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Optimization Design Of Quantized Control Systems Based On LMI Technique

Posted on:2009-07-12Degree:DoctorType:Dissertation
Country:ChinaCandidate:W W CheFull Text:PDF
GTID:1118360308478804Subject:Navigation, guidance and control
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With the networked control and full digital control becoming the main stream of control system design, the problem of quantization has ignited enormous attentions. There are two aspects on the problem of quantization.One is the digital implementation of control systems.Another is the use of digital communication channels with limited bandwidth for feedback control.In the traditional designing, the quantization effects have not been considered,so when the quantization happens in the systems, which will result in the degradation of the system performance or system instability.For the first aspect, attentions are mainly payed to the design or realization problem of the non-fragile controller due to the FWL effects.All the existing works deal with the non-fragile controller design problem with the consideration of norm-bounded type of gain uncertainty. However, this type of uncertainty cannot reflect the uncertain information due to the FWL effects exactly. Correspondingly, the interval type of uncertainty is more exact than the former type to describe the uncertain information. But for this type of uncertainty, the vertices of the set of uncertain parameters grow exponentially with the number of uncertain parameters, which may result in numerical computation problem for systems with high dimensions.At present, there is no method for dealing with this numerical computation problem.In addition, it is well known that the computational efficiency is critical in real time applications, so it is highly desirable for a controller to have a sparse structure.However, up to now, there is no work related to filters design with sparse structure.Another is the use of digital communication channels with limited bandwidth for feedback control.In the problem of quantized feedback control, quantization policies with memory (dynamic quantization policies) are payed to attention for the advantage to scale the quantization levels dynamically so that the quantized system is asymptotical stable and satisfy prescribed performance.But the existing works with dynamic quantization policies do not consider the minimum number of quantization levels required to assure the H∞performance requirements for quantized systems.However, in the practical systems, due to the limitation of the communication, the quantizer range is with bound.So a major question about the quantized systems concerns the minimum number of quantization levels required to assure closed loop system stability and performance, which may have many benefits that include lower cost, higher reliability, and easier maintenance.This thesis, based on previous works of others, studies the quantization problem according to the above two aspects of quantization.On one hand, considering the non-fragile controller and filter design problem with the interval gain variations.A notion of structured vertex separator is proposed to approach the numerical computation problem caused by interval gain variations.It has been proved in theory that the proposed method is with less conservative than the existing method.At the same time, this thesis studies a class of non-fragile H∞controllers and filters design with sparse structure for linear discrete-time systems.The method proposed here not only reduces the number of nontrivial parameters but also designs the sparse structured filters with non-fragility. On the other hand, for the quantized feedback control problem, considering optimizing the minimum number of quantization levels required to assure the H∞performance requirements for quantized systems, presents a systematically new quantized control and filtering methodologies such that the quantizer range is minimized which guarantees the asymptotic stability of quantized systems and with prescribed H∞performance.The main contributions are as follows:Chapters 1-2 first summarize and analyze the development and main research methods in quantization problem.Preliminaries about the considered problem are also given.Chapter 3 investigates non-fragile H∞filters design problems of discrete-time linear time-invariant systems, based on the linear matrix inequality (LMI).On one hand, this part investigates the non-fragile H∞filtering problem with full parameters and interval gain variations.A notion of structured vertex separator is proposed to approach the numerical computation problem caused by interval gain variations, and presents a new design method for non-fragile H∞filters with full parameters.And we have proved in theory that the proposed method is with less conservative than the existing method.On the other hand,a class of sparse structured filter is specified, and with the restriction of this structure, the design method of the sparse structured non-fragile H∞filters is given.The numerical example has shown the effectiveness of the proposed approach.Based on the results in Chapter 3,Chapter 4 focuses on non-fragile H∞controllers design problems for linear discrete-time systems.The first part investigates the non-fragile H∞controllers design problem with full parameters and interval gain variations.With the help of the structured vertex separator proposed in Chapter 3,an LMI-based two-step procedure is presented to solve the numerical computation problem caused by interval gain variations, and presents a new sufficient condition for non-fragile H∞controllers design with full parameters and interval gain variations. Similarly, we have proved in theory that the proposed method is with less conservative than the existing method.The second part studies the non-fragile H∞filtering problem with sparse structures.Firstly, a class of sparse structured controller is specified, and with the restriction of this structure, the design method of the sparse structured non-fragile H∞controllers is given.The numerical example has shown the effectiveness of the proposed approach.Chapter 5 studies the problem of designing new quantized feedback H∞controller via state feedback and dynamic output feedback, respectively. The quantizers considered here are dynamic quantizers, which are conjuncted with static quantizers via dynamic scalings.The static quantizer ranges are fully considered here for practical transmission channels requirements.Quantized H∞control strategies are proposed with the consideration of optimizing static quantizer ranges.These guarantee the quantized systems asymptotically stable and with the prescribed H∞performance under the condition that the quantizers are with the optimized quantizer ranges.The numerical example has shown the effectiveness of the optimization approach.Chapter 6 investigates the quantized H∞filtering problems based on the linear matrix inequality (LMI) technique for continuous-time and discrete-time systems, respectively. The quantizer considered here is dynamic and composed of a dynamic scaling and a static quantizer. Quantized H∞filtering strategies are proposed with the consideration of optimizing static quantizer ranges for guaranteeing the prescribed filtering objective.Different from the former chapter, convex conditions for quantized filtering strategies design are presented in this chapter. In contrast, design conditions given in Chapter 5 are non-convex. A numerical and a practical example have shown the effectiveness of the optimization approach, respectively.Finally, the results of the dissertation are summarized and further research topics are pointed out.
Keywords/Search Tags:Linear systems, non-fragile control, fragility, sparse structure, additive gain variations, dynamic quantizer, static quantizer, optimization, quantizer range, quantization level, quantization errors, H_∞filtering, dynamic output feedback, LMI
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