Variable structure control of discretized continuous-time systems

A discrete-time variable structure control technique is presented for uncertain continuous-time systems. The design algorithm makes use of the concept of time-delay control in order to estimate the effects of the system perturbations inside the switching region. The controller performances have been evaluated by simulation using a benchmark problem proposed in literature. A satisfactory behavior is obtained also in the presence of remarkable uncertainties, showing noticeable robustness with respect to parameter variations and external disturbances. Moreover, the time-response characteristics can be shaped by the designer, properly tuning the control algorithm parameters     

Authors' reply [to comments on "A fuzzy approach to strategic games"]

For original paper see ibid., vol.7, no.6, p.634-42 (1999). We have no problem with the comments presented by Mathew and Kaimal (see ibid., p.415, 2005) regarding the investigation discussed in our original paper. The fact is that the general result in the investigated cases, that for a prisoner in both situations (noncooperative and selfish) the optional strategy is still to "confess" irrespective of the strategic choice made by the opponent party, really is in agreement with our original discussions. We thank the authors of the comments for their interest in our work, which has been recently expanded into "software testing via fuzzy strategic games" as well as "fighting terrorism in cyberspace using fuzzy strategic games." It is interesting to note that, especially in these two applications, the comments made by Mathew and Kaimal may make a significant impact.     

Comments on "Variable structure control of discretized continuous-time Systems"

In this note, we point out that the control proposed in the above paper can actually work under milder assumption with respect to the size of uncertainty in the control input vector.     

Authors' reply [Comment on "A robust state observer scheme"]

We agree that the conditions given in the original paper (ibid. vol.46, 2001) are incomplete. The counterexample actually raises an interesting and important issue, i.e., the controllability of an observer.     

Authors' reply to comment on "stability of fuzzy control systems with bounded uncertain delays"

For comment see ibid., p.285-6 (2004). The authors reply to a comment on their paper (Z. Yi and P.A. Heng, see ibid., vol.10, p.92-7, 2002) by agreeing with the comment.     

Authors' reply [fuzzy adaptive sliding-mode control for MIMO nonlinear systems]

We have studied the comment about our original paper and we agree that a minor mistake was made in Eq. 37 of our original paper (see ibid., vol. 11, no. 3, p. 354-60 (2003)).     

Authors' reply [to comments on 'Comments on "Robust trucking enhancement of robot systems including motor dynamics: A fuzzy-based dynamic game approach"']

For 'Comments on "Robust trucking enhancement of robot systems including motor dynamics: A fuzzy-based dynamic game approach"' see ibid., vol. 10, p.412-414. For Comments on Comments on "Robust trucking enhancement of robot systems including motor dynamics: A fuzzy-based dynamic game approach", see ibid., p. 701-2.     

A simple method to guarantee closed-loop stability when continuous-time systems are discretized

Sophisticated techniques fail to guarantee closed loop stability of discretized continuous-time systems. The simple, foolproof approach of mapping eigenvalues under z=esT is explored here. The result has a partial fraction type solution, implementable by such common teaching aids as Program CC. An increase in controller order may be necessary, but guidance on extra pole locations is given based on elementary measures such as gain and phase margin.     

Variable structure control of stochastic systems

In this paper, the problem of variable structure control of stochastic (SVSC) systems is proposed and the corresponding variable structure control strategies with complete and incomplete state information are established. The concepts of stochastic sliding mode and sliding motion band are introduced which may be regarded as the basic characteristics of SVSC systems. Robustness of SVSC systems is considered and a general design procedure for SVSC systems is presented. The effectiveness of the proposed control method is shown by simulation results.     

凸胞型不确定系统的变结构控制

讨论了凸胞型不确定系统的变结构控制,利用LMI方法,给出了滑模面存在的充分条件,并且给出了线性滑模面的显式表达式.所设计的变结构控制律不仅能保证系统在有限时间到达滑模面,并且保证受限在滑模面上的降阶等价系统是D_R稳定的.最后,给出一个设计实例来阐明该控制方法的有效性.     

Distributed predictive control of continuous-time systems

In the last years focus has been put in the development of distributed Model Predictive Control (MPC) algorithms. With a few exceptions, they have been mostly developed in the discrete-time framework. However, discretization of large-scale systems may destroy the sparsity of the original continuous-time models, making distributed control design and implementation more difficult. Also, more in general, discrete-time control of continuous-time systems does not allow to consider the process inter-sampling behavior. In this paper we present a novel non-cooperative distributed predictive control algorithm for continuous-time systems based on robust MPC concepts. The convergence properties of the proposed control scheme are stated, and its realizability is tested through a simulation case study.     

Variable structure systems nonlinear in the control law

The most relevant results of Utkin's work obtained for variable structure systems linear in the control law which slide on suitable manifolds in the state space, are extended to some class of fully nonlinear plants. The equivalence between the Filippov solution concept is proved for this class. Further, the approximability property (convergence to the nonideal sliding motion to the ideal) is shown to hold for an important subclass.     

一种不确定离散时间系统的变结构控制方法

针对离散时间系统变结构控制中存在的问题,利用指数趋近律的趋近特性,提出一种新的离散变结构控制方法.利用递推估计的方法设计变结构控制律,有效地抵消了线性系统中慢变不确定性的影响,实现了对慢变非线性系统的控制.该方法克服了以往控制方法中需已知扰动上界的限制,降低了抖振,加快了趋近速度.仿真结果证明了该方法的有效性.     

Variable structure control of a class of uncertain systems

This brief paper proposes a method for tuning the parameters of a variable structure controller. The approach presented extracts the error at the output of the controller and applies a nonlinear tuning law using this error measure. The adaptation mechanism drives the state tracking error vector to the sliding hypersurface and maintains the sliding mode. In the simulations, the approach presented has been tested on the control of Duffing oscillator and the analytical claims have been justified under the existence of measurement noise, uncertainty and large nonzero initial errors.     

Optimal periodic feedback design for continuous-time LTI systems with constrained control structure

This paper aims to design a high-performance controller with any predefined structure for continuous-time LTI systems. The control law employed is the generalized sampled-data hold function (GSHF), which can have any special form, e.g. polynomial, exponential, piecewise constant, etc. The GSHF is first written as a linear combination of a set of basis functions obtained in accordance with its desired form and structure. The objective is to find the coefficients of this linear combination, such that a prespecified linear-quadratic performance index is minimized. A necessary and sufficient condition for the existence of such GSHF is first obtained in the form of matrix inequality, which can be solved by using the existing methods to obtain a set of stabilizing initial values for the coefficients or to conclude the non-existence of such structurally constrained GSHF. An efficient algorithm is then presented to compute the optimal coefficients from their initial values, so that the performance index is minimized. The paper utilizes the latest developments in the area of sum-of-square polynomials. The effectiveness of the proposed method is demonstrated in two numerical examples.     

Variable structure control of systems with uncertain nonlinear friction

A new approach to control system design for systems containing sandwiched, uncertain, non-smooth friction is proposed. The method is based on a multi-state backstepping approach to variable structure control design. Stability and robustness properties are investigated and examples are given.     

Author's reply [to comments on 'On Routh-Pade model reduction of interval systems']

The paper is reply to the article by Shih-Feng Yang (see ibid., p.273-4, 2005). Previously (Dolgin and Zeheb, 2003), it was shown that the existing generalization of the direct Routh table truncation method for interval systems fails to produce a stable system. Additionally, it was shown how to extend the method to ensure the stability of the resulting interval system. Although the main statement of Dolgin and Zeheb (2003) is correct, there is, however, an omission in the proposed algorithm of building interval Routh table:the newly calculated line in the table may be inconsistent with the last existing line. Two additional conditions should be formulated to avoid this situation. The main idea is to shrink the uncertainty of the elements of the last existing line of the table, in the procedure of building the new line.     

Adaptive control of continuous-time linear stochastic systems

An adaptive control problem for linear, continuous-time stochastic systems is described and solved in this paper. A solution of the adaptive control problem means that the family of maximum likelihood estimators is shown to be strongly consistent and the average costs are shown to converge to the optimal average costs. The unknown parameters in the model appear affinely in the drift term of the stochastic differential equation. The assumptions that are made for the solution are natural and verifiable. A recursive equation is given for the maximum likelihood estimates. This research was partially supported by NSF Grants ECS-8403286-A01 and ECS-8718026.