13,928 research outputs found
Stability and Performance Analysis of Systems Under Constraints
All real world control systems must deal with actuator and state constraints. Standard conic sector bounded nonlinearity stability theory provides methods for analyzing the stability and performance of systems under constraints, but it is well-known that these conditions can be very conservative. A method is developed to reduce conservatism in the analysis of constraints by representing them as nonlinear real parametric uncertainty
Robust model predictive control: robust control invariant sets and efficient implementation
Robust model predictive control (RMPC) is widely used in industry. However, the online computational burden of this algorithm restricts its development and application to systems with relatively slow dynamics. We investigate this problem in this thesis with the overall aim of reducing the online computational burden and improving the online efficiency.
In RMPC schemes, robust control invariant (RCI) sets are vitally important in dealing with constraints and providing stability. They can be used as terminal (invariant) sets in RMPC schemes to reduce the online computational burden and ensure stability simultaneously. To this end, we present a novel algorithm for the computation of full-complexity polytopic RCI sets, and the corresponding feedback control law, for linear discrete-time systems subject to output and initial state constraints, performance bounds, and bounded additive disturbances. Two types of uncertainty, structured norm-bounded and polytopic uncertainty, are considered. These algorithms are then extended to deal with systems subject to asymmetric initial state and output constraints.
Furthermore, the concept of RCI sets can be extended to invariant tubes, which are fundamental elements in tube based RMPC scheme. The online computational burden of tube based RMPC schemes is largely reduced to the same level as model predictive control for nominal systems. However, it is important that the constraint tightening that is needed is not excessive, otherwise the performance of the MPC design may deteriorate, and there may even not exist a feasible control law. Here, the algorithms we proposed for RCI set approximations are extended and applied to the problem of reducing the constraint tightening in tube based RMPC schemes.
In order to ameliorate the computational complexity of the online RMPC algorithms, we propose an online-offline RMPC method, where a causal state feedback structure on the controller is considered. In order to improve the efficiency of the online computation, we calculate the state feedback gain offline using a semi-definite program (SDP). Then we propose a novel method to compute the control perturbation component online. The online optimization problem is derived using Farkas' Theorem, and then approximated by a quadratic program (QP) to reduce the online computational burden. A further approximation is made to derive a simplified online optimization problem, which results in a large reduction in the number of variables.
Numerical examples are provided that demonstrate the advantages of all our proposed algorithms over current schemes.Open Acces
Model predictive control techniques for hybrid systems
This paper describes the main issues encountered when applying model predictive control to hybrid processes. Hybrid model predictive control (HMPC) is a research field non-fully developed with many open challenges. The paper describes some of the techniques proposed by the research community to overcome the main problems encountered. Issues related to the stability and the solution of the optimization problem are also discussed. The paper ends by describing the results of a benchmark exercise in which several HMPC schemes were applied to a solar air conditioning plant.Ministerio de Eduación y Ciencia DPI2007-66718-C04-01Ministerio de Eduación y Ciencia DPI2008-0581
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
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
On the Sample Size of Random Convex Programs with Structured Dependence on the Uncertainty (Extended Version)
The "scenario approach" provides an intuitive method to address chance
constrained problems arising in control design for uncertain systems. It
addresses these problems by replacing the chance constraint with a finite
number of sampled constraints (scenarios). The sample size critically depends
on Helly's dimension, a quantity always upper bounded by the number of decision
variables. However, this standard bound can lead to computationally expensive
programs whose solutions are conservative in terms of cost and violation
probability. We derive improved bounds of Helly's dimension for problems where
the chance constraint has certain structural properties. The improved bounds
lower the number of scenarios required for these problems, leading both to
improved objective value and reduced computational complexity. Our results are
generally applicable to Randomized Model Predictive Control of chance
constrained linear systems with additive uncertainty and affine disturbance
feedback. The efficacy of the proposed bound is demonstrated on an inventory
management example.Comment: Accepted for publication at Automatic
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