The open-loop linear quadratic differential game for index one descriptor systems

Engwerda, Jacob; Salmah,

doi:10.1016/j.automatica.2008.09.012

Cited by 27 publications

(14 citation statements)

References 13 publications

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“…Maksud dari permainan dengan tipe informasi lingkar terbuka adalah bahwa selama permainan berlangsung dalam waktu setiap pemain hanya mengetahui state awal dan struktur model (bisanya dinotasikan dengan , ). Skenario ini dapat diinterpretasikan dengan di awal permainan setiap pemain menentukan strateginya masingmasing secara serempak, kemudian mereka mendaftarkan strategi tersebut kepada bandar permainan yang akan menjalankan strategi tersebut secara konsisten (Engwerda Salmah, 2009). Sedangkan dalam permainan lingkar tertutup informasi yang dimiliki oleh masing-masing pemain adalah keseluruhan (Engwerda Salmah, 2011).…”

Section: Permainan Dinamisunclassified

Masalah Peredaman Gangguan (Disturbance Attenuation Problem) Untuk Sistem Linear Time Invariant Lingkar Terbuka Dengan Pendekatan Permainan Dinamis

Musthofa

2016

JFOURIER

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AbstrakMakalah ini membahas tentang desain kendali robust untuk mengatasi peredaman gangguan yang terjadi pada suatu sistem dinamik Linear Time Invariant (LTI). Tidak seperti metode yang biasa dilakukan dalam mendesain kendali robust, dalam makalah ini kendali robust didesain dengan menggunakan pendekatan permainan dinamis. Disamping desain kendali, dalam makalah ini juga dibahas batas terkecil dari parameter  sebagai level peredaman gangguan.Selanjutnya disajikan contoh numerik desain kendali robust melalui pendekatan domain frekuensi dan permainan dinamis.Kata Kunci: Masalah Peredaman Gangguan; Kendali Robust; Permainan Dinamis; sistem LTI. AbstractThis paper discusses the design of robust control to overcome disturbance attenuation in a dynamic system linear time invariant (LTI). Unlike the usual method in designing robust control, robust control in this paper is designed using dynamic game approach. Besides the design of the control, in this paper also discussed the small end of the parameters as the level of interference suppression. Further presented numerical example of robust control design via frequency domain approach and dynamic game.Keywords: Interference Suppression problem; Robust Control; Dynamic Games; LTI system. PendahuluanGangguan adalah suatu hal yang hampir pasti dialami oleh semua sistem. Gangguan dapat berasal dari faktor eksternal sistem seperti turbulensi angin pada pesawat terbang yang sedang mengudara. Selain itu gangguan dapat pula berasal dari faktor internal sistem sebagai akibat ketidakakuratan pemodelan seperti fluktuasi inflasi akibat ketidakakuratan pemodelan sistem makro ekonomi (Engwerda, 2005). Tersaji dalam bentuk apapun, gangguan selalu merugikan sistem. Oleh karena itu permasalahan yang banyak dihadapi oleh desainer kendali adalah mendesain kendali yang mampu mengatasi gangguan-gangguan yang mungkin muncul pada sistem.Fokus dari masalah redaman gangguan (disturbance attenuation problem) adalah mendesain sebuah kendali optimal (yang meminimalkan biaya pengendalian) untuk meredam berbagai tipe gangguan yang bermacam-macam yang muncul pada sistem yang tidak hanya dapat diaplikasikan pada suatu jenis plant dengan masukan tunggal yang tidak diketahui, akan tetapi desain kendali tersebut mampu diaplikasikan pada berbagai jenis plant sehingga tujuan pengendalian yang diinginkan dapat tercapai.Tingkat kuantitas gangguan yang teredam ditunjukkan oleh suatu parameter yang menyatakan nilai minimax dari kuantitas output terkendali dengan kuantitas gangguan yang keduanya dinyatakan dalam bentuk norm ruang H  dari fungsi transfer sistemnya (Basar Bernhard, 1995).Masalah redaman gangguan merupakan bagian dari masalah desain kendali robust. Kendali robust adalah sebuah jenis kendali yang kokoh terhadap gangguan dan ketidakpastian yang dialami oleh suatu sistem. Dalam dua dekade ini pengembangan metode desain sistem kendali yang robust masih

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Section: Permainan Dinamisunclassified

Masalah Peredaman Gangguan (Disturbance Attenuation Problem) Untuk Sistem Linear Time Invariant Lingkar Terbuka Dengan Pendekatan Permainan Dinamis

Musthofa

2016

JFOURIER

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“…Of course problem (7,8) is not completely specified, as we did not specify the set of admissible feedback strategies yet. Throughout this note we restrict the analysis to the set of linear state feedback controls that stabilize the system for all consistent initial states.…”

Section: Preliminariesmentioning

confidence: 99%

“…[20,21], derived some first results for descriptor systems, in particular for zero-sum games assuming a closed-loop perfect state information structure. Engwerda et al [8] recently solved the general problem for index one systems assuming an open-loop information structure. Based on an equivalence result in linear-quadratic theory we derive in Section III for the general indefinite linear-quadratic control problem a both necessary and sufficient condition for the existence of a stabilizing feedback control.…”

Section: Introductionmentioning

confidence: 99%

The Optimal Linear Quadratic Feedback State Regulator Problem for Index One Descriptor Systems

2008

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In this note we present both necessary and sufficient conditions for the existence of a linear static state feedback controller if the system is described by an index one descriptor system. A priori no definiteness restrictions are made w.r.t. the quadratic performance criterium. It is shown that in general the set of solutions that solve the problem constitutes a manifold. This feedback formulation of the optimization problem is natural in the context of differential games and we provide a characterization of feedback Nash equilibria in a deterministic context.

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“…The differential games of singular systems can describe many practical situations and have been widely studied by many researchers for several decades. Among these, most researchers studied the differential games of deterministic singular systems in finite-time horizon and infinite-time horizon, we refer the reader to [17][18][19][20][21] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

“…It is worth mentioning that many researchers discussed the Nash differential games of singular systems by disintegrating the systems into two: fast and slow [18,19,21] . Recently Zhang and Xing deal with the stochastic singular systems as a whole by using the square completion technique, and get the results for optimal control problems involving new stochastic generalized Riccati equation.…”

Section: Introductionmentioning

confidence: 99%

Linear Quadratic Nash Differential Games of Stochastic Singular Systems

Zhou

Zhu

Zhang

2014

Journal of Systems Science and Information

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In this paper, we deal with the Nash differential games of stochastic singular systems governed by Itô-type equation in finite-time horizon and infinite-time horizon, respectively. Firstly, the Nash differential game problem of stochastic singular systems in finite time horizon is formulated. By applying the results of stochastic optimal control problem, the existence condition of the Nash strategy is presented by means of a set of cross-coupled Riccati differential equations. Similarly, under the assumption of the admissibility of the stochastic singular systems, the existence condition of the Nash strategy in infinite-time horizon is presented by means of a set of cross-coupled Riccati algebraic equations. The results show that the strategies of each players interact.

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The open-loop linear quadratic differential game for index one descriptor systems

Abstract: In this paper we consider the linear quadratic differential game for descriptor systems that have index one. We derive both necessary and sufficient conditions for existence of an open-loop Nash equilibrium.

Cited by 27 publications

References 13 publications

Masalah Peredaman Gangguan (Disturbance Attenuation Problem) Untuk Sistem Linear Time Invariant Lingkar Terbuka Dengan Pendekatan Permainan Dinamis

Masalah Peredaman Gangguan (Disturbance Attenuation Problem) Untuk Sistem Linear Time Invariant Lingkar Terbuka Dengan Pendekatan Permainan Dinamis

The Optimal Linear Quadratic Feedback State Regulator Problem for Index One Descriptor Systems

Linear Quadratic Nash Differential Games of Stochastic Singular Systems

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