On the inherent robustness of optimal and suboptimal nonlinear MPC

Allan, D. J.; Bates, Cuyler N.; Risbeck, Michael J.; Rawlings, James B.

doi:10.1016/j.sysconle.2017.03.005

Cited by 86 publications

(66 citation statements)

References 17 publications

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“…As shown in [19], the RTI scheme can be considered as a standard NMPC Figure 3. Closed-loop state and control trajectories using the three NMPC schemes for problem (24) algorithm with the first control element fixed to the value from the previous sampling instant. Therefore, the same result apply to the RTI case, where the convergence rate of input MB RTI is the same with the standard RTI.…”

Section: Convergence and Stabilitymentioning

confidence: 99%

“…Therefore, the same result apply to the RTI case, where the convergence rate of input MB RTI is the same with the standard RTI. For stability analysis, input MB NMPC can be considered as a sub-optimal NMPC algorithm which benefits from (suboptimal) NMPC stability theories [21], [22], [23], [24]. As shown in [11] (Theorem 5.1) and [10], a stabilizing nonequidistantly discretized NMPC can be obtained by choosing a sufficiently long prediction horizon, properly shifting the optimal input trajectory, properly designing the cost function, the terminal cost and constraints.…”

Section: Convergence and Stabilitymentioning

confidence: 99%

“…Since the input MB scheme considers more state and path constraints, its time for solving QP is slightly higher than that of nonuniform grid scheme. It is interesting to compare performance of a specific parameterization of scheme B that shows similar computational time to that of scheme C. This can be achieved by increasing the number of intervals for non-uniform grid NMPC (scheme B) to M = 42 with I =[0, 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,26,28,32,35,37,40,42,44,46,48,50,52,55,60,65,70,75,80] The state and control trajectories are shown in Fig. 4 and the KKT values are shown in Fig.…”

Section: A Control Of An Inverted Pendulummentioning

confidence: 99%

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Efficient move blocking strategy for multiple shooting‐based non‐linear model predictive control

Chen

Scarabottolo²,

Bruschetta³

et al. 2020

IET Control Theory & Applications

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Move blocking (MB) is a widely used strategy to reduce the degrees of freedom of the Optimal Control Problem (OCP) arising in receding horizon control. The size of the OCP is reduced by forcing the input variables to be constant over multiple discretization steps. In this paper, we focus on developing computationally efficient MB schemes for multiple shooting based nonlinear model predictive control (NMPC). The degrees of freedom of the OCP is reduced by introducing MB in the shooting step, resulting in a smaller but sparse OCP. Therefore, the discretization accuracy and level of sparsity is maintained. A condensing algorithm that exploits the sparsity structure of the OCP is proposed, that allows to reduce the computation complexity of condensing from quadratic to linear in the number of discretization nodes. As a result, active-set methods with warm-start strategy can be efficiently employed, thus allowing the use of a longer prediction horizon. A detailed comparison between the proposed scheme and the nonuniform grid NMPC is given. Effectiveness of the algorithm in reducing computational burden while maintaining optimization accuracy and constraints fulfillment is shown by means of simulations with two different problems.

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Section: Convergence and Stabilitymentioning

confidence: 99%

Section: Convergence and Stabilitymentioning

confidence: 99%

Section: A Control Of An Inverted Pendulummentioning

confidence: 99%

See 1 more Smart Citation

Efficient move blocking strategy for multiple shooting‐based non‐linear model predictive control

Chen

Scarabottolo²,

Bruschetta³

et al. 2020

IET Control Theory & Applications

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“…One approach for reducing the computational cost of MPC is time distributed optimization (TDO). TDO distributes optimizer iterations over time by exploiting the robustness of MPC to suboptimality [2,35,41]. Rather than accurately solving the OCP at each sampling instant, TDO maintains a guess of the optimal solution and improves it at each timestep by performing a finite number of iterations of an optimization algorithm.…”

Section: Introductionmentioning

confidence: 99%

Time-distributed optimization for real-time model predictive control: Stability, robustness, and constraint satisfaction

2020

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Time distributed optimization is an implementation strategy that can significantly reduce the computational burden of model predictive control by exploiting its robustness to incomplete optimization. When using this strategy, optimization iterations are distributed over time by maintaining a running solution estimate for the optimal control problem and updating it at each sampling instant. The resulting controller can be viewed as a dynamic compensator which is placed in closedloop with the plant. This paper presents a general systems theoretic analysis framework for time distributed optimization. The coupled plant-optimizer system is analyzed using input-to-state stability concepts and sufficient conditions for stability and constraint satisfaction are derived. When applied to time distributed sequential quadratic programming, the framework significantly extends the existing theoretical analysis for the real-time iteration scheme. Numerical simulations are presented that demonstrate the effectiveness of the scheme.

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“…The paper [4] established that, in the presence of a suitable terminal set, any feasible solution of the OCP is stabilizing. The robustness properties of SOMPC were studied in [5], [6] which established sufficient conditions on the warmstart to ensure stability of the closed-loop system.…”

Section: Introductionmentioning

confidence: 99%

A Semismooth Predictor Corrector Method for Suboptimal Model Predictive Control

Liao‐McPherson

Nicotra

Kolmanovsky

2019

2019 18th European Control Conference (ECC)

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Suboptimal model predictive control is a technique that can reduce the computational cost of model predictive control (MPC) by exploiting its robustness to incomplete optimization. Instead of solving the optimal control problem exactly, this method maintains an estimate of the optimal solution and updates it at each sampling instance. The resulting controller can be viewed as a dynamic compensator which runs in parallel with the plant. This paper explores the use of the semismooth predictor-corrector method to implement suboptimal MPC. The dynamic interconnection of the combined plant-optimizer system is studied using the input-to-state stability framework and sufficient conditions for closed-loop asymptotic stability and constraint enforcement are derived using small gain arguments. Numerical simulations demonstrate the efficacy of the scheme. D. Liao-McPherson and I.V. Kolmanovsky are with the University of Michigan, Ann Arbor. Email:{dliaomcp,ilya}@umich.edu. M. M. Nicotra is with the University of Colorado Boulder.

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On the inherent robustness of optimal and suboptimal nonlinear MPC

Cited by 86 publications

References 17 publications

Efficient move blocking strategy for multiple shooting‐based non‐linear model predictive control

Efficient move blocking strategy for multiple shooting‐based non‐linear model predictive control

Time-distributed optimization for real-time model predictive control: Stability, robustness, and constraint satisfaction

A Semismooth Predictor Corrector Method for Suboptimal Model Predictive Control

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