Nondifferentiable optimization algorithm for designing control systems having singular value inequalities

It has been known for some time that many control system design requirements can be expressed as differentiable inequalities. More recently, it has been shown that important structural properties such as robustness and low noise sensitivity can be expressed as nondifferentiable inequalities involving the singular values of a system or return difference transfer function matrix. This paper presents an optimization algorithm which permits all these constraints to be considered.     

A regularization algorithm for singular controls of parabolic systems

A practically convenient method of regularization is proposed to solve an optimal control problem for a parabolic equation with a delta function on its right-hand side. The corresponding regularized analogue is proved to converge to a delta function in a negative space. The differential characteristics of the performance criterion are analyzed. An algorithm for finding the optimal control is developed for a regularized problem. Results from a numerical testing of the algorithm are presented. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 86–94, January–February 2006.     

A Jordan control canonical form for singular systems

A canonical form for controllable singular systems modulo restricted system equivalence is presented. The canonical form respects the decomposition of the singular system into a regular and an impulsive part. The construction is based on Popov's control canonical form and on the Jordan canonical form recently developed by Hinrichsen and Prätzel-Wolters. Continuity properties are analysed and the cellular partition of the orbit space induced by the canonical form is briefly discussed.     

A frequency domain approach to control of singular systems

In this paper, singular control systems are studied from the frequency domain point of view. The proper stable factorization of a singular system is derived. The stability of the closed-loop system consisting of a singular system and controller is addressed. Most significantly, all proper stabilizing controllers are parameterized for a given singular system     

Algebraic properties of singular systems subject to decentralized output feedback

This paper investigates algebraic properties of decentralized singular systems (DSSs) under local static output feedback. New concepts of the geometric multiplicity (GM) of the finite decentralized fixed mode (DFM), the decentralized output feedback variable polynomial (DVP), and the finite decentralized output feedback cycle index (DCI) of the DSS are defined. The formulas for determining the GM and the DCI are given in terms of the DFM and the system matrices. It is shown that almost any decentralized output feedback can make the zeros of the DVP (i.e., the closed-loop poles that are variable) distinct and away from any given finite set in the complex plane. It is also shown that the finite DFM of the DSS are those uncontrollable and/or observable finite modes of the closed-loop DSS through any single channel. Finally, the minimal number of the inputs and outputs that guarantee the finite modes of the closed-loop DSS controllable and observable is shown to be the finite DCI of the DSS. An illustrative example is provided.     

Feedback linearization control design for systems with fuzzyuncertainty

We derive a state feedback control design for nonlinear systems with fuzzy uncertainty. We use a fuzzy version of the Kolmogorov forward equation and an equivalent deterministic system to represent the effects of the fuzzy uncertainty. Feedback linearization of the equivalent deterministic system cancels both the system nonlinearities and the effects of the fuzzy uncertainty on the state membership function. Our controller obtains asymptotic stability and an approximation to our controller drives the system state to a small bounded set     

Feedback control for non-linear singular systems

An invertible non-linear map is developed, which transforms a non-linear singular system into a regular one and preserves local properties under the application of specific feedback control laws. The presented algorithm is easily implementable on a digital computer, since it is of closed form. An application of the above algorithm is presented on an autonomous vehicle.     

Rapid distributed model predictive control design using singular value decomposition for linear systems

The issue of model predictive control design of distribution systems using a popular singular value decomposition (SVD) technique is addressed. Namely, projection to a set of conjugate structure is dealt with in this paper. The structure of the resulting predictive model is decomposed into small sets of subsystems. The optimal inputs can be separately designed at each subsystem in parallel without any interaction problems. The optimal inputs can be directly obtained and the communication among the subsystems can be significantly reduced. In addition, the design of distribution model predictive control (DMPC) with constraints using the SVD framework is also presented. The unconstraint inputs are checked in parallel in the conjugate space. Without solving the QP problem of each subsystem, the suboptimal solution can be quickly obtained by selecting the bigger singular values and discarding the small singular values in the singular value space. The convergence condition of the proposed algorithm is also proved. Two case studies are used to illustrate the distribution control systems using the suggested approach. Comparisons between the centralized model predictive control method and the proposed DMPC method are carried out to show the advantages of the newly proposed method.     

A neural approach for control of nonlinear systems with feedback linearization.

Several schemes for feedback linearization using neural networks have been investigated and compared. Then an approach to design a neurocontroller in the sense of feedback linearization is introduced. The contents include: (1) full input-output linearization when a system has relative degree n; (2) partial input-output linearization when a system has relative degree r (r相似文献   

Two singular value inequalities and their implications in H∞approach to control system design

In this note we prove that ifAandBare both nonnegative definite Hermitian matrices andA - Bis also nonnegative definite, then the singular values of A and B satisfy the inequalitiessigma_{i}(A)geq sigma_{i}(B), wherebar{sigma}(cdot) = sigma_{1}(cdot) geq sigma_{2}(cdot) geq '" geq sigma_{m}(cdot) = underbar{sigma}(.)denote the singular values of a matrix. A consequence of this property is that, in a nonsquare H^{infty} optimization problem, ifsup_{omega} bar{sigma}[Z(jsigma)] {underline{underline Delta}} sup_{omega} bar{sigma}[x(jomega)^{T}/ Y(jomega)^{T}]^{T} = lambda, then the singular values ofXandYsatisfy the inequalitylambda^{2} geq max_{i} sup_{omega} [sigma_{i}^{2}(X) + sigma_{m-i-1}^{2}(Y)]wheremis the number of columns of the matrixZ.     

A multi-colony ant algorithm for optimizing join queries in distributed database systems

Distributed database systems provide a new data processing and storage technology for decentralized organizations of today. Query optimization, the process to generate an optimal execution plan for the posed query, is more challenging in such systems due to the huge search space of alternative plans incurred by distribution. As finding an optimal execution plan is computationally intractable, using stochastic-based algorithms has drawn the attention of most researchers. In this paper, for the first time, a multi-colony ant algorithm is proposed for optimizing join queries in a distributed environment where relations can be replicated but not fragmented. In the proposed algorithm, four types of ants collaborate to create an execution plan. Hence, there are four ant colonies in each iteration. Each type of ant makes an important decision to find the optimal plan. In order to evaluate the quality of the generated plan, two cost models are used—one based on the total time and the other on the response time. The proposed algorithm is compared with two previous genetic-based algorithms on chain, tree and cyclic queries. The experimental results show that the proposed algorithm saves up to about 80 % of optimization time with no significant difference in the quality of generated plans compared with the best existing genetic-based algorithm.     

On approximate linearization of nonlinear control systems

A method for the approximate linearization of nonlinear control systems based on the ‘state-space exact linearization’ method is presented. An explicit procedure, both for the single-input and for the multiple-input case, is given, which is straightforward to implement.     

Output-feedback control for switched linear systems subject to actuator saturation

This article is devoted to the output-feedback ?_∞ control problem for switched linear systems subject to actuator saturation. We consider both continuous- and discrete-time switched systems. Using the minimal switching rule, nonlinear output feedbacks expressed in the form of quasi-linear parameter varying system are designed to satisfy a pre-specified disturbance attenuation level defined by the regional ?₂ (?₂)-gains over a class of energy-bounded disturbances. The conditions are expressed in bilinear matrix inequalities and can be solved by line search coupled with linear matrix inequalities optimisation. A spherical inverted pendulum example is used to illustrate the effectiveness of the proposed approach.     

Adaptive neural control for uncertain systems subject to actuator failure

In this paper, the design of controller based on neural network is investigated for a class of uncertain systems subject to actuator failures. An adaptive neural controller is designed by utilizing the approximation technique of neural network. The key feature in this work is to remove the requirement on the boundedness of unknown nonlinear functions that is usually encountered in the existing works. Moreover, sufficient conditions are derived such that the closed-loop system is robustly stable. Finally, numerical simulation results are given.     

On impulsive modes of linear singular systems subject to decentralized output feedback

Some algebraic properties of linear singular systems at infinity under static decentralized output feedback are studied in this note. New concepts of algebraic multiplicity and geometric multiplicity of the impulsive decentralized fixed modes, and the impulsive decentralized cycle index of the singular system are defined. These concepts indicate how much a singular system can be made close to being impulse-free by decentralized output feedback, and the results are shown to be generic. The geometric multiplicity and the impulsive decentralized cycle index are determined in terms of the system matrices explicitly. The number of impulsive modes that can be eliminated is given in terms of these indexes. The impulsive decentralized cycle index is shown to characterize generic properties on controllability and observability of the closed-loop system through an individual channel (or an external channel). Illustrative examples are provided.     

A new superconvergent method for systems of nonlinear singular boundary value problems

A new superconvergent method based on a sextic spline is described and analysed for the solution of systems of nonlinear singular two-point boundary value problems (BVPs). It is well known that the optimal orders of convergence could not be achieved using standard formulation of a sextic spline for the solution of BVPs. Based on the method used in our earlier research papers [J. Rashidinia and M. Ghasemi, B-spline collocation for solution of two-point boundary value problems, J. Comput. Appl. Math. 235 (2011), pp. 2325–2342; J. Rashidinia, M. Ghasemi, and R. Jalilian, An o(h ⁶) numerical solution of general nonlinear fifth-order two point boundary value problems, Numer. Algorithms 55(4) (2010), pp. 403–428], we construct a new O(h ⁸) locally superconvergent method for the solution of general nonlinear two-point BVPs up to order 6. The error bounds and the convergence properties of the method have been proved theoretically. Then, the method is extended to solve the system of nonlinear two-point BVPs. Some test problems are given to demonstrate the applicability and the superconvergent properties of the proposed method numerically. It is shown that the method is very efficient and applicable for stiff BVPs too.     

A singular system approach to robust sliding mode control for uncertain Markov jump systems

The robust sliding mode control for Markov jump systems with parameter uncertainties and an unknown nonlinear function is discussed. Based on a singular system approach and linear matrix inequality (LMI), a sufficient condition which guarantees the existence of linear switching surface and the stochastic stability of sliding mode dynamics is given. A sliding mode controller is designed such that the closed-loop system is convergent to the switching surface in finite time. A numerical example is given to show the effectiveness of the proposed method.