Design of robust model-based controllers via parametric programming

Sakizlis, Vassilis; Kakalis, Nikolaos M.P.; Dua, Vivek; Perkins, John D.; Pistikopoulos, Efstratios N.

doi:10.1016/j.automatica.2003.08.011

Cited by 109 publications

(45 citation statements)

References 25 publications

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“…If α(A(δ)) = Re λ with λ = α + jω, then we search for ω in [0, 0.9 ω], and for ω in [2 ω, 20 ω]. In several cases (6,7,8,12,13,16,17,25,26,28,29) the value ω = 0 was obtained, in which event ω = 0 was chosen. In a number of cases the algorithm turns much faster with the frequency sweep method to reach the same precision.…”

Section: Results For Algorithmmentioning

confidence: 99%

See 1 more Smart Citation

Branch and bound algorithm with applications to robust stability

2016

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We discuss a branch and bound algorithm for global optimization of NP-hard problems related to robust stability. This includes computing the distance to instability of a system with uncertain parameters, computing the minimum stability degree of a system over a given set of uncertain parameters, and computing the worst case H ∞ norm over a given parameter range. The success of our method hinges (1) on the use of an efficient local optimization technique to compute lower bounds fast and reliably, (2) a method with reduced conservatism to compute upper bounds, and (3) the way these elements are favorably combined in the algorithm.

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Section: Results For Algorithmmentioning

confidence: 99%

“…Related branch and bound approaches in robust stability are Bemporad et al [7], Romero-Monsivais et al [24], or Sakizlis et al [26], see also [22]. Here we discuss a novel branch and bound algorithm, which has three key ingredients leading to a significantly better performance.…”

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confidence: 99%

Branch and bound algorithm with applications to robust stability

2016

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“…The recent research of robust explicit MPC has been focused on the design of robust explicit MPC controllers for linear dynamic systems with additive disturbances in the linear state-space models and/or parametric model uncertainties in the system matrices. The case of robust explicit MPC of linear systems with additive disturbances was first examined in the previous work of Sakizlis et al (2004c). The design of robust explicit MPC for linear systems with model parametric uncertainties and linear objective functions, was also investigated in Bemporad et al (2003).…”

Section: Robust Explicit Mpcmentioning

confidence: 99%

Theoretical and algorithmic advances in multi-parametric programming and control

Pistikopoulos¹,

Domínguez²,

Panos³

et al. 2012

Comput Manag Sci

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This paper presents an overview of recent theoretical and algorithmic advances, and applications in the areas of multi-parametric programming and explicit/multi-parametric model predictive control (mp-MPC). In multi-parametric programming, advances include areas such as nonlinear multi-parametric programming (mp-NLP), bi-level programming, dynamic programming and global optimization for multi-parametric mixed-integer linear programming problems (mp-MILPs). In multi-parametric/explicit MPC (mp-MPC), advances include areas such as robust multi-parametric control, multi-parametric nonlinear MPC (mp-NMPC) and model reduction in mp-MPC. A comprehensive framework for multi-parametric programming and control is also presented. Recent applications include a hydrogen storage device, a fuel cell power generation system, an unmanned autonomous vehicle (UAV) and a hybrid pressure swing adsorption (PSA) system.

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“…In mp-MPC, e orts have been made to develop a multi-parametric model-based controller that guarantees performance while satisfying the constraints, termed robust mp-MPC. While early approaches focused on (i) additive disturbances [6,259,286,306], (ii) model uncertainties [35,279], (iii) Min-max robust mp-MPC [6,35,81,172] and (iv) linear input/output models [82,259], recent advances point towards a more general approach for robust mp-MPC [188,279]. The key idea is thereby (i) a dynamic programming reformulation of the original problem, (ii) the formulation of the robust counter-part and (iii) the solution of the resulting mp-P problem.…”

Section: Robust Mp-mpcmentioning

confidence: 99%