Adaptive model predictive control for a class of constrained linear systems based on the comparison model

Fukushima, Hiroaki; Kim, Tae‐Hyoung; Sugie, Toshiharu

doi:10.1016/j.automatica.2006.08.026

Cited by 141 publications

(99 citation statements)

References 10 publications

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“…The first is an ancillary controller that aims to drive the current state, x k , (now treated as deterministic) to the state mean sequence, µ k , produced by (11). The corresponding unconstrained MPC formulation,…”

Section: Robust Epc Formulationmentioning

confidence: 99%

“…This enables the use of a Kalman filter to predict the evolution of state uncertainty instead of the recursive Pontryagin difference operations required for deterministic sets [21]. Many adaptive MPC formulations also include a robust component that is coupled to estimator uncertainty [1,10,11]. The resulting robust-adaptive formulations allow the adaptive component to estimate and compensate for low frequency components of the uncertainty, while variability about the current estimate is handled by the robust constraints.…”

Section: Introductionmentioning

confidence: 99%

“…Adaptive formulations seek to estimate the uncertainty in the dynamics and update the predictive model to more accurately anticipate the system's interaction with the constraints [4,8,11,27]. However, in practice, this may still lead to constraint violations due to the difference in timescales between the disturbance estimator and high-frequency noise in the state estimate.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Experience-driven Predictive Control with Robust Constraint Satisfaction under Time-Varying State Uncertainty

Desaraju

Spitzer

Michael

2017

Robotics: Science and Systems XIII

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Abstract-We present an extension to Experience-driven Predictive Control (EPC) that leverages a Gaussian belief propagation strategy to compute an uncertainty set bounding the evolution of the system state in the presence of time-varying state uncertainty. This uncertainty set is used to tighten the constraints in the predictive control formulation via a chance constrained approach, thereby providing a probabilistic guarantee of constraint satisfaction. The parameterized form of the controllers produced by EPC coupled with online uncertainty estimates ensures this robust constraint satisfaction property persists even as the system switches controllers and experiences variations in the uncertainty model. We validate the online performance and robust constraint satisfaction of the proposed Robust EPC algorithm through a series of experimental trials with a small quadrotor platform subjected to changes in state estimate quality.

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Section: Robust Epc Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Experience-driven Predictive Control with Robust Constraint Satisfaction under Time-Varying State Uncertainty

Desaraju

Spitzer

Michael

2017

Robotics: Science and Systems XIII

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show abstract

“…In addition, it seems extremely difficult to guarantee both feasibility and stability theoretically whenever an adaptive approach to MPC is adopted. Recently, one of the adaptive-type MPC schemes was proposed by Fukushima et al (2007) for a class of constrained continuous-time linear systems. However, it would be convenient to have discrete-time formula from the viewpoint of implementation.…”

Section: Introductionmentioning

confidence: 99%

Adaptive receding horizon predictive control for constrained discrete-time linear systems with parameter uncertainties

Kim

Sugie

2008

International Journal of Control

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This paper proposes a discrete-time model predictive control (MPC) scheme combined with an adaptive mechanism. To this end, first, an adaptive parameter estimation algorithm suitable for MPC is proposed, which uses the available input and output signals to estimate the unknown system parameters. It enables the prediction of a monotonically decreasing worst-case estimation error bound over the prediction horizon of MPC. These distinctive features allow for future model improvement to be explicitly considered in MPC. Thus, a less conservative adaptive-type MPC controller can be developed based on the proposed estimation method. Second, we show how the discrete-time adaptive-type state-feedback MPC controller is constructed by combining the on-line parameter estimation scheme with a modified robust MPC method based on the comparison model. The developed MPC controller guarantees feasibility and stability of the closed-loop system theoretically in the presence of input and state constraints. A numerical example is given to demonstrate its effectiveness.

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“…The class of predictive control methods that explicitly account for the modeling errors (or uncertainties) is Robust Model Predictive Control (RMPC). This type of MPC has been thoroughly investigated for many years (see e.g [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]). One widely used technique for improving robustness in MPC consists of the min-max optimization [20] where a quadratic cost function is minimized with respect to its worst-case, the latter being taken over the set of all possible plant uncertainties.…”

Section: Introductionmentioning

confidence: 99%

A GGP approach to solve non convex min-max predictive controller for a class of constrained MIMO systems described by state-space models

Kheriji

Bouani

Ksouri

2011

Int. J. Control Autom. Syst.

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This paper proposes a new method to solve non convex min-max predictive controller for a class of constrained linear Multi Input Multi Output (MIMO) systems. A parametric uncertainty state space model is adopted to describe the dynamic behavior of the real process. Moreover, the output deviation method is used to design the j-step ahead output predictor. The control law is obtained by the resolution of a non convex min-max optimization problem under input constraints. The key idea is to transform the initial non convex optimization problem to a convex one by means of variable transformations. To this end, the Generalized Geometric Programming (GGP) which is a global deterministic optimization method is used. An efficient implementation of this approach will lead to an algorithm with a low computational burden. Simulation results performed on Multi Input Multi Output (MIMO) system show successful set point tracking, constraints satisfaction and good non-zero disturbance rejection.

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Adaptive model predictive control for a class of constrained linear systems based on the comparison model

Cited by 141 publications

References 10 publications

Experience-driven Predictive Control with Robust Constraint Satisfaction under Time-Varying State Uncertainty

Experience-driven Predictive Control with Robust Constraint Satisfaction under Time-Varying State Uncertainty

Adaptive receding horizon predictive control for constrained discrete-time linear systems with parameter uncertainties

A GGP approach to solve non convex min-max predictive controller for a class of constrained MIMO systems described by state-space models

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