Design of an optimal preview controller for linear time-varying discrete systems in a multirate setting

Optim Control Appl Methods

2017

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Summary For a class of uncertain discrete‐time systems, a preview controller based on linear matrix inequality is proposed. A new method is derived to construct an augmented error system instead of taking the difference of the error signal and the system equation. The new approach avoids applying the difference operator to the time‐varying matrix and can simplify the augmented error system. For the augmented error system of the uncertain system, state feedback is introduced. The sufficient condition of asymptotic stability of the closed‐loop system is derived for the performance index by using the relevant theorems of robust control theory. The condition can be realised by solving a linear matrix inequality optimization problem. By incorporating the controller obtained into the original system, we obtain the preview controller. Moreover, introducing an integrator allows the closed‐loop system to robustly track the desired tracking signal without steady‐state error.

Section: Derivation Of the Augmented Error Systemmentioning

confidence: 99%

“…To achieve the robust servo property mentioned above, we apply the method in 1 study to introduce the discrete integrator defined by

v ((),, i + 1) = v ((),, i) + e ((),, i),

where v (0) can be arbitrarily assigned.…”

Section: Derivation Of the Augmented Error Systemmentioning

confidence: 99%

“…The method proposed in this article does not have the advantage of an integrator, but this can be easily achieved by adding an integrator. 16 The integrator will then be added.…”

Section: Derivation Of the Augmented Error Systemmentioning

confidence: 99%

“…, and H > 0, as shown in Equation 5. To achieve the robust servo property mentioned above, we apply the method in 1 study 16 to introduce the discrete integrator defined by…”

Section: Derivation Of the Augmented Error Systemmentioning

confidence: 99%

See 2 more Smart Citations

Robust preview control for uncertain discrete‐time systems based on LMI

Optim Control Appl Methods

2017

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“…In recent years, a number of significant results about the preview theory were produced by combing with other control issues. For instance, the preview control problem for linear discrete-time multi-rate systems with time-delay was addressed in Liao, Takaba, Katayama, and Katsuura (2003). Recently, the preview control theory was also extended to continuous-time linear descriptor systems, and a design method of optimal preview controller was obtained under the assumption of impulse-free (Liao, Ren, Tomizuka, & Wu, 2015).…”

Section: Introductionmentioning

confidence: 99%

Cooperative global optimal preview tracking control of linear multi-agent systems: an internal model approach

International Journal of Systems Science

Deng

et al. 2017

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This paper investigates the cooperative global optimal preview tracking problem of linear multi-agent systems under the assumption that the output of a leader is a previewable periodic signal and the topology graph contains a directed spanning tree. First, a type of distributed internal model is introduced, and the cooperative preview tracking problem is converted to a global optimal regulation problem of an augmented system. Second, an optimal controller, which can guarantee the asymptotic stability of the augmented system, is obtained by means of the standard linear quadratic optimal preview control theory. Third, on the basis of proving the existence conditions of the controller, sufficient conditions are given for the original problem to be solvable, meanwhile a cooperative global optimal controller with error integral and preview compensation is derived. Finally, the validity of theoretical results is demonstrated by a numerical simulation.

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

Asian Journal of Control

Deng

2017

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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