Efficient Off-Line Solutions to Robust Model Predictive Control Using Orthogonal Partitioning

Cychowski, Marcin; O'Mahony, Tom

doi:10.3182/20050703-6-cz-1902.00882

Cited by 8 publications

(3 citation statements)

References 16 publications

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“…Whichever “alternative” is incorporated into PDOLMPC, its computational burden is alwaysprohibitive for large L and N . Nevertheless, techniques exist 33–35 that could be utilized on PDOLMPC to yield significant reduction of the on‐line computational effort at the expense of slight degradation in performance.…”

Section: Monotonicity Properties With Increasing N In Pdolmpcmentioning

confidence: 99%

Properties of parameter‐dependent open‐loop MPC for uncertain systems with polytopic description

Ding

2009

Asian Journal of Control

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This paper investigates the parameter-dependent open-loop model predictive control (PDOLMPC) scheme for systems with a polytopic uncertainty description. PDOLMPC parameterizes the infinite horizon control moves into a number of free control moves followed by a single state feedback law. The free control moves (excluding the first one) are parameter dependent and constructed upon all of the extreme realizations of the uncertainty before the switching horizon N . Our primary contribution is to point out that this PDOLMPC is a relaxed version of the feedback MPC. Thus, some properties of nominal MPC, such as enhancement of optimality and enlargement of region of attraction by increasing the switching horizon, can be inherited in PDOLMPC. These properties are theoretically important for robust MPC and a simulation example is given for demonstration.

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Section: Monotonicity Properties With Increasing N In Pdolmpcmentioning

confidence: 99%

Properties of parameter‐dependent open‐loop MPC for uncertain systems with polytopic description

Ding

2009

Asian Journal of Control

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“…Alternatively, one can construct the binary search tree [14] to perform the region traversal in time logarithmic in R. Once the index a is found, the a-th elements K a and L a are extracted from memory and κ(x) = K a x + L a is computed. Finally, the function value is clipped by passing it through (5), which always performs only 2n u comparisons, insignificant compared to the complexity of region traversal. The extra memory required to store κ and κ for φ(·) is 2n u floating point numbers, negligible compared to the memory footprint of regions R i .…”

Section: : Returnmentioning

confidence: 99%

“…[3], [16], [9]. In [8], [5] the authors propose to use an orthogonal grid of the regions, while in [7], [12] the regions are computed using triangulation. In all cases a suboptimal approximation κ(x) is obtained.…”

Section: Introductionmentioning

confidence: 99%

Performance-lossless complexity reduction in Explicit MPC

Kvasnica

Fikar

2010

49th IEEE Conference on Decision and Control (CDC)

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The idea of Explicit Model Predictive Control (MPC) is to find the optimal control input as an explicit Piecewise Affine (PWA) function of the initial conditions. The function, however, is often too complex to be processed by a typical control hardware setup in real time. Therefore the paper proposes a novel method of replacing a generic continuous PWA function by a different function of significantly lower complexity in such a way that optimal closed-loop performance, stability and constraint satisfaction are preserved. The idea is based on eliminating a significant portion of the regions of the PWA function over which the function attains a saturated value. An extensive case study is presented which confirms that a significant reduction of complexity is achieved in general.

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Explicit Min-Max MPC of Constrained Nonlinear Systems with Bounded Uncertainties

Grancharova

Johansen

2012

Explicit Nonlinear Model Predictive Control

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Efficient Off-Line Solutions to Robust Model Predictive Control Using Orthogonal Partitioning

Cited by 8 publications

References 16 publications

Properties of parameter‐dependent open‐loop MPC for uncertain systems with polytopic description

Properties of parameter‐dependent open‐loop MPC for uncertain systems with polytopic description

Performance-lossless complexity reduction in Explicit MPC

Explicit Min-Max MPC of Constrained Nonlinear Systems with Bounded Uncertainties

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