IMA Journal of Mathematical Control and Information - current issue

Approximate controllability for semi-linear retarded stochastic systems in Hilbert spaces

Muthukumar, P., Balasubramaniam, P. — 2009-06-01

In this paper, semi-linear retarded stochastic control systems together with conditions for approximate controllability of associated linear system is used to obtain sufficient conditions for approximate controllability results in Hilbert spaces. An example is also provided to illustrate the theory.

State estimation for non-linear discrete-time systems with input signals

Xiao, M. — 2009-06-01

One of the typical approaches to construct an observer for non-linear systems is to seek a change of coordinates such that the observer design can be implemented in a relatively easier way. Thus, for such an approach, the main challenge is how to find such a change of coordinates. In this paper, we will provide an explicit expression of a change of coordinates which can transform a non-linear discrete-time system with inputs into a linear system with output injections. This leads to a linearizable error dynamics and thus the estimated state converges to the actual state exponentially in the new coordinates. We also discuss the observability and controllability issues which are related to the proposed change of coordinates.

Optimal control of vibrations of an elastic beam

Sun, B. — 2009-06-01

This paper is concerned with the optimal control problem of the vibrations of an elastic beam, which is governed by a non-linear partial differential equation. The functional analytical approach of Dubovitskii and Milyutin is adopted in investigation of the Pontryagin's maximum principle of the system. The necessary condition is presented for the optimal control problem in fixed final horizon case.

Delay feedback control in exponential stabilization of linear time-varying systems with input delay

Hien, L. V., Phat, V. N. — 2009-06-01

In this paper, we investigate the memory controller design for the exponential stabilization of linear time-varying systems with control delay. Based on state transformation and an improved Lyapunov–Krasovskii functional, new sufficient conditions for the exponential stabilization of the system are derived to design memory feedback controller which makes the system exponentially stabilizable. The conditions are given in terms of the solution of appropriate Riccati differential equations, which allows to compute simultaneously the two bounds that characterize the exponential stability rate of the solution. An application to robust control of uncertain linear control systems with input delay as well as illustrative examples to show the effectiveness of the obtained results is given.

Adaptive stabilization of a sine-Gordon equation with input disturbances

Kobayashi, T. — 2009-06-01

This paper is concerned with adaptive stabilization of the system governed by the sine-Gordon equation with input disturbances. The adaptive boundary controller is constructed by the concept of high-gain adaptive feedback and the estimation mechanism for the unknown parameters of the disturbances. The well posedness of the closed-loop system is justified. After the boundedness of the solution is shown, the stability of the closed-loop system and the convergence of the system state to zero are guaranteed by the LaSalle's invariance principle. The system with output disturbances is also discussed.

EP-based robustness analysis of optimal load allocation for boiler systems

Tsai, J. S. H., Du, Y. Y., Dunn, A. C., Shieh, L. S. — 2009-06-01

Based on evolutionary programming, a universal approach to examine the non-analytic solution robustness of an optimal allocation methodology for industrial boilers that is designed based on the second-order gradient method is proposed in this paper. The allocation algorithm is easy to implement without any specialized software and the precise robustness analysis considers the worst-case scenario when uncertainty factors are introduced into some of the boiler system parameters.

Stability of abstract non-linear non-autonomous difference-delay equations

Medina, R. — 2009-06-01

We consider a class of functional–difference equations in a Banach space with causal operators, which have the local Lipschitz property. Sufficient conditions for the boundedness of solutions and the Lyapunov stability are given. We offer some explicit stability criteria when the equations are defined on separable Hilbert spaces. Our approach is based on the representation of solutions combined with new norm estimates for operator-valued functions. Applications of the main results of the paper to the stability of abstract discrete-time control systems are especially investigated.

Supplement to: 'Boundary stabilization of hyperbolic systems related to overhead cranes' [H. Sano, IMA J. Math. Control Inf. (2008) vol. 25, 353-366, doi:10.1093/imamci/dnm031]

Sano, H. — 2009-06-01

In the paper cited in the heading, we treated the problem of stabilizing a flexible cable with two rigid loads, which was described by two kinds of hyperbolic equations. To show the asymptotic stability of the closed-loop system with a controller derived there, we used the LaSalle's invariance principle. However, in that paper, we need to supplement the proof of Theorem 5.1 and to revise the proof of Theorem 5.2. Throughout this note, we use the same notation as in the paper cited in the heading.

Identification of non-parametric FIR non-linear systems with low-degree interactive terms

Bai, E.-W., Chan, K.-S., Erdahl, C. — 2009-06-01

In this paper, an interactive term identification approach is proposed for identification of non-parametric finite impulse response non-linear systems under i.i.d. random sequences. The idea is to make a high-dimensional non-linear identification problem into a number of low-dimensional problems and thus to effectively combat the problem of the curse of dimensionality. Convergence results are established in the paper and numerical results support the theoretical analysis and demonstrate that the proposed approach is an attractive alternative to existing non-linear identification methods.