Robust output feedback controller design via genetic algorithms and LMIs: the mixed /spl Hscr//sub 2///spl Hscr//sub /spl infin// problem

In this paper, a structure-specified mixed H2/H∞ controller design using particle swarm optimization (PSO) is proposed for control balancing of Bicyrobo, which is an unstable system associated with many sources of uncertainties due to un-model dynamics, parameter variations, and external disturbances. The structure-specified mixed H2/H∞ control is a robust and optimal control technique. However, the design process normally comes up with a complex and non-convex optimization problem which is difficult to solve by the conventional optimization methods. PSO is a recently useful meta-heuristic search method used to solve multi-objective and non-convex optimization problems. In the method, PSO is used to search for parameters of a structure-specified controller which satisfies mixed H2/H∞ performance index. The simulation and experimental results show the robustness of the proposed controller in compared with the conventional proportional plus derivative (PD) controller, and the efficiency of the proposed algorithm in compared with the genetic algorithm (GA).

show abstract

“…& Rotea, M.A., 1991;Rotea, M.A. & Khargonekar, P.P., 1991;Scherer, C.W., 1995;Pereira, G.J. & Araujo, H.X., 2004;Wu, B.L., et al, 2006).…”

Section: Introductionunclassified

Balancing Control of Bicyrobo by Particle Swarm Optimization-Based Structure-Specified Mixed H2/H∞ Control

Thanh

Parnichkun

2008

International Journal of Advanced Robotic Systems

View full text Add to dashboard Cite

show abstract

“…An approach similar to that used in [25] but with improved efficiency and applicable to a variety of design techniques was proposed in [10] and [9]. To outline the idea, we consider again the LMI condition (2), which represents a necessary and sufficient condition for the H ∞ norm of (1) to be less than γ .…”

Section: A Hybrid Evolutionary-algebraic Algorithmmentioning

confidence: 99%

“…The design of a robust, decentralized low-order controller using GA with the structured singular value µ as fitness measure is reported in [21], however again without considering computational efficiency, leading to very long computation times. An evolutionary approach to the mixed H 2 /H ∞ problem was proposed in [25], where a genetic algorithm is used to search for reduced order controllers, while the H 2 and H ∞ norms are computed by solving LMI problems. In [7], the use of genetic algorithms and Youla parameters is proposed for solving non-convex design problems involving mixed L 1 /H 2 /H ∞ objectives; this approach again does not allow to impose structural constraints and leads to controllers whose order is at least the order of the generalized plant.…”

Section: Evolutionary Approachmentioning

confidence: 99%

A Hybrid Evolutionary-Algebraic Approach to Optimal and Robust Controller Design (Hybride evolutionär-algebraische Verfahren für den Entwurf optimaler und robuster Regler)

Werner¹,

Farag²

2005

Auto

View full text Add to dashboard Cite

Dedicated to Prof. Dr.-Ing. Heinz Unbehauen at the occasion of his 70th birthday Modern control techniques -such as H 2 or H ∞ optimal controller design -offer powerful synthesis tools, provided the controller has the same order as the plant, and there are no constraints on the information structure of the feedback loop (e. g. decentralized control). If these assumptions do not hold -as is often the case in practical applications -the synthesis problem becomes non-convex and hard to solve. A frequently encountered situation is however that a synthesis problem is intractable, whereas the corresponding analysis problem is convex and easy to solve. In this case, it is often more efficient to use the easily available analysis results to guide a stochastic search for the solution, rather than to address the hard synthesis problem directly. In this paper, such an approach -based on a combination of algebraic tools from optimal control theory and evolutionary search techniques -is presented. Four benchmark problems representing ''hard" control problems are used to illustrate the approach and to compare its efficiency with that of previously published solutions.Moderne H 2 -und H ∞ -optimale Reglerentwurfsverfahren sind nur anwendbar wenn der Regler die gleiche dynamische Ordnung wie die Strecke hat, und wenn keine Beschränkungen der Reglerstruktur (wie etwa bei dezentraler Regelung) vorliegen. Sind diese Voraussetzungen nicht erfüllt -was in der Praxis oft vorkommt -dann liegt ein nicht-konvexes Entwurfsproblem vor. Häufig ist jedoch das Analyse-Problem, das einem nicht-konvexen Entwurfsproblem entspricht, konvex und kann mit relativ geringem Rechenaufwand gelöst werden. In solchen Fällen ist es oft effizienter, Lösungen dieser Analyse-Probleme für stochastische Suchverfahren zu verwenden, als das nicht-konvexe Entwurfsproblem direkt zu lösen. In der vorliegenden Arbeit wird ein auf dieser Idee beruhender hybrider evolutionär-algebraischer Ansatz vorgestellt, der Werkzeuge aus der Theorie der optimalen Regelung kombiniert mit evolutionären Suchstrategien. Vier Benchmark-Probleme illustrieren die Vielseitigkeit und Effizienz des vorgeschlagenen Verfahrens.

show abstract

“…Genetic algorithm belongs to the larger class of evolutionary algorithms, which get solutions using techniques inspired by natural evolution, such as inheritance, mutation, selection, and crossover, etc. Genetic algorithm is a useful method for controller design, see e.g., Campos-Delgado & Zhou (2003); Neumann & Araujo (2004); Pereira & Araujo (2004). In the field of quantum control, genetic algorithm methods are applied to design quantum coherent feedback controllers, see e.g., and Harno & Petersen (2015).…”

Section: Genetic Algorithmmentioning

confidence: 99%

Mixed LQG and H_∞ coherent feedback control for linear quantum systems

Cui

Dong

Lee

2016

International Journal of Control

View full text Add to dashboard Cite

The purpose of this paper is to study the mixed linear quadratic Gaussian (LQG) and H∞ optimal control problem for linear quantum stochastic systems, where the controller itself is also a quantum system, often referred to as "coherent feedback controller". A lower bound of the LQG control is proved. Then two different methods, rank constrained linear matrix inequality (LMI) method and genetic algorithm are proposed for controller design. A passive system (cavity) and a non-passive one (degenerate parametric amplifier, DPA) demonstrate the effectiveness of these two proposed algorithms.

show abstract

Robust output feedback controller design via genetic algorithms and LMIs: the mixed /spl Hscr//sub 2///spl Hscr//sub /spl infin// problem

Cited by 10 publications

References 9 publications

Balancing Control of Bicyrobo by Particle Swarm Optimization-Based Structure-Specified Mixed H2/H∞ Control

Balancing Control of Bicyrobo by Particle Swarm Optimization-Based Structure-Specified Mixed H2/H∞ Control

A Hybrid Evolutionary-Algebraic Approach to Optimal and Robust Controller Design (Hybride evolutionär-algebraische Verfahren für den Entwurf optimaler und robuster Regler)

Mixed LQG and H_∞ coherent feedback control for linear quantum systems

Contact Info

Product

Resources

About

Robust output feedback controller design via genetic algorithms and LMIs: the mixed /spl Hscr//sub 2///spl Hscr//sub /spl infin// problem

Cited by 10 publications

References 9 publications

Balancing Control of Bicyrobo by Particle Swarm Optimization-Based Structure-Specified Mixed H2/H∞ Control

Balancing Control of Bicyrobo by Particle Swarm Optimization-Based Structure-Specified Mixed H2/H∞ Control

A Hybrid Evolutionary-Algebraic Approach to Optimal and Robust Controller Design (Hybride evolutionär-algebraische Verfahren für den Entwurf optimaler und robuster Regler)

Mixed LQG and H∞ coherent feedback control for linear quantum systems

Contact Info

Product

Resources

About

Mixed LQG and H_∞ coherent feedback control for linear quantum systems