An optimal control approach to robust tracking of linear systems

Tan, Haihua; Shu, Shaolong; Lin, Feng

doi:10.1080/00207170802187239

Cited by 49 publications

(27 citation statements)

References 24 publications

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“…Optimal controller contains both robustness as well as the optimal characteristic. There is a close relationship between robust controllers and optimal controllers [6]- [7].…”

Section: Introductionmentioning

confidence: 99%

Emulation design based linear quadratic regulation

Ali

Malik

2013

2013 XXIV International Conference on Information, Communication and Automation Technologies (ICAT)

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With the encouraging rapid advancement in digital controller design, there is a need to explore further the optimal and robust digital controller implementation schemes. The ease in implementation of the discrete time controller urge the designers to adopt the emulation design technique, in which discrete-time systems are treated in a continuous-time framework. In emulation design, a discrete-time controller is obtained after the discretization of continuous-time controller at a high sampling rate. Keeping in view the valuable advantages of emulation design, a linear discrete time closed loop structure is proposed with emulation design based linear quadratic regulator (LQR). The suggested scheme provides optimal tracking of a reference signal even in the presence of external disturbances. Prior knowledge about the external disturbance is utilized by the control scheme to effectively minimize its effect on the system. Through computer simulations, a comparison is also drawn between the proposed emulation based control scheme and the corresponding continuous-time control scheme. Results shows that sampling time and weighing parameters of the cost function play important roles in defining the system performance.

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“…Optimal controller contains both robustness as well as the optimal characteristic. There is a close relationship between robust controllers and optimal controllers [6]- [7].…”

Section: Introductionmentioning

confidence: 99%

Emulation design based linear quadratic regulation

Ali

Malik

2013

2013 XXIV International Conference on Information, Communication and Automation Technologies (ICAT)

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“…Based on generalized inverses theory and Bellman's dynamic programming approach, [12] presents a linear quadratic tracking controller design. Reference [23] solves a class of robust tracking problems of linear systems by translating them into linear quadratic regulator problem. Both state feedback and output feedback cases are considered when the uncertainties are matched and the separation principle is applied in the analysis of the latter case.…”

Section: Introductionmentioning

confidence: 99%

“…The 1380 S. LIU, L. XIE AND H. ZHANG studies have also been extended to time-delay systems; see, e.g. [17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Linear quadratic tracking problem for discrete‐time systems with multiple delays in single input channel

Liu

Xie

Zhang

2010

Intl J Robust & Nonlinear

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SUMMARYThe linear quadratic tracking problem for discrete-time systems with multiple delays in single input channel is considered. In this paper, we provide an approach without resorting to system state augmentation. The optimal tracking control is given in terms of the current state, the previous inputs, and the output of an auxiliary backward deterministic delay system which is formulated for the first time in this paper. The solution relies on a Riccati difference equation of the same dimension as the plant (ignoring the delays). The key to our development is the establishment of a duality between the optimal tracking control and the optimal smoothing estimation of an associated stochastic backward system as well as the introduction of the auxiliary backward deterministic delay system. An analysis of the computational complexity of the proposed approach and its comparison with that of the augmentation method, which is to incorporate the delayed inputs into the augmented state, are provided. An example is given to demonstrate the effectiveness of the results.

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“…The practical control systems contain nonlinear and time-varying behavior with various uncertainties and external disturbances due to the linearization approximations, modeling errors and measurement errors that can make the performance differ from the nominal design [22,23,26,28]. Therefore, control of such systems has attracted great research interest in the past decades [24].…”

Section: Introductionmentioning

confidence: 99%

A new LMI-based robust finite-time sliding mode control strategy for a class of uncertain nonlinear systems

Mobayen¹,

Tchier²

2016

Kybernetika

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A new LMI-based robust finite-time sliding mode control strategy for a class of uncertain nonlinear systems Kybernetika, Vol. 51 (2015) This paper presents a novel sliding mode controller for a class of uncertain nonlinear systems. Based on Lyapunov stability theorem and linear matrix inequality technique, a sufficient condition is derived to guarantee the global asymptotical stability of the error dynamics and a linear sliding surface is existed depending on state errors. A new reaching control law is designed to satisfy the presence of the sliding mode around the linear surface in the finite time, and its parameters are obtained in the form of LMI. This proposed method is utilized to achieve a controller capable of drawing the states onto the switching surface and sustain the switching motion. The advantage of the suggested technique is that the control scheme is independent of the order of systems model and then, it is fairly simple. Therefore, there is no complexity in the utilization of this scheme. Simulation results are provided to illustrate the effectiveness of the proposed scheme.,

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An optimal control approach to robust tracking of linear systems

Cited by 49 publications

References 24 publications

Emulation design based linear quadratic regulation

Emulation design based linear quadratic regulation

Linear quadratic tracking problem for discrete‐time systems with multiple delays in single input channel

A new LMI-based robust finite-time sliding mode control strategy for a class of uncertain nonlinear systems

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