Multiobjective Robust Control with HIFOO 2.0

Gümüşsoy, Suat; Henrion, Didier; Millstone, Marc; Overton, Michael L.

doi:10.3182/20090616-3-il-2002.00025

Cited by 132 publications

(107 citation statements)

References 11 publications

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“…Note that RS CPU time appearing in the third column of Table 1 relates to running the RS algorithm for known optimal value of the abscissa. The RS algorithm is sufficiently fast also for this purpose, but other methods such as the HIFOO algorithm (see [19]) can be applied for this purpose as well.…”

Section: Methodsmentioning

confidence: 99%

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On Application of the Ray-Shooting Method for LQR via Static-Output-Feedback

Peretz¹

2018

Algorithms

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Abstract:In this article we suggest a randomized algorithm for the LQR (Linear Quadratic Regulator) optimal-control problem via static-output-feedback. The suggested algorithm is based on the recently introduced randomized optimization method called the Ray-Shooting Method that efficiently solves the global minimization problem of continuous functions over compact non-convex unconnected regions. The algorithm presented here is a randomized algorithm with a proof of convergence in probability. Its practical implementation has good performance in terms of the quality of controllers obtained and the percentage of success.

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Section: Methodsmentioning

confidence: 99%

“…Assume that K (0) ∈ int (S α ) was found by the RS algorithm (see [16]) or by any other method (see [19][20][21]). Let h > 0 and let U (0) be a unit vector w.r.t.…”

Section: The Practical Algorithm For the Problem Of Lqr Via Sofmentioning

confidence: 99%

On Application of the Ray-Shooting Method for LQR via Static-Output-Feedback

Peretz¹

2018

Algorithms

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“…The suggested method was evaluated and compared to HIFOO 3.0 1 see [10] and HINFSTRUCT which is part of the ROBUST CONTROL TOOLBOX in MATLAB, version 7.11 (R2010b), and based on the paper [11].…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…HIFOO and HIN-FSTRUCT, see [10] and [11] respectively. These methods are based on nonconvex, nonsmooth approaches for minimizing the H ∞ norm of a closed loop system that do not involve any LMIs.…”

Section: Introductionmentioning

confidence: 99%

A partially augmented Lagrangian method for low order H-infinity controller synthesis using rational constraints

Ankelhed

Helmersson

Hansson

2011

IEEE Conference on Decision and Control and European Control Conference

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When designing robust controllers, H-in nity synthesis is a common tool to use. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the (augmented) system, the problem becomes nonconvex and it is relatively hard to solve. These problems become very complex, even when the order of the system is low. The approach used in this work is based on formulating the constraint on the maximum order of the controller as a polynomial (or rational) equation. This equality constraint is added to the optimization problem of minimizing an upper bound on the H-in nity norm of the closed loop system subject to linear matrix inequality (LMI) constraints. The problem is then solved by reformulating it as a partially augmented Lagrangian problem where the equality constraint is put into the objective function, but where the LMIs are kept as constraints. The proposed method is evaluated together with two well-known methods from the literature. The results indicate that the proposed method has comparable performance in most cases, especially if the synthesized controller has many parameters, which is the case if the system to be controlled has many input and output signals. Abstract-When designing robust controllers, H-infinity synthesis is a common tool to use. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the (augmented) system, the problem becomes nonconvex and it is relatively hard to solve. These problems become very complex, even when the order of the system is low.The approach used in this work is based on formulating the constraint on the maximum order of the controller as a polynomial (or rational) equation. This equality constraint is added to the optimization problem of minimizing an upper bound on the H-infinity norm of the closed loop system subject to linear matrix inequality (LMI) constraints. The problem is then solved by reformulating it as a partially augmented Lagrangian problem where the equality constraint is put into the objective function, but where the LMIs are kept as constraints.The proposed method is evaluated together with two wellknown methods from the literature. The results indicate that the proposed method has comparable performance in most cases, especially if the synthesized controller has many parameters, which is the case if the system to be controlled has many input and output signals.

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“…The first one consists of directly optimizing performance and robustness measures as a function of the controller parameters. This approach, which is at the basis of the package HIFOO [1,12], has been generalized to time-delay systems [13]. It aims at computing locally optimal solutions, hence, it heavily relies on good starting values for the controller.…”

Section: Introductionmentioning

confidence: 99%

Reduced modelling and fixed‐order control of delay systems applied to a heat exchanger

Michiels

Hilhorst

Pipeleers

et al. 2017

IET Control Theory & Applications

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This paper presents an integrated approach for designing low-order multi-objective controllers for linear time-delay systems, combining recently developed methods for reduction of delay systems and fixed-order control design, respectively. First, as a benchmark problem for process control applications, a model of an experimental heat transfer setup is discussed in detail, which serves to motivate the adopted combination of model reduction and control technique. The former corresponds to a Krylov based reduction procedure, which is generalized to multiple-input-multiple-output systems with state, input and output delays, and allows the adaptive construction of an accurate low-order linear time-invariant approximation of the original linear time-delay system. Concerning the latter, a fixed-order controller is synthesized for the delay-free approximation, exploiting a recently proposed linear matrix inequality based framework for fixed-order controller design, and validated on the original linear time-delay system. In this way, the systematic overall design procedure, which is grounded in convex optimization, complements approaches based on directly optimizing stability and performance measures as a function of the controller parameters, which may lead to highly nonconvex and even non-smooth optimization problems. The successful design of a fixed-order multi-H 2 controller is validated on the benchmark problem, confirming the potential of the adopted approach for realistic industrial applications. IntroductionWe consider continuous-time models for control systems, described in terms of delay differential equations of the form(1) i = 1, . . . , my, where x(t) ∈ R n is the state, u i (t) ∈ R, i = 1, . . . , mu are the inputs, and y i (t) ∈ R, i = 1, . . . , my correspond to the outputs at time t. The quantities τ i , i = 1, . . . , mx, µ i , i = 1, . . . , mu and ν i , i = 1, . . . , my represent time-delays in the system's state, inputs and outputs, respectively, where the largest state delay is denoted by τmax = max i∈{1,...,mx} τ i . The inputs u i and outputs y i are grouped in vectors as follows:where we assume that the number of scalar inputs does not exceed the dimension of the system state, i.e., mu ≤ n. Without loss of generality, the input u and output y are subdivided asto distinguish between exogenous inputs u 1 and control inputs u 2 on the one hand, and regulated outputs y 1 and measured outputs y 2 on the other hand. The targeted class of delay systems described by (1) results from the physics based modeling of complex interconnections of components, where time-delay elements naturally appear in modeling propagation phenomena. The latter are due to the fact that the transfer of material, energy and information is mostly not instantaneous. For this class of systems, the experimental heat-transfer setup described in Section 3 serves as a benchmark problem for the control design. An analogous model has been derived in [25] for a greenhouse. More applications include chemical reactors [26], plate...

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Multiobjective Robust Control with HIFOO 2.0

Cited by 132 publications

References 11 publications

On Application of the Ray-Shooting Method for LQR via Static-Output-Feedback

On Application of the Ray-Shooting Method for LQR via Static-Output-Feedback

A partially augmented Lagrangian method for low order H-infinity controller synthesis using rational constraints

Reduced modelling and fixed‐order control of delay systems applied to a heat exchanger

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