10,907 research outputs found
Robust Temporal Logic Model Predictive Control
Control synthesis from temporal logic specifications has gained popularity in
recent years. In this paper, we use a model predictive approach to control
discrete time linear systems with additive bounded disturbances subject to
constraints given as formulas of signal temporal logic (STL). We introduce a
(conservative) computationally efficient framework to synthesize control
strategies based on mixed integer programs. The designed controllers satisfy
the temporal logic requirements, are robust to all possible realizations of the
disturbances, and optimal with respect to a cost function. In case the temporal
logic constraint is infeasible, the controller satisfies a relaxed, minimally
violating constraint. An illustrative case study is included.Comment: This work has been accepted to appear in the proceedings of 53rd
Annual Allerton Conference on Communication, Control and Computing,
Urbana-Champaign, IL (2015
Bayesian model predictive control: Efficient model exploration and regret bounds using posterior sampling
Tight performance specifications in combination with operational constraints
make model predictive control (MPC) the method of choice in various industries.
As the performance of an MPC controller depends on a sufficiently accurate
objective and prediction model of the process, a significant effort in the MPC
design procedure is dedicated to modeling and identification. Driven by the
increasing amount of available system data and advances in the field of machine
learning, data-driven MPC techniques have been developed to facilitate the MPC
controller design. While these methods are able to leverage available data,
they typically do not provide principled mechanisms to automatically trade off
exploitation of available data and exploration to improve and update the
objective and prediction model. To this end, we present a learning-based MPC
formulation using posterior sampling techniques, which provides finite-time
regret bounds on the learning performance while being simple to implement using
off-the-shelf MPC software and algorithms. The performance analysis of the
method is based on posterior sampling theory and its practical efficiency is
illustrated using a numerical example of a highly nonlinear dynamical
car-trailer system
Intermittent predictive control of an inverted pendulum
Intermittent predictive pole-placement control is successfully applied to the constrained-state control of a prestabilised experimental inverted pendulum
Robust Model Predictive Control via Scenario Optimization
This paper discusses a novel probabilistic approach for the design of robust
model predictive control (MPC) laws for discrete-time linear systems affected
by parametric uncertainty and additive disturbances. The proposed technique is
based on the iterated solution, at each step, of a finite-horizon optimal
control problem (FHOCP) that takes into account a suitable number of randomly
extracted scenarios of uncertainty and disturbances, followed by a specific
command selection rule implemented in a receding horizon fashion. The scenario
FHOCP is always convex, also when the uncertain parameters and disturbance
belong to non-convex sets, and irrespective of how the model uncertainty
influences the system's matrices. Moreover, the computational complexity of the
proposed approach does not depend on the uncertainty/disturbance dimensions,
and scales quadratically with the control horizon. The main result in this
paper is related to the analysis of the closed loop system under
receding-horizon implementation of the scenario FHOCP, and essentially states
that the devised control law guarantees constraint satisfaction at each step
with some a-priori assigned probability p, while the system's state reaches the
target set either asymptotically, or in finite time with probability at least
p. The proposed method may be a valid alternative when other existing
techniques, either deterministic or stochastic, are not directly usable due to
excessive conservatism or to numerical intractability caused by lack of
convexity of the robust or chance-constrained optimization problem.Comment: This manuscript is a preprint of a paper accepted for publication in
the IEEE Transactions on Automatic Control, with DOI:
10.1109/TAC.2012.2203054, and is subject to IEEE copyright. The copy of
record will be available at http://ieeexplore.ieee.or
Real-Time Motion Planning of Legged Robots: A Model Predictive Control Approach
We introduce a real-time, constrained, nonlinear Model Predictive Control for
the motion planning of legged robots. The proposed approach uses a constrained
optimal control algorithm known as SLQ. We improve the efficiency of this
algorithm by introducing a multi-processing scheme for estimating value
function in its backward pass. This pass has been often calculated as a single
process. This parallel SLQ algorithm can optimize longer time horizons without
proportional increase in its computation time. Thus, our MPC algorithm can
generate optimized trajectories for the next few phases of the motion within
only a few milliseconds. This outperforms the state of the art by at least one
order of magnitude. The performance of the approach is validated on a quadruped
robot for generating dynamic gaits such as trotting.Comment: 8 page
On Stochastic Model Predictive Control with Bounded Control Inputs
This paper is concerned with the problem of Model Predictive Control and
Rolling Horizon Control of discrete-time systems subject to possibly unbounded
random noise inputs, while satisfying hard bounds on the control inputs. We use
a nonlinear feedback policy with respect to noise measurements and show that
the resulting mathematical program has a tractable convex solution in both
cases. Moreover, under the assumption that the zero-input and zero-noise system
is asymptotically stable, we show that the variance of the state, under the
resulting Model Predictive Control and Rolling Horizon Control policies, is
bounded. Finally, we provide some numerical examples on how certain matrices in
the underlying mathematical program can be calculated off-line.Comment: 8 page
Stochastic MPC Design for a Two-Component Granulation Process
We address the issue of control of a stochastic two-component granulation
process in pharmaceutical applications through using Stochastic Model
Predictive Control (SMPC) and model reduction to obtain the desired particle
distribution. We first use the method of moments to reduce the governing
integro-differential equation down to a nonlinear ordinary differential
equation (ODE). This reduced-order model is employed in the SMPC formulation.
The probabilistic constraints in this formulation keep the variance of
particles' drug concentration in an admissible range. To solve the resulting
stochastic optimization problem, we first employ polynomial chaos expansion to
obtain the Probability Distribution Function (PDF) of the future state
variables using the uncertain variables' distributions. As a result, the
original stochastic optimization problem for a particulate system is converted
to a deterministic dynamic optimization. This approximation lessens the
computation burden of the controller and makes its real time application
possible.Comment: American control Conference, May, 201
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