Improving off-line approach to robust MPC based-on nominal performance cost

Ding, Baocang; Xi, Yugeng; Cychowski, Marcin; O'Mahony, Tom

doi:10.1016/j.automatica.2006.07.022

Cited by 95 publications

(51 citation statements)

References 6 publications

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“…Using Lemma 3, it can be proved that the convex combination (γ,Q Q Q 0 ,Q Q Q 1 , · · · ,Q Q Q N−1 ) would also be the solution of conditions (8a), (8b), (10), and (11). Remark 2.…”

Section: Reduction Of Computation Burdenmentioning

confidence: 97%

“…For the uncertain system (1)-(4), suppose that the two groups (γ1, Q Q Q 1,0 , Q Q Q 1,1 , · · · , Q Q Q 1,N−1 ) and (γ2, Q Q Q 2,0 , Q Q Q 2,1 , · · · , Q Q Q 2,N−1 ) satisfy conditions (8a), (8b), (10), and (11), respectively, and that the convex combination (γ,Q Q Q 0 ,Q Q Q 1 , · · · ,Q Q Q N−1 ) would also satisfy the conditions (8a), (8b), (10), and (11)…”

Section: Reduction Of Computation Burdenmentioning

confidence: 99%

“…Since both (γ1, Q Q Q 1,0 , Q Q Q 1,1 , · · · , Q Q Q 1,N−1 ) and (γ2, Q Q Q 2,0 , Q Q Q 2,1 , · · · , Q Q Q 2,N−1 ) are assumed to be the solutions of conditions (8a), (8b), (10), and (11), for each i, we multiply (8a) and (8b) by λ1 and λ2, where (γ, Q Q Q 0 , Q Q Q 1 , · · · , Q Q Q N−1 ) are replaced with (γ1, Q Q Q 1,0 , Q Q Q 1,1 , · · · , Q Q Q 1,N−1 ) and (γ2, Q Q Q 2,0 , Q Q Q 2,1 , · · · , Q Q Q 2,N−1 ), respectively, and sum the resulting inequalities to get…”

Section: Reduction Of Computation Burdenmentioning

confidence: 99%

“…In order to improve the control performance and decrease the computational burden at the same time, many synthesis approaches of MPC were proposed [4−7] . Based on the concept of invariant set, [8][9][10] off-line constructed a sequence of explicit control laws corresponding to a sequence of invariant sets and on-line calculated the control input with low computational burden. Recently, the authors of [11][12][13][14] have proposed a systematic way to derive a sequence of state feedback control laws to enlarge the size of region of attraction, where system state is allowed not to be in an invariant set.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An improved robust model predictive control approach to systems with linear fractional transformation perturbations

Zheng

2011

Int. J. Autom. Comput.

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In this paper, a robust model predictive control approach is proposed for a class of uncertain systems with time-varying, linear fractional transformation perturbations. By adopting a sequence of feedback control laws instead of a single one, the control performance can be improved and the region of attraction can be enlarged compared with the existing model predictive control (MPC) approaches. Moreover, a synthesis approach of MPC is developed to achieve high performance with lower on-line computational burden. The effectiveness of the proposed approach is verified by simulation examples.Keywords: Robust model predictive control, linear fractional transformation (LFT) perturbations, linear matrix inequalities (LMIs), feedback model predictive control (MPC) framework, sequence of feedback control laws.

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“…Using Lemma 3, it can be proved that the convex combination (γ,Q Q Q 0 ,Q Q Q 1 , · · · ,Q Q Q N−1 ) would also be the solution of conditions (8a), (8b), (10), and (11). Remark 2.…”

Section: Reduction Of Computation Burdenmentioning

confidence: 97%

Section: Reduction Of Computation Burdenmentioning

confidence: 99%

Section: Reduction Of Computation Burdenmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An improved robust model predictive control approach to systems with linear fractional transformation perturbations

Zheng

2011

Int. J. Autom. Comput.

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“…This is due to the fact that the algorithm directly solves off-line the optimization problem presented in [1]. In [6], an ellipsoidal off-line MPC algorithm based on nominal performance cost was presented. The algorithm directly extends the algorithm presented in [5] by choosing the nominal performance cost to substitute the worst-case performance cost.…”

Section: Introductionmentioning

confidence: 99%

MPC for LPV Systems Based on Parameter-Dependent Lyapunov Function with Perturbation on Control Input Strategy

Bumroongsri

Kheawhom

2012

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Abstract. In this paper, the model predictive control (MPC) algorithm for linear parameter varying (LPV) systems is proposed. The proposed algorithm consists of two steps. The first step is derived by using parameter-dependent Lyapunov function and the second step is derived by using the perturbation on control input strategy. In order to achieve good control performance, the bounds on the rate of variation of the parameters are taken into account in the controller synthesis. An overall algorithm is proved to guarantee robust stability. The controller design is illustrated with two case studies of continuous stirredtank reactors. Comparisons with other MPC algorithms for LPV systems have been undertaken. The results show that the proposed algorithm can achieve better control performance.

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Properties of parameter‐dependent open‐loop MPC for uncertain systems with polytopic description

Ding

2009

Asian Journal of Control

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This paper investigates the parameter-dependent open-loop model predictive control (PDOLMPC) scheme for systems with a polytopic uncertainty description. PDOLMPC parameterizes the infinite horizon control moves into a number of free control moves followed by a single state feedback law. The free control moves (excluding the first one) are parameter dependent and constructed upon all of the extreme realizations of the uncertainty before the switching horizon N . Our primary contribution is to point out that this PDOLMPC is a relaxed version of the feedback MPC. Thus, some properties of nominal MPC, such as enhancement of optimality and enlargement of region of attraction by increasing the switching horizon, can be inherited in PDOLMPC. These properties are theoretically important for robust MPC and a simulation example is given for demonstration.

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Improving off-line approach to robust MPC based-on nominal performance cost

Cited by 95 publications

References 6 publications

An improved robust model predictive control approach to systems with linear fractional transformation perturbations

An improved robust model predictive control approach to systems with linear fractional transformation perturbations

MPC for LPV Systems Based on Parameter-Dependent Lyapunov Function with Perturbation on Control Input Strategy

Properties of parameter‐dependent open‐loop MPC for uncertain systems with polytopic description

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