Design of an optimal controller for a discrete-time system subject to previewable demand

Katayama, Tohru; Ohki, Takahira; Inoue, Taiki; Kato, Toshikazu

doi:10.1080/0020718508961156

Cited by 218 publications

(169 citation statements)

References 13 publications

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“…The difference method in [2,[5][6][17][18][19][20] will be found to be the equivalent to the choice of the auxiliary variables in (7) (i.e., ( )…”

Section: Problem Formulation and Basic Assumptionsmentioning

confidence: 99%

“…In addition, in designing the observer, the eigenvalues of Based on the above analysis, the condition of existence of an observer (47) for the nominal system of system (45) is that the nominal system is observable. In the following, the PBH rank test [2] will be employed to prove the observability of the nominal system of augmented error system (45). For the sake of notational convenience, we denote the state matrix of the nominal system of system (45) …”

Section: Design Of State Observermentioning

confidence: 99%

“…Since the uncertainties are time-varying and unknown in this paper, construction of the augmented error system through the usual difference method in [2,[5][6][18][19][20][21] is impossible. If we use ( ) ( ) u k u  and ( ) ( ) x k x  , the information on the nominal system cannot be fully used.…”

Section: Problem Formulation and Basic Assumptionsmentioning

confidence: 99%

“…Sheridan proposed the concept of preview control via three models [1]. Subsequently, for discrete-time constant coefficient linear systems, Katayama et al constructed an augmented system that is equivalent to the original system [2], applying the difference in some degree between the state variables, tracking error variables. And based on optimal control theory, the optimal preview controller for the original system was obtained.…”

mentioning

confidence: 99%

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H_∞ Preview Control of A Class of Uncertain Discrete‐Time Systems

Liao

Deng

2017

Asian Journal of Control

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Abstract:This paper investigates the problem of H∞ preview tracking control with robust performance for uncertain discrete-time systems. In order to avoid applying the difference operator to the time-varying matrix, by taking advantage of the difference between the system state variables, input variables, and the corresponding auxiliary variables, instead of the usual difference between system states, an augmented error system including previewed information is constructed, which converts the tracking problem into a regulator problem. A sufficient condition based on the free-weighting matrices technique and the Lyapunov stability theory is derived for the robust asymptotic stability of uncertain systems. Moreover, a state feedback control law with preview action design method is obtained via linear matrix inequality (LMI) approach. Based on these, a state observer for preview control systems is formulated. Previewable reference signals are fully utilized through reformulation of the output equation while designing the state observer. The proposed construction method of augmented error system is applicable to uncertain discrete-time system in which the uncertainties are general. Also an integrator is introduced to ensure the closed-loop system tracking performance with no static error. The numerical results also show the effectiveness of the preview control law for uncertain systems in the paper. Asian Journal of Control

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“…The difference method in [2,[5][6][17][18][19][20] will be found to be the equivalent to the choice of the auxiliary variables in (7) (i.e., ( )…”

Section: Problem Formulation and Basic Assumptionsmentioning

confidence: 99%

Section: Design Of State Observermentioning

confidence: 99%

Section: Problem Formulation and Basic Assumptionsmentioning

confidence: 99%

mentioning

confidence: 99%

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H_∞ Preview Control of A Class of Uncertain Discrete‐Time Systems

Liao

Deng

2017

Asian Journal of Control

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“…This generator outputs a COM trajectory which results in a ZMP trajectory that tracks the reference one. An optimal control strategy [17] is used to resolve this tracking problem by synthesizing future information. It is therefore also called preview control since it takes future reference into account.…”

Section: Mathematical Modelingmentioning

confidence: 99%

Trajectory generation of straightened knee walking for humanoid robot iCub

Tsagarikis

Caldwell

et al. 2010

2010 11th International Conference on Control Automation Robotics &Amp; Vision

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Abstract-Most humanoid robots walk with bent knees, which particularly requires high motor torques at knees and gives an unnatural walking manner. It is therefore essential to design a control method that produces a motion which is more energy efficient and natural comparable to those performed by humans. In this paper, we address this issue by modeling the virtual springdamper based on the cart-table model. This strategy utilizes the preview control, which generates the desired horizontal motion of the center of mass (COM), and the virtual spring-damper for generating the vertical COM motion. The theoretical feasibility of this hybrid strategy is demonstrated in Matlab simulation of a multi-body bipedal model. Knee joint patterns, ground reaction force (GRF) patterns, COM trajectories are presented. The successful walking gaits of the child humanoid "iCub" in the dynamic simulator validate the proposed scheme. The joint torques required by the proposed strategy are reduced, compared with the one required by the cart-table model.

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