Model-free control of Lorenz chaos using an approximate optimal control strategy

Li, Shuai; Li, Yangming; Liu, Bu; Murray, Timmy

doi:10.1016/j.cnsns.2012.05.024

Cited by 32 publications

(9 citation statements)

References 32 publications

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“…In this last case, although exact POMDP techniques (capable of finding the optimal solution of POMDP problems with small spaces) are not valid due to the big state space of the MTS problem, approximated recently developed POMDP model based methods [ 34 – 36 ] and model-free algorithms [ 37 ], used successfully to solve other tracking [ 38 – 40 ] and detection/recognition [ 41 ] problems, can be applied. Although the model-free approaches, also used in other control problems [ 42 , 43 ], have the advantage of not requiring the knowledge of the probabilistic transition and sensorial models, the method used in this paper and the techniques analyzed hereafter, exploit these knowledge to tackle search problems.…”

Section: Related Workmentioning

confidence: 99%

Minimum Time Search in Uncertain Dynamic Domains with Complex Sensorial Platforms

Lanillos

Besada-Portas

López-Orozco

et al. 2014

Sensors

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The minimum time search in uncertain domains is a searching task, which appears in real world problems such as natural disasters and sea rescue operations, where a target has to be found, as soon as possible, by a set of sensor-equipped searchers. The automation of this task, where the time to detect the target is critical, can be achieved by new probabilistic techniques that directly minimize the Expected Time (ET) to detect a dynamic target using the observation probability models and actual observations collected by the sensors on board the searchers. The selected technique, described in algorithmic form in this paper for completeness, has only been previously partially tested with an ideal binary detection model, in spite of being designed to deal with complex non-linear/non-differential sensorial models. This paper covers the gap, testing its performance and applicability over different searching tasks with searchers equipped with different complex sensors. The sensorial models under test vary from stepped detection probabilities to continuous/discontinuous differentiable/non-differentiable detection probabilities dependent on distance, orientation, and structured maps. The analysis of the simulated results of several static and dynamic scenarios performed in this paper validates the applicability of the technique with different types of sensor models.

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Section: Related Workmentioning

confidence: 99%

Minimum Time Search in Uncertain Dynamic Domains with Complex Sensorial Platforms

Lanillos

Besada-Portas

López-Orozco

et al. 2014

Sensors

View full text Add to dashboard Cite

show abstract

“…They verified the existence of global synchronization and antisynchronization attractors with intermingled basins of attraction, such that the basin of one attractor is riddled with holes belonging to the basin of the other attractor and vice versa [17]. Finally, Li et al concerned with model-free control of the Lorenz chaotic system, where only the online input and output are available, while the mathematic model of the system is unknown [18].…”

Section: Introductionmentioning

confidence: 99%

Stability and Stabilizing of Fractional Complex Lorenz Systems

Ibrahim

2013

Abstract and Applied Analysis

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“…The mathematical meteorologist Lorenz discovered chaos in a simple system of three autonomous ordinary differential equations in order to describe the simplified Rayleigh-Bénard problem [21] in 1963 which is the most popular system for studying [22][23][24][25][26]. Chen and Lee reported a new chaotic system [27] in 2004, which is now called the Chen-Lee system [28].…”

Section: Introductionmentioning

confidence: 99%

Chaotic Motions in the Real Fuzzy Electronic Circuits

Yang

Lin

et al. 2013

Abstract and Applied Analysis

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Fuzzy electronic circuit (FEC) is firstly introduced, which is implementing Takagi-Sugeno (T-S) fuzzy chaotic systems on electronic circuit. In the research field of secure communications, the original source should be blended with other complex signals. Chaotic signals are one of the good sources to be applied to encrypt high confidential signals, because of its high complexity, sensitiveness of initial conditions, and unpredictability. Consequently, generating chaotic signals on electronic circuit to produce real electrical signals applied to secure communications is an exceedingly important issue. However, nonlinear systems are always composed of many complex equations and are hard to realize on electronic circuits. Takagi-Sugeno (T-S) fuzzy model is a powerful tool, which is described by fuzzy IF-THEN rules to express the local dynamics of each fuzzy rule by a linear system model. Accordingly, in this paper, we produce the chaotic signals via electronic circuits through T-S fuzzy model and the numerical simulation results provided by MATLAB are also proposed for comparison. T-S fuzzy chaotic Lorenz and Chen-Lee systems are used for examples and are given to demonstrate the effectiveness of the proposed electronic circuit.

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Model-free control of Lorenz chaos using an approximate optimal control strategy

Cited by 32 publications

References 32 publications

Minimum Time Search in Uncertain Dynamic Domains with Complex Sensorial Platforms

Minimum Time Search in Uncertain Dynamic Domains with Complex Sensorial Platforms

Stability and Stabilizing of Fractional Complex Lorenz Systems

Chaotic Motions in the Real Fuzzy Electronic Circuits

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