamics. This entails that ENMPC can be used as a new type of
function approximator within RL. Furthermore, we investigate our results in the
context of ENMPC and formally connect them to the concept of dissipativity,
which is central for the ENMPC stability. Finally, we detail how these results
can be used to deploy classic RL tools for tuning (E)NMPC schemes. We apply
these tools on both a classical linear MPC setting and a standard nonlinear
example from the ENMPC literature
Neural Networks for Fast Optimisation in Model Predictive Control: A Review
Model Predictive Control (MPC) is an optimal control algorithm with strong
stability and robustness guarantees. Despite its popularity in robotics and
industrial applications, the main challenge in deploying MPC is its high
computation cost, stemming from the need to solve an optimisation problem at
each control interval. There are several methods to reduce this cost. This
survey focusses on approaches where a neural network is used to approximate an
existing controller. Herein, relevant and unique neural approximation methods
for linear, nonlinear, and robust MPC are presented and compared. Comparisons
are based on the theoretical guarantees that are preserved, the factor by which
the original controller is sped up, and the size of problem that a framework is
applicable to. Research contributions include: a taxonomy that organises
existing knowledge, a summary of literary gaps, discussion on promising
research directions, and simple guidelines for choosing an approximation
framework. The main conclusions are that (1) new benchmarking tools are needed
to help prove the generalisability and scalability of approximation frameworks,
(2) future breakthroughs most likely lie in the development of ties between
control and learning, and (3) the potential and applicability of recently
developed neural architectures and tools remains unexplored in this field.Comment: 34 pages, 6 figures 3 tables. Submitted to ACM Computing Survey
Towards parallelizable sampling-based Nonlinear Model Predictive Control
This paper proposes a new sampling-based nonlinear model predictive control
(MPC) algorithm, with a bound on complexity quadratic in the prediction horizon
N and linear in the number of samples. The idea of the proposed algorithm is to
use the sequence of predicted inputs from the previous time step as a warm
start, and to iteratively update this sequence by changing its elements one by
one, starting from the last predicted input and ending with the first predicted
input. This strategy, which resembles the dynamic programming principle, allows
for parallelization up to a certain level and yields a suboptimal nonlinear MPC
algorithm with guaranteed recursive feasibility, stability and improved cost
function at every iteration, which is suitable for real-time implementation.
The complexity of the algorithm per each time step in the prediction horizon
depends only on the horizon, the number of samples and parallel threads, and it
is independent of the measured system state. Comparisons with the fmincon
nonlinear optimization solver on benchmark examples indicate that as the
simulation time progresses, the proposed algorithm converges rapidly to the
"optimal" solution, even when using a small number of samples.Comment: 9 pages, 9 pictures, submitted to IFAC World Congress 201
Nonlinear Model Predictive Control for Constrained Output Path Following
We consider the tracking of geometric paths in output spaces of nonlinear
systems subject to input and state constraints without pre-specified timing
requirements. Such problems are commonly referred to as constrained output
path-following problems. Specifically, we propose a predictive control approach
to constrained path-following problems with and without velocity assignments
and provide sufficient convergence conditions based on terminal regions and end
penalties. Furthermore, we analyze the geometric nature of constrained output
path-following problems and thereby provide insight into the computation of
suitable terminal control laws and terminal regions. We draw upon an example
from robotics to illustrate our findings.Comment: 12 pages, 4 figure
Shifting strategy for efficient block-based nonlinear model predictive control using real-time iterations
Nonlinear Model Predictive Control (NMPC) requires the use of efficient solutions and strategies for its implementation in fast/real-time systems. A popular approach for this is the Real Time Iteration (RTI) Scheme which uses a shifting strategy, namely the Initial Value Embedding (IVE), that shifts the solution from one sampling time to the next. However, this strategy together with other efficient strategies such as Move Blocking, present a recursive feasibility problem. This paper proposes a
novel modified shifting strategy which preserve both recursive feasibility and stability properties, as well as achieves a significant reduction in the computational burden associated with the optimisation. The proposed approach is validated through a simulation of an inverted pendulum where it clearly outperforms other standard solutions in terms of performance and recursive feasibility properties. Additionally, the approach was tested on two computing platforms: a laptop with an i7 processor and a Beaglebone Blue Linux-based computer for robotic systems, where computational gains compared to existing approaches are shown to be as high as 100 times faster
Nonlinear Model Predictive Control of Robotic Systems with Control Lyapunov Functions
The theoretical unification of Nonlinear Model Predictive Control (NMPC) with Control Lyapunov Functions (CLFs) provides a framework for achieving optimal control performance while ensuring stability guarantees. In this paper we present the first real-time realization of a unified NMPC and CLF controller on a robotic system with limited computational resources. These limitations motivate a set of approaches for efficiently incorporating CLF stability constraints into a general NMPC formulation. We evaluate the performance of the proposed methods compared to baseline CLF and NMPC controllers with a robotic Segway platform both in simulation and on hardware. The addition of a prediction horizon provides a performance advantage over CLF based controllers, which operate optimally point-wise in time. Moreover, the explicitly imposed stability constraints remove the need for difficult cost function and parameter tuning required by NMPC. Therefore the unified controller improves the performance of each isolated controller and simplifies the overall design process
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