Abstract
In this paper, a new off-line model predictive control strategy is presented for a kind of linear parameter varying system with polytopic uncertainty. A nest of shrinking ellipsoids is constructed by solving linear matrix inequality. By splitting the objective function into two parts, the proposed strategy moves most computations off-line. The on-line computation is only calculating the current control to assure the system shrinking into the smaller ellipsoid. With the proposed formulation, the stability of the closed system is proved, followed with two numerical examples to demonstrate the proposed method’s effectiveness in the end.
Highlights
Model predictive control (MPC), known as receding or moving horizon control, is an effective control algorithm widely adopted in industry to deal with multivariable constrained control problem
It is introduced by Shamma [13] and it is an intermediate step between linear timeinvariant (LTI) systems and non-linear plants
It is proposed that a state feedback MPC scheme based on a quasi-min-max algorithm [15], the first stage cost can be computed without any uncertainty, the first state cost can be determined separately from the rest of parameter changes
Summary
Model predictive control (MPC), known as receding or moving horizon control, is an effective control algorithm widely adopted in industry to deal with multivariable constrained control problem. A robust MPC design method is proposed by Cao and Lin[21] to solve the influence of the actuator saturation, which degrades system performance and destroys the system’s stability This method is improved by placing heavier weighting on the system corresponding to the actual linear feedback law[22]. A series of controllers corresponding to a sequence of nested asymptotically stable invariant ellipsoids is constructed off-line one with another[23] This result is improved based on the nominal performance and followed with the improvement of the closed loop system’s feasibility and optimality[24]. In the former case, the aforementioned researches have little use of the measured parameter vector To solve this problem, this article aims to provide a formulation of decreasing the computation of the robust MPC for LPV system. Ã denotes the corresponding transpose of the lower block part of symmetric matrices
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