Robust MPC with recursive model update

Lorenzen, Matthias; Cannon, Mark; Allgöwer, Frank

doi:10.1016/j.automatica.2019.02.023

Cited by 154 publications

(280 citation statements)

References 30 publications

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“…and (24) for the same random initial condition x 0 ∈ CS 12 and disturbance realization. As reported in Table II, on average it takes ∼ 5ms to evaluate the safe policy (21) and ∼ 4.6s to evaluate the LMPC policy (24). This result is expected as the safe policy (21) is evaluated solving a LP and the LMPC policy (24) solving N + 1 = 4 QPs.…”

Section: Exploiting the Safe Policymentioning

confidence: 77%

“…where κ j, * (·) is the safe policy defined in (21). Proof 2: The proof can be found in the Appendix.…”

Section: Set Of Safe Policiesmentioning

confidence: 99%

“…Finally, we compare the performance of the uncertain system (1) in closed-loop with the safe policy (21) and the LMPC (23) and (24). In particular, we simulated both the closed-loop system (1) and (21) and the closed-loop system (1) Fig. 6.…”

Section: Exploiting the Safe Policymentioning

confidence: 99%

“…Proof 11: First we show that the set O is robust positive invariant for the closed-loop system (1) and (21). Assume that at time t of iteration j the state x j t ∈ O, be definitions (13), (15), (17) and (21) we have that Q j (x j t ) = 0 and κ j, * (x j t ) = −Kx j t . Therefore, by Assumption 2 we have that closed-loop system x j t+1 = Ax j t +Bκ j, * (x j t )+w j t ∈ O, ∀w j t ∈ W and that O is robust positive invariant for the closed-loop system (1)- (21).…”

Section: Proof Of Propositionmentioning

confidence: 99%

See 3 more Smart Citations

Sample-Based Learning Model Predictive Control for Linear Uncertain Systems

Rosolia

Borrelli

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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A robust Learning Model Predictive Controller (LMPC) for uncertain systems performing iterative tasks is presented. At each iteration of the control task the closed-loop state, input and cost are stored and used in the controller design. This paper first illustrates how to construct robust invariant sets and safe control policies exploiting historical data. Then, we propose an iterative LMPC design procedure, where data generated by a robust controller at iteration j are used to design a robust LMPC at the next j + 1 iteration. We show that this procedure allows us to iteratively enlarge the domain of the control policy and it guarantees recursive constraints satisfaction, input to state stability and performance bounds for the certainty equivalent closed-loop system. The use of an adaptive prediction horizon is the key element of the proposed design. The effectiveness of the proposed control scheme is illustrated on a linear system subject to bounded additive disturbance. arXiv:1911.09234v1 [eess.SY]

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Section: Exploiting the Safe Policymentioning

confidence: 77%

“…where κ j, * (·) is the safe policy defined in (21). Proof 2: The proof can be found in the Appendix.…”

Section: Set Of Safe Policiesmentioning

confidence: 99%

Section: Exploiting the Safe Policymentioning

confidence: 99%

Section: Proof Of Propositionmentioning

confidence: 99%

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Sample-Based Learning Model Predictive Control for Linear Uncertain Systems

Rosolia

Borrelli

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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“…In general, RAMPC schemes [5], [6], [7], [8], [9], [10], [11], [12] use set membership estimation to provide a set of non falsified parameters, which is utilized in a robust tubebased MPC approach to provide robustness w.r.t. uncertain parameters and disturbances.…”

Section: Related Workmentioning

confidence: 99%

A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems

Köhler

Soloperto

Müller

et al. 2021

IEEE Trans. Automat. Contr.

123

133

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In this paper, we present a tube-based framework for robust adaptive model predictive control (RAMPC) for nonlinear systems subject to parametric uncertainty and additive disturbances. Set-membership estimation is used to provide accurate bounds on the parametric uncertainty, which are employed for the construction of the tube in a robust MPC scheme. The resulting RAMPC framework ensures robust recursive feasibility and robust constraint satisfaction, while allowing for less conservative operation compared to robust MPC schemes without model/parameter adaptation. Furthermore, by using an additional mean-squared point estimate in the objective function the framework ensures finite-gain L2 stability w.r.t. additive disturbances.As a first contribution we derive suitable monotonicity and non-increasing properties on general parameter estimation algorithms and tube/set based RAMPC schemes that ensure robust recursive feasibility and robust constraint satisfaction under recursive model updates. Then, as the main contribution of this paper, we provide similar conditions for a tube based formulation that is parametrized using an incremental Lyapunov function, a scalar contraction rate and a function bounding the uncertainty. With this result, we can provide simple constructive designs for different RAMPC schemes with varying computational complexity and conservatism. As a corollary, we can demonstrate that state of the art formulations for nonlinear RAMPC are a special case of the proposed framework. We provide a numerical example that demonstrates the flexibility of the proposed framework and showcase improvements compared to state of the art approaches.

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Dynamic Process Operation Under Demand Response – A Review of Methods and Tools

Esche

Repke

2020

Chemie Ingenieur Technik

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Participating in electricity markets through demand response causes new requirements for optimizing process control of chemical plants. The last ten years have brought great advances in the formulation and solution of economic nonlinear model predictive control and state estimation to support operation of processes under dynamic constraints. However, gaps remain regarding the availabilities of suitable plant models capable of describing processes active in demand response as well as of robust schemes for state estimation and economic nonlinear model predictive control in commercial tools.

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Robust MPC with recursive model update

Cited by 154 publications

References 30 publications

Sample-Based Learning Model Predictive Control for Linear Uncertain Systems

Sample-Based Learning Model Predictive Control for Linear Uncertain Systems

A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems

Dynamic Process Operation Under Demand Response – A Review of Methods and Tools

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