9,485 research outputs found
A Family of Iterative Gauss-Newton Shooting Methods for Nonlinear Optimal Control
This paper introduces a family of iterative algorithms for unconstrained
nonlinear optimal control. We generalize the well-known iLQR algorithm to
different multiple-shooting variants, combining advantages like
straight-forward initialization and a closed-loop forward integration. All
algorithms have similar computational complexity, i.e. linear complexity in the
time horizon, and can be derived in the same computational framework. We
compare the full-step variants of our algorithms and present several simulation
examples, including a high-dimensional underactuated robot subject to contact
switches. Simulation results show that our multiple-shooting algorithms can
achieve faster convergence, better local contraction rates and much shorter
runtimes than classical iLQR, which makes them a superior choice for nonlinear
model predictive control applications.Comment: 8 page
Robust nonlinear receding horizon control with constraint tightening: off line approximation and application to networked control system
2007/2008Nonlinear Receding Horizon (RH) control, also known as moving horizon control or nonlinear
Model Predictive Control (MPC), refers to a class of algorithms that make explicit use of a
nonlinear process model to optimize the plant behavior, by computing a sequence of future ma-
nipulated variable adjustments. Usually the optimal control sequence is obtained by minimizing
a multi-stage cost functional on the basis of open-loop predictions. The presence of uncertainty
in the model used for the optimization raises the question of robustness, i.e., the maintenance
of certain properties such as stability and performance in the presence of uncertainty.
The need for guaranteeing the closed-loop stability in presence of uncertainties motivates
the conception of robust nonlinear MPC, in which the perturbations are explicitly taken in
account in the design of the controller. When the nature of the uncertainty is know, and it is
assumed to be bounded in some compact set, the robust RH control can be determined, in a
natural way, by solving a min–max optimal control problem, that is, the performance objective
is optimized for the worst-case scenario. However, the use of min-max techniques is limited
by the high computational burden required to solve the optimization problem. In the case of
constrained system, a possibility to ensure the robust constraint satisfaction and the closed-loop
stability without resorting to min-max optimization consists in imposing restricted (tightened)
constraints on the the predicted trajectories during the optimization.
In this framework, an MPC scheme with constraint tightening for discrete-time nonlinear
systems affected by state-dependent and norm bounded uncertainties is proposed and discussed.
A novel method to tighten the constraints relying on the nominal state prediction is described,
leading to less conservative set contractions than in the existing approaches. Moreover, by
imposing a stabilizing state constraint at the end of the control horizon (in place of the usual
terminal one placed at the end of the prediction horizon), less stringent assumptions can be posed on the terminal region, while improving the robust stability properties of the MPC closed-loop
system.
The robust nonlinear MPC formulation with tightened constraints is then used to design off-
line approximate feedback laws able to guarantee the practical stability of the closed-loop system.
By using off-line approximations, the computational burden due to the on-line optimization is
removed, thus allowing for the application of the MPC to systems with fast dynamics. In this
framework, we will also address the problem of approximating possibly discontinuous feedback
functions, thus overcoming the limitation of existent approximation scheme which assume the
continuity of the RH control law (whereas this condition is not always verified in practice, due
to both nonlinearities and constraints).
Finally, the problem of stabilizing constrained systems with networked unreliable (and de-
layed) feedback and command channels is also considered. In order to satisfy the control ob-
jectives for this class of systems, also referenced to as Networked Control Systems (NCS’s), a
control scheme based on the combined use of constraint tightening MPC with a delay compen-
sation strategy will be proposed and analyzed.
The stability properties of all the aforementioned MPC schemes are characterized by using
the regional Input-to-State Stability (ISS) tool. The ISS approach allows to analyze the depen-
dence of state trajectories of nonlinear systems on the magnitude of inputs, which can represent
control variables or disturbances. Typically, in MPC the ISS property is characterized in terms
of Lyapunov functions, both for historical and practical reasons, since the optimal finite horizon
cost of the optimization problem can be easily used for this task. Note that, in order to study
the ISS property of MPC closed-loop systems, global results are in general not useful because,
due to the presence of state and input constraints, it is impossible to establish global bounds for
the multi-stage cost used as Lyapunov function. On the other hand local results do not allow to
analyze the properties of the predictive control law in terms of its region of attraction. There-
fore, regional ISS results have to employed for MPC controlled systems. Moreover, in the case of
NCS, the resulting control strategy yields to a time-varying closed-loop system, whose stability
properties can be analyzed using a novel regional ISS characterization in terms of time-varying
Lyapunov functions.XXI Ciclo198
Stochastic Model Predictive Control with Discounted Probabilistic Constraints
This paper considers linear discrete-time systems with additive disturbances,
and designs a Model Predictive Control (MPC) law to minimise a quadratic cost
function subject to a chance constraint. The chance constraint is defined as a
discounted sum of violation probabilities on an infinite horizon. By penalising
violation probabilities close to the initial time and ignoring violation
probabilities in the far future, this form of constraint enables the
feasibility of the online optimisation to be guaranteed without an assumption
of boundedness of the disturbance. A computationally convenient MPC
optimisation problem is formulated using Chebyshev's inequality and we
introduce an online constraint-tightening technique to ensure recursive
feasibility based on knowledge of a suboptimal solution. The closed loop system
is guaranteed to satisfy the chance constraint and a quadratic stability
condition.Comment: 6 pages, Conference Proceeding
Performance-oriented model learning for data-driven MPC design
Model Predictive Control (MPC) is an enabling technology in applications
requiring controlling physical processes in an optimized way under constraints
on inputs and outputs. However, in MPC closed-loop performance is pushed to the
limits only if the plant under control is accurately modeled; otherwise, robust
architectures need to be employed, at the price of reduced performance due to
worst-case conservative assumptions. In this paper, instead of adapting the
controller to handle uncertainty, we adapt the learning procedure so that the
prediction model is selected to provide the best closed-loop performance. More
specifically, we apply for the first time the above "identification for
control" rationale to hierarchical MPC using data-driven methods and Bayesian
optimization.Comment: Accepted for publication in the IEEE Control Systems Letters (L-CSS
Robust MPC of constrained nonlinear systems based on interval arithmetic
A robust MPC for constrained discrete-time nonlinear systems with additive
uncertainties is presented. The proposed controller is based on the concept of reachable sets, that
is, the sets that contain the predicted evolution of the uncertain system for all possible uncertainties.
If processes are nonlinear these sets are very difficult to compute. A conservative approximation
based on interval arithmetic is proposed for the online computation of these sets. This technique
provides good results with a computational effort only slightly greater than the one corresponding to
the nominal prediction. These sets are incorporated into the MPC formulation to achieve robust
stability. By choosing a robust positively invariant set as a terminal constraint, a robustly stabilising
controller is obtained. Stability is guaranteed in the case of suboptimality of the computed solution.
The proposed controller is applied to a continuous stirred tank reactor with an exothermic reaction.Ministerio de Ciencia y TecnologÃa DPI-2001-2380-03- 01Ministerio de Ciencia y TecnologÃa DPI-2002-4375-C02-0
Koopman operator-based model reduction for switched-system control of PDEs
We present a new framework for optimal and feedback control of PDEs using
Koopman operator-based reduced order models (K-ROMs). The Koopman operator is a
linear but infinite-dimensional operator which describes the dynamics of
observables. A numerical approximation of the Koopman operator therefore yields
a linear system for the observation of an autonomous dynamical system. In our
approach, by introducing a finite number of constant controls, the dynamic
control system is transformed into a set of autonomous systems and the
corresponding optimal control problem into a switching time optimization
problem. This allows us to replace each of these systems by a K-ROM which can
be solved orders of magnitude faster. By this approach, a nonlinear
infinite-dimensional control problem is transformed into a low-dimensional
linear problem. In situations where the Koopman operator can be computed
exactly using Extended Dynamic Mode Decomposition (EDMD), the proposed approach
yields optimal control inputs. Furthermore, a recent convergence result for
EDMD suggests that the approach can be applied to more complex dynamics as
well. To illustrate the results, we consider the 1D Burgers equation and the 2D
Navier--Stokes equations. The numerical experiments show remarkable performance
concerning both solution times and accuracy.Comment: arXiv admin note: text overlap with arXiv:1801.0641
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