Systems with persistent disturbances: predictive control with restricted constraints

Chisci, Luigi; Rossiter, J.A.; Zappa, G.

doi:10.1016/s0005-1098(01)00051-6

Cited by 565 publications

(451 citation statements)

References 16 publications

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“…Remark 2 Note that the state feedback policy (4) subsumes the well-known class of "pre-stabilizing" control policies [1,6,19,25], in which the control policy takes the form u i = Kx i + c i , where K is computed off-line and on-line computation is limited to finding an admissible perturbation sequence {c i } N −1 i=0 .…”

Section: State Feedback Parameterizationmentioning

confidence: 99%

“…By definition, for a given x ∈ X sf N , there exists a pair (L, g) that satisfies the constraints in (6). For a given disturbance sequence w ∈ W, the inputs and states of the system can be written as :…”

Section: Equivalence Between State and Disturbance Feedback Parametermentioning

confidence: 99%

“…Hence, a popular approach in the predictive control literature is to compute one or more stabilizing linear state feedback control laws off-line and restrict the on-line computation to the selection of one of these control laws, followed by the computation of a finite sequence of admissible perturbations to the selected control law [1,6,19,25]. Though this approach considerably reduces the computational complexity, it is not always obvious how to best choose the linear control laws off-line so as to minimize conservativeness.…”

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: State Feedback Parameterizationmentioning

confidence: 99%

Section: Equivalence Between State and Disturbance Feedback Parametermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimization over state feedback policies for robust control with constraints

2006

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“…Many methods have been developed to endow conventional synchronous MPC with robustness [19,1]. For use with MMPC, we have adopted the constraint tightening approach [11,8,27,25], in which the constraints of the optimization are modified to retain a margin for future feedback action. Since only the constraint limits are modified, the computational complexity remains the same as for the equivalent nominal MPC.…”

Section: The Basic Ideamentioning

confidence: 99%

Multiplexed model predictive control

et al. 2012

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This paper proposes a form of MPC in which the control variables are moved asynchronously. This contrasts with most MIMO control schemes, which assume that all variables are updated simultaneously. MPC outperforms other control strategies through its ability to deal with constraints. This requires online optimization, hence computational complexity can become an issue when applying MPC to complex systems with fast response times. The multiplexed MPC scheme described in this paper solves the MPC problem for each subsystem sequentially, and updates subsystem controls as soon as the solution is available, thus distributing the control moves over a complete update cycle. The resulting computational speed-up allows faster response to disturbances, which may result in improved performance, despite finding sub-optimal solutions to the original problem.

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“…, µ N −1 (·)} of control laws. Determination of a feedback control policy is usually prohibitively difficult and various simplifying approximations have been proposed in the literature (Kouvaritakis et al, 2000;Chisci et al, 2001;Mayne and Langson, 2001;Löfberg, 2003;van Hessem and Bosgra, 2003;Kerrigan and Alamo, 2004;Smith, 2004 loop and feedback model predictive controller generate a tube of trajectories when uncertainty is present. Feedback model predictive control reduces the spread of predicted trajectories resulting from uncertainty.…”

Section: Introductionmentioning

confidence: 99%

A Simple Tube Controller for Efficient Robust Model Predictive Control of Constrained Linear Discrete Time Systems Subject to Bounded Disturbances

Raković

Mayne

2005

IFAC Proceedings Volumes

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We present a simple tube controller for efficient robust model predictive control of constrained linear, discrete-time systems in the presence of bounded disturbances. The proposed control policy ensures that controlled trajectories are confined to a given tube despite uncertainty. The robust optimal control problem that is solved on-line is a standard quadratic programming problem of marginally increased complexity compared with that required for model predictive control in the deterministic case. We show how to optimize the tube cross section, how to construct an adequate tube terminal set and we establish robust exponential stability of a suitable robust control invariant set (the 'origin' for uncertain system) with enlarged domain of attraction. Copyright

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Systems with persistent disturbances: predictive control with restricted constraints

Cited by 565 publications

References 16 publications

Optimization over state feedback policies for robust control with constraints

Optimization over state feedback policies for robust control with constraints

Multiplexed model predictive control

A Simple Tube Controller for Efficient Robust Model Predictive Control of Constrained Linear Discrete Time Systems Subject to Bounded Disturbances

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