Controlled Invariance of Discrete Time Systems

Vidal, René; Schaffert, S.; Lygeros, John; Sastry, S. Shankar

doi:10.1007/3-540-46430-1_36

Cited by 47 publications

(47 citation statements)

References 25 publications

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“…These three operations are easily implemented for LTI systems subject to linear inequality constraints [2,6,7,8,10,14]. Though the algorithms presented in this paper are difficult to implement for general nonlinear systems, there exist some classes of nonlinear systems for which the building blocks already are in place, such as piecewise affine systems and some classes of hybrid systems [1].…”

Section: Algorithm 21 (Controllable Sets) the Controllable Sets Of mentioning

confidence: 99%

“…Though the algorithms presented in this paper are difficult to implement for general nonlinear systems, there exist some classes of nonlinear systems for which the building blocks already are in place, such as piecewise affine systems and some classes of hybrid systems [1]. Some work on developing algorithms for computing robust control invariant sets for hybrid systems has also been carried out by the authors of [14].…”

Section: Algorithm 21 (Controllable Sets) the Controllable Sets Of mentioning

confidence: 99%

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Invariant sets for constrained nonlinear discrete-time systems with application to feasibility in model predictive control

Kerrigan

Maciejowski

Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187)

136

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An understanding of invariant set theory is essential in the design of controllers for constrained systems, since state and control constraints can be satisfied if and only if the initial state belongs to a positively invariant set for the closed-loop system. The paper briefly reviews some concepts in invariant set theory and shows that the various sets can be computed using a single recursive algorithm. The ideas presented in the first part of the paper are applied to the fundamental design goal of guaranteeing feasibility in predictive control. New necessary and sufficient conditions based on the control horizon, prediction horizon and terminal constraint set are given in order to guarantee that the predictive control problem will be feasible for all time, given any feasible initial state.

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Section: Algorithm 21 (Controllable Sets) the Controllable Sets Of mentioning

confidence: 99%

Section: Algorithm 21 (Controllable Sets) the Controllable Sets Of mentioning

confidence: 99%

Invariant sets for constrained nonlinear discrete-time systems with application to feasibility in model predictive control

Kerrigan

Maciejowski

Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187)

136

View full text Add to dashboard Cite

show abstract

“…In contrast, the computation of the maximal controlled invariant sets is recursive [3], [10]. Since controllable invariants are also controlled invariants, we could use the approach of this section for a nonrecursive computation of controlled invariants.…”

Section: Proposition 42 Xmentioning

confidence: 99%

“…The computation involves linear programming and projections (also known as FourierMotzkin eliminations). Related approaches have been used in [5], [10] for predecessor operator computations, in [3], [11] for the computation of the maximal controlled invariant set, and also in other contexts, e.g. [4], [2].…”

Section: Introductionmentioning

confidence: 99%

On a class of controlled invariant sets

Iordache

Antsaklis

2004

Proceedings of the 2004 American Control Conference

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Abstract-In this paper we introduce a new class of controlled invariant sets, called controllable invariant sets. Intuitively, a controllable invariant set has the property that from any "large enough" connected region of the set it is possible to reach any such other region of the set, regardless of disturbances. Disturbances are assumed to be bounded. The range of the control inputs is assumed to be given and is allowed to be bounded. The main result of the paper is a nonrecursive approach for the computation of controllable invariants. The other results of the paper deal with properties of the proposed method and of controllable invariance. The results of the paper assume hybrid system modes with linear discrete-time dynamics.

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“…For example, in control theory, projection is required for reachability analysis [1] and in decision theory for the elimination of existential quantifiers [2]. It can be shown that the calculation of affine maps or Minkowski sums of polyhedra are both polynomially equivalent to orthogonal projection [3,Sect.…”

Section: Introductionmentioning

confidence: 99%

On Polyhedral Projection and Parametric Programming

Jones

Kerrigan

Maciejowski

2008

J Optim Theory Appl

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This paper brings together two fundamental topics: polyhedral projection and parametric linear programming. First, it is shown that, given a parametric linear program (PLP), a polyhedron exists whose projection provides the solution to the PLP. Second, the converse is tackled and it is shown how to formulate a PLP whose solution is the projection of an appropriately defined polyhedron described as the intersection of a finite number of halfspaces. The input to one operation can be converted to an input of the other operation and the resulting output can be converted back to the desired form in polynomial time-this implies that algorithms for computing projections or methods for solving parametric linear programs can be applied to either problem class.

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Controlled Invariance of Discrete Time Systems

Cited by 47 publications

References 25 publications

Invariant sets for constrained nonlinear discrete-time systems with application to feasibility in model predictive control

Invariant sets for constrained nonlinear discrete-time systems with application to feasibility in model predictive control

On a class of controlled invariant sets

On Polyhedral Projection and Parametric Programming

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