2,678 research outputs found
Stability Analysis of Piecewise Affine Systems with Multi-model Model Predictive Control
Constrained model predictive control (MPC) is a widely used control strategy,
which employs moving horizon-based on-line optimisation to compute the optimum
path of the manipulated variables. Nonlinear MPC can utilize detailed models
but it is computationally expensive; on the other hand linear MPC may not be
adequate. Piecewise affine (PWA) models can describe the underlying nonlinear
dynamics more accurately, therefore they can provide a viable trade-off through
their use in multi-model linear MPC configurations, which avoid integer
programming. However, such schemes may introduce uncertainty affecting the
closed loop stability. In this work, we propose an input to output stability
analysis for closed loop systems, consisting of PWA models, where an observer
and multi-model linear MPC are applied together, under unstructured
uncertainty. Integral quadratic constraints (IQCs) are employed to assess the
robustness of MPC under uncertainty. We create a model pool, by performing
linearisation on selected transient points. All the possible uncertainties and
nonlinearities (including the controller) can be introduced in the framework,
assuming that they admit the appropriate IQCs, whilst the dissipation
inequality can provide necessary conditions incorporating IQCs. We demonstrate
the existence of static multipliers, which can reduce the conservatism of the
stability analysis significantly. The proposed methodology is demonstrated
through two engineering case studies.Comment: 28 pages 9 figure
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
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
Stochastic model predictive control for constrained networked control systems with random time delay
In this paper the continuous time stochastic constrained optimal control problem is formulated for the class of networked control systems assuming that time delays follow a discrete-time, finite Markov chain . Polytopic overapproximations of the system's trajectories are employed to produce a polyhedral inner approximation of the non-convex constraint set resulting from imposing the constraints in continuous time. The problem is cast in a Markov jump linear systems (MJLS) framework and a stochastic MPC controller is calculated explicitly, oine, coupling dynamic programming with parametric piecewise quadratic (PWQ) optimization. The calculated control law leads to stochastic stability of the closed loop system, in the mean square sense and respects the state and input constraints in continuous time
Robust explicit MPC design under finite precision arithmetic
We propose a design methodology for explicit Model Predictive Control (MPC) that guarantees hard constraint satisfaction in the presence of finite precision arithmetic errors. The implementation of complex digital control techniques, like MPC, is becoming increasingly adopted in embedded systems, where reduced precision computation techniques are embraced to achieve fast execution and low power consumption. However, in a low precision implementation, constraint satisfaction is not guaranteed if infinite precision is assumed during the algorithm design. To enforce constraint satisfaction under numerical errors, we use forward error analysis to compute an error bound on the output of the embedded controller. We treat this error as a state disturbance and use this to inform the design of a constraint-tightening robust controller. Benchmarks with a classical control problem, namely an inverted pendulum, show how it is possible to guarantee, by design, constraint satisfaction for embedded systems featuring low precision, fixed-point computations
An Extended Kalman Filter for Data-enabled Predictive Control
The literature dealing with data-driven analysis and control problems has
significantly grown in the recent years. Most of the recent literature deals
with linear time-invariant systems in which the uncertainty (if any) is assumed
to be deterministic and bounded; relatively little attention has been devoted
to stochastic linear time-invariant systems. As a first step in this direction,
we propose to equip the recently introduced Data-enabled Predictive Control
algorithm with a data-based Extended Kalman Filter to make use of additional
available input-output data for reducing the effect of noise, without
increasing the computational load of the optimization procedure
Feedback min-max model predictive control using a single linear program: robust stability and the explicit solution
In this paper we introduce a new stage cost and show that the use of this cost allows one to formulate a robustly stable feedback min-max model predictive control problem that can be solved using a single linear program. Furthermore, this is a multi-parametric linear program, which implies that the optimal control law is piecewise affine, and can be explicitly pre-computed so that the linear program does not have to be solved on-line. We assume that the plant model is known, is discrete-time and linear time-invariant, is subject to unknown but bounded state disturbances and that the states of the system are measured. Two numerical examples are presented; one of these is taken from the literature, so that a direct comparison of solutions and computational complexity with earlier proposals is possible. This is a preprint of an article published in International Journal of Robust and Nonlinea
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