Min-max feedback model predictive control for constrained linear systems

Scokaert, P.O.M.; Mayne, D. Q.

doi:10.1109/9.704989

Cited by 805 publications

(494 citation statements)

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“…This is important because it allows one to efficiently compute the value of the RHC law u = µ N (x) via the minimization of a convex function over a convex set. In particular, we note that if W is a polytope as in Example 7,then (26) can be written as a convex quadratic program (QP) in a tractable number of variables and constraints. If W is an ellipsoid or the affine map of a Euclidean ball as in Example 8, then the optimization problem in (26) can be converted to a tractable SOCP [20].…”

Section: Exploiting Equivalence To Compute the Rhc Lawmentioning

confidence: 99%

“…However, optimization over arbitrary (nonlinear) feedback policies is particularly difficult if constraints have to be satisfied. Current proposals for achieving this using finite dimensional optimization, such as [26], are computationally intractable since the size of the optimization problem grows exponentially with the size of the problem data.…”

Section: Introductionmentioning

confidence: 99%

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Optimization over state feedback policies for robust control with constraints

2006

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This paper is concerned with the optimal control of linear discrete-time systems subject to unknown but bounded state disturbances and mixed polytopic constraints on the state and input. It is shown that the class of admissible affine state feedback control policies with knowledge of prior states is equivalent to the class of admissible feedback policies that are affine functions of the past disturbance sequence. This implies that a broad class of constrained finite horizon robust and optimal control problems, where the optimization is over affine state feedback policies, can be solved in a computationally efficient fashion using convex optimization methods. This equivalence result is used to design a robust receding horizon control (RHC) state feedback policy such that the closed-loop system is input-to-state stable (ISS) and the constraints are satisfied for all time and all allowable disturbance sequences. The cost to be minimized in the associated finite horizon optimal control problem is quadratic in the disturbance-free state and input sequences. The value of the receding horizon control law can be calculated at each sample instant using a single, tractable and convex quadratic program (QP) if the disturbance set is polytopic, or a tractable second-order cone program (SOCP) if the disturbance set is given by a 2-norm bound.

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Section: Exploiting Equivalence To Compute the Rhc Lawmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimization over state feedback policies for robust control with constraints

2006

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“…Note that, if memberships are considered as "uncertainty" and the controller cannot depend on them, the above problem statement would be that of the so-called minimax predictive control [18,19]. Intermediate cases with partiallyknown membership components [36,Eq.…”

Section: Remarkmentioning

confidence: 99%

Shape-independent model predictive control for Takagi–Sugeno fuzzy systems

Ariño

Querol

Sala³

2017

Engineering Applications of Artificial Intelligence

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Predictive control of TS fuzzy systems has been addressed in prior literature with some simplifying assumptions or heuristic approaches. This paper presents a rigorous formulation of the model predictive control of TS systems, so that results are valid for any membership value (shape-independent) with a suitable account of causality (control can depend on current and past memberships and state). As in most fuzzy control results, a family of progressively better controllers can be obtained by increasing Polya-related complexity parameters, generalising over prior proposals.

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“…Kassmann et al [171] on-line Apply robustness constraints to steady state target calculation. Scokaert and Mayne [266] on-line min worst case quadratic, invariant set for stability. Lee and Cooley [195] on-line min worst case quadratic cost s.t.…”

Section: The Paroc Frameworkmentioning

confidence: 99%