Nominally Robust Model Predictive Control With State Constraints

Grimm, G.; Messina, Michael J.; Tuna, S. Emre; Teel, Andrew R.

doi:10.1109/tac.2007.906187

Cited by 98 publications

(49 citation statements)

References 17 publications

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“…is an equilibrium point for systems (18) and with X f containing the origin as an interior point. In order to define the terminal set and the terminal penalty, one needs to introduce an auxiliary control law κ i f (e i ) that can be…”

Section: Model Predictive Controllermentioning

confidence: 99%

MPC for Robot Manipulators With Integral Sliding Modes Generation

Incremona

Ferrara

Magni

2017

IEEE/ASME Trans. Mechatron.

136

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Abstract-This paper deals with the design of a robust hierarchical multi-loop control scheme to solve motion control problems for robot manipulators. The key elements of the proposed control approach are the inverse dynamics-based feedback linearized robotic MIMO system and the combination of a Model Predictive Control (MPC) module with an Integral Sliding Mode (ISM) controller. The ISM internal control loop has the role to compensate the matched uncertainties due to unmodelled dynamics, which are not rejected by the inverse dynamics approach. The external loop is closed relying on the MPC, which guarantees an optimal evolution of the controlled system while fulfilling state and input constraints. The motivation for using ISM, apart from its property of providing robustness to the scheme with respect to a wide class of uncertainties, is also given by its capability of enforcing sliding modes of the controlled system since the initial time instant, allowing one to solve the model predictive control optimization problem relying on a set of linearized decoupled SISO systems which are not affected by uncertain terms. The proposal has been verified and validated in simulation, relying on a model of a COMAU Smart3-S2 industrial robot manipulator, identified on the basis of real data.Index Terms-Model predictive control, integral sliding mode, robot manipulators, uncertain systems.

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Section: Model Predictive Controllermentioning

confidence: 99%

MPC for Robot Manipulators With Integral Sliding Modes Generation

Incremona

Ferrara

Magni

2017

IEEE/ASME Trans. Mechatron.

136

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“…Using convexity ofP j ∩ S r , and the explicit form of X f as in (11), (35) can be written in terms of the vertices of each polytopeP j ∩ S r , j ∈ {1, . .…”

Section: B Positive Invariance Of X Fmentioning

confidence: 99%

Approximation of explicit model predictive control using regular piecewise affine functions: an input-to-state stability approach

Genuit

Heemels

2012

IET Control Theory &Amp; Applications

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Piecewise affine (PWA) feedback control laws defined on general polytopic partitions, as for instance obtained by explicit MPC, will often be prohibitively complex for fast systems. In this work we study the problem of approximating these high-complexity controllers by low-complexity PWA control laws defined on more regular partitions, facilitating faster on-line evaluation. The approach is based on the concept of input-to-state stability (ISS). In particular, the existence of an ISS Lyapunov function (LF) is exploited to obtain a priori conditions that guarantee asymptotic stability and constraint satisfaction of the approximate low-complexity controller. These conditions can be expressed as local semidefinite programs (SDPs) or linear programs (LPs), in case of 2-norm or 1, ∞-norm based ISS, respectively, and apply to PWA plants. In addition, as ISS is a prerequisite for our approximation method, we provide two tractable computational methods for deriving the necessary ISS inequalities from nominal stability. A numerical example is provided that illustrates the main results.The authors are with the Hybrid and

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“…On one hand, nominal robustness to measurement noise of an MPC feedback was already established in Grimm et al (2003) for discrete-time systems, and in Findeisen et al (2003) for sampled-data implementations. However, Tuna et al (2005) demonstrates that as the sampling frequency becomes arbitrarily fast, the margin of this robustness may approach zero.…”

Section: Robustness Considerationsmentioning

confidence: 99%