Discrete-time Incremental ISS: A framework for Robust NMPC

Bayer, Florian A.; Bürger, Mathias; Allgöwer, Frank

doi:10.23919/ecc.2013.6669322

Cited by 56 publications

(92 citation statements)

References 17 publications

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“…The considered restriction for κ is equivalent to assuming that some nonlinear feedback κ x (x) exists, such that the system is incrementally stable. While most formulations in the robust MPC literature satisfy the conditions using linear feedbacks K [6], [7], [8], [15], [18], [31], [32], quasi-LPV based designs can only be applied if the feedback K(z, v) is not parametrized by the input v (c.f. [37, Prop.…”

Section: Stability Results and Lms Updatesmentioning

confidence: 99%

“…In particular, the approach in [6] considers general polytopic parameter sets Θ and a homothetic 3 In approaches directly utilizing sets, e.g. [6], [7], [32], the candidate solution X k|t+1 = X * k+1|t is standard. However, most tube-based approaches, e.g.…”

Section: Setup and General Theorymentioning

confidence: 99%

“…However, similar to the Lipschitz based approach, unless the considered tube parametrization X contains a robust positive invariant (RPI) set, the tube is growing unbounded along the prediction horizon and thus only short horizons and/or small uncertainty can be considered. In [22], [32] additive disturbances are considered and a fixed RPI set X is computed offline as an incremental Lyapunov function or using control contraction metrics.…”

Section: Setup and General Theorymentioning

confidence: 99%

See 2 more Smart Citations

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

Köhler

Soloperto

Müller

et al. 2021

IEEE Trans. Automat. Contr.

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127

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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Section: Stability Results and Lms Updatesmentioning

confidence: 99%

Section: Setup and General Theorymentioning

confidence: 99%

Section: Setup and General Theorymentioning

confidence: 99%

See 1 more Smart Citation

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

Köhler

Soloperto

Müller

et al. 2021

IEEE Trans. Automat. Contr.

Self Cite

127

133

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show abstract

“…Tube-based approaches for nonlinear discrete-time systems have been considered in other works. [19][20][21][22][23] Farina and Scattolini 24 have addressed the linear continuous-time case. In the works of Wang et al 25 and Sun et al, 26 regarding the computation of the offline feedback controller, the discrepancy between the nominal nonlinear system with the corresponding linear system has been considered.…”

Section: Discussionmentioning

confidence: 99%

Decentralized tube‐based model predictive control of uncertain nonlinear multiagent systems

Νίκου

Dimarogonas

2019

Intl J Robust & Nonlinear

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Summary This paper addresses the problem of decentralized tube‐based nonlinear model predictive control (NMPC) for a general class of uncertain nonlinear continuous‐time multiagent systems with additive and bounded disturbance. In particular, the problem of robust navigation of a multiagent system to predefined states of the workspace while using only local information is addressed under certain distance and control input constraints. We propose a decentralized feedback control protocol that consists of two terms: a nominal control input, which is computed online and is the outcome of a decentralized finite horizon optimal control problem that each agent solves at every sampling time, for its nominal system dynamics; and an additive state‐feedback law which is computed offline and guarantees that the real trajectories of each agent will belong to a hypertube centered along the nominal trajectory, for all times. The volume of the hypertube depends on the upper bound of the disturbances as well as the bounds of the derivatives of the dynamics. In addition, by introducing certain distance constraints, the proposed scheme guarantees that the initially connected agents remain connected for all times. Under standard assumptions that arise in nominal NMPC schemes, controllability assumptions, communication capabilities between the agents, it is guaranteed that the multiagent system is input‐to‐state stable with respect to the disturbances, for all initial conditions satisfying the state constraints. Simulation results verify the correctness of the proposed framework.

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“…1). For κ(x, x r , u r ) = u r this reduces to incremental stability and correspondingly the robust MPC method in [42] can also be used. This assumption can be verified by using Algorithm 2 to compute a terminal cost that is valid on Z, compare Proposition 2.…”

Section: B Robust Reference Trackingmentioning

confidence: 99%

A Nonlinear Model Predictive Control Framework Using Reference Generic Terminal Ingredients

Köhler

Müller

Allgöwer

2020

IEEE Trans. Automat. Contr.

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In this paper, we present a quasi infinite horizon nonlinear model predictive control (MPC) scheme for tracking of generic reference trajectories. This scheme is applicable to nonlinear systems, which are locally incrementally stabilizable. For such systems, we provide a reference generic offline procedure to compute an incrementally stabilizing feedback with a continuously parameterized quadratic quasi infinite horizon terminal cost. As a result we get a nonlinear reference tracking MPC scheme with a valid terminal cost for general reachable reference trajectories without increasing the online computational complexity. As a corollary, the terminal cost can also be used to design nonlinear MPC schemes that reliably operate under online changing conditions, including unreachable reference signals. The practicality of this approach is demonstrated with a benchmark example.

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Discrete-time Incremental ISS: A framework for Robust NMPC

Cited by 56 publications

References 17 publications

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

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

Decentralized tube‐based model predictive control of uncertain nonlinear multiagent systems

A Nonlinear Model Predictive Control Framework Using Reference Generic Terminal Ingredients

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