Computation of minimum-time feedback control laws for discrete-time systems with state-control constraints

Keerthi, S.S.; Gilbert, Éric

doi:10.1109/tac.1987.1104625

Cited by 231 publications

(108 citation statements)

References 7 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%

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%

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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“…Note that we distinguish between the input u(t) and the state x(t) of plant (16) at time t and the variables u k and x k of the optimization problem (20). We will also denote byX k ⊆ R 2n the set of states x k and references x ref that are feasible for (18)- (20):…”

Section: Problem Formulationmentioning

confidence: 99%

“…Theorem 2: Consider the optimal control problem (18)- (20). Then, there exists a solution in the form of a PWA state-feedback control law Proof.…”

Section: Problem Formulationmentioning

confidence: 99%

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A reference governor approach for constrained piecewise affine systems

Falcone

Borrelli

Pekař

et al. 2009

2009 European Control Conference (ECC)

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Abstract-In this paper we present a novel approach to the design of reference tracking controllers for constrained, discrete-time piecewise affine systems and apply it to a vehicle yaw control problem. The paper is divided in two parts. In the first part, we present a methodology for designing reference tracking controllers for constrained, discrete-time piecewise affine systems. The approach follows the idea of reference governor techniques where the desired set-point is filtered by a system called the "reference governor". Based on the system current state, set-point, and prescribed constraints, the reference governor computes a new set-point for a low-level controller so that the state and input constraints are satisfied and convergence to the original set-point is guaranteed.In the second part of the paper, we apply the proposed approach to a vehicle dynamics control problem where the vehicle yaw rate have to be controlled through an Active Front Steering (AFS) system.

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“…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]. Note that some model uncertainties could be incorporated in this framework [6].…”

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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Computation of minimum-time feedback control laws for discrete-time systems with state-control constraints

Cited by 231 publications

References 7 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

A reference governor approach for constrained piecewise affine systems

On a class of controlled invariant sets

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