On feasible sets for MPC and their approximations

Scibilia, Francesco; Olaru, Sorin; Hovd, Morten

doi:10.1016/j.automatica.2010.10.022

Cited by 36 publications

(22 citation statements)

References 21 publications

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“…Any point in the complement of cl A  with respect to  will ensure the invariance. A similar idea is explored in [14]. It also should be noted that the problem of approximating an ellipsoidal set with a polyhedral set is close to the one addressed in [15].…”

Section: Remarkmentioning

confidence: 93%

Explicit interpolation-based nonlinear model predictive control with a convex approximation of the feasible set

Grancharova

Olaru

2014

2014 IEEE Conference on Control Applications (CCA)

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In this paper, an approach to explicit interpolation-based MPC of constrained nonlinear systems is proposed, which is based on the ideas in [9], [10] for explicit constrained control of linear systems by applying interpolation techniques. The developed approach can be considered as an extension of the method in [9], [10] in the following directions: (i) nonlinear discrete-time systems are considered, which are regulated to the origin by solving an NMPC problem, (ii) a method for construction of a convex approximation of the feasible set for the formulated NMPC problem is suggested, (iii) the vertex control (the control values at the vertices of the approximate feasible set) is determined by solving the NMPC problem, instead of maximizing the control action, (iv) an algorithm for explicit interpolation-based NMPC is developed, where the explicit approximate solution is defined on a simplicial partition of the convex approximate feasible set. The proposed approach is illustrated on a numerical example.

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Section: Remarkmentioning

confidence: 93%

Explicit interpolation-based nonlinear model predictive control with a convex approximation of the feasible set

Grancharova

Olaru

2014

2014 IEEE Conference on Control Applications (CCA)

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“…The feasible is naturally computed by orthogonal projection of polytope {GZ −Sx t ≤W } onto the x-coordinate. More computationally efficient approach is proposed in [33] to compute exact and inner approximate feasible set.…”

Section: The First Proposition Is Immediate By Forward Multiplicationmentioning

confidence: 99%

Multi-Resolution Explicit Model Predictive Control: Delta-Model Formulation and Approximation

Bayat

Johansen

2013

IEEE Trans. Automat. Contr.

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This paper deals with the explicit solution and approximation of the constrained linear finite time optimal control problem for systems with fast sampling rates. To this aim, the recently developed explicit model predictive control (eMPC) is reformulated and characterized using the δ-operator to enjoy its promising advantages compared to the time-shift operator. Using the proposed δ-model eMPC formulation, a systematic method is proposed for first designing a low-complexity approximate eMPC solution and then improving its closed loop action without first determining an exact optimal solution that might be of prohibitive complexity. It is shown that the stability and feasibility of the proposed sub-optimal solution is guaranteed. Index TermsExplicit Model Predictive Control, Delta-operator, Multi-resolution MPC, Approximate explicit MPC, Multi-Parametric Programming.

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“…This is obviously a computational dead-end and a error-prone approach. A more convenient from the computational point of view is to use an iterative procedure, as developed in Scibilia, 1932 H.-N. Nguyen et al Olaru, and Hovd (2011). With the assumption that the matrix A is invertible, the feasible set for the MPC can be computed as follows:…”

Section: Some Remarks On the Feasible Set And The Relationship With Mmentioning

confidence: 99%

“…It is clear that any reduction of the vertex complexity of the feasible set X N will be a benefit, as detailed, for example, in Scibilia et al (2011). The important impediment in this vertex simplification is the need for controlled invariance preservation.…”

Section: Corollary 42mentioning

confidence: 99%

A patchy approximation of explicit model predictive control

Nguyen¹,

Olaru²,

Hovd³

2012

International Journal of Control

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The explicit solution of multi-parametric optimisation problems (MPOP) has been used to construct an off-line solution to relatively small- and medium-sized constrained control problems. The control design principles are based on receding horizon optimisation and generally use linear prediction models for the system dynamics. In this context, it can be shown that the optimal control law is a piecewise linear (PWL) state feedback defined over polytopic cells of the state space. However, as the complexity of the related optimisation problems increases, the memory footprint and implementation of such explicit optimal solution may be burdensome for the available hardware, principally due to the high number of polytopic cells in the state-space partition. In this article we provide a solution to this problem by proposing a patchy PWL feedback control law, which intend to approximate the optimal control law. The construction is based on the linear interpolation of the exact solution at the vertices of a feasible set and the solution of an unconstrained linear quadratic regulator (LQR) problem. With a hybrid patchy control implementation, we show that closed-loop stability is preserved in the presence of additive measurement noise despite the existence of discontinuities at the switch between the overlapping regions in the state-space partition

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On feasible sets for MPC and their approximations

Cited by 36 publications

References 21 publications

Explicit interpolation-based nonlinear model predictive control with a convex approximation of the feasible set

Explicit interpolation-based nonlinear model predictive control with a convex approximation of the feasible set

Multi-Resolution Explicit Model Predictive Control: Delta-Model Formulation and Approximation

A patchy approximation of explicit model predictive control

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