H∞ model reduction for negative imaginary systems

This paper is concerned with the H_∞ model reduction for negative imaginary (NI) systems. For a given linear time-invariant system that is stable and NI, our goal is to find a stable reduced-order NI system satisfying a pre-specified H_∞ approximation error bound. Sufficient conditions in terms of matrix inequalities are derived for the existence and construction of an H_∞ reduced-order NI system. Iterative algorithms are provided to solve the matrix inequalities and to minimise the H_∞ approximation error. Finally, a numerical example is used to demonstrate the effectiveness of the proposed model reduction method.     

On the design of optimal and sub-optimal control systems†

Though dynamic programming is an excellent and versatile algorithm, there are many cases in which we cannot apply this algorithm favourably to control system design because of the limited capacity of a digital computer and other difficulties.

Considering these facts, the successively optimizing method and the combined algorithm of dynamic programming and successively optimizing method are presented in this paper.

One of the objects of this paper is to present a practical method for obtaining the optimal solution of control systems with an integral form performance index by the use of dynamic programming.

The other is to present sub-optiinal solutions by the successively optimizing method and the combined algorithm.

These methods are very easy when compared with dynamic programming. Furthermore, these sub-optimal solutions can be made to converge to the optimum by using the recurrent equations repeatedly.     

On “Superstable” discrete systems

For the class of nonstationary discrete linear systems whose parameters have only multiple estimates, the sufficient condition for their robust stability was obtained on the basis of a discrete analog of the Lyapunov method. If satisfied at each time instant, this condition can be interpreted as the sufficient stability condition for systems with “frozen” coefficients. Robust stability of the stationary systems of the specified class follows from it as a special case.     

On the conjunction practical stability and controllability of large-scale impulsive control systems

1Introduction Asystem may be defined as a series of programs whichare designed to run sequentially.With the development ofscience,the scale of the systems with complicated structureis increasing.This causes the generationand development ofthe theory oflarge_scale system.Now,thelarge_scale systemhas become one of the important theoretic foundations ofthe systems engineering.There has been a significantdevelopment in the theory of impulsive differentialequations inthe past10years[1~3].If we wan…     

On the stability of interconnected systems†

This paper investigates the stability of systems which can be regarded as composed of interconnected subsystems. A sufficient condition for inputs-output L ^p stability, in terms of the L ^p gains of the subsystems and their interconnections is derived. For the case of L ² stability, it is compared with other criteria for asymptotic stability, obtained by Lyapunov techniques, and shown to give better results for a certain class of systems.     

On optimization of non-linear stochastic systems†

Results of application of the perturbation approach along with stochastic approximations to the problem of optimizing non-linear stochastic systems subject to quadratic index are discussed. The perturbation approach is first introduced with the help of linear regulator systems. This is combined subsequently with statistical linearization in order to derive sub-optimal solutions for the problem of optimizing a non-linear system. Finally, a new stochastic approximation technique, that permits more accuracy than the linearization, is suggested for the non-linear problem. Numerical examples are presented to compare the results of the various approximation methods and also to illustrate the possible advantages of non-linearization.     

On linear modelling of non-linear systems†

In many cases of interest, systems described by non-linear differential equations are modelled by linear equations for purposes of synthesizing feedback controllers. A theorem relating the stability properties of the linear model and the non-linear system is presented and discussed.     

On Hamiltonian realization of time-varying nonlinear systems

This paper investigates Hamiltonian realization of time-varying nonlinear (TVN) systems, and proposes a number of new methods for the problem. It is shown that every smooth TVN system can be expressed as a generalized Hamiltonian system if the origin is the equilibrium of the system. If the Jacopian matrix of a TVN system is nonsingu-lar, the system has a generalized Hamiltonian realization whose structural matrix and Hamiltonian function are given explicitly. For the case that the Jacobian matrix is singular, this paper provides a constructive decomposition method, and then proves that a TVN system has a generalized Hamiltonian realization if its Jacobian matrix has a non-singular main diagonal block. Furthermore, some sufficient (necessary and sufficient) conditions for dissipative Hamiltonian realization of TVN systems are also presented in this paper.     

On some properties of Goursat–Darboux systems with distributed and boundary controls

In this paper, a Goursat–Darboux control system is considered. In the first part, the bang-bang principle and some approximation results concerning the piecewise constant controls, for a linear system with distributed and boundary controls, are proved. In the second part, an approximation result concerning the bang-bang controls, for a special case of nonlinear (in a state) system with distributed controls, is derived.     

Linear differential and difference systems: EGδ- and EGσ- eliminations

Systems of linear ordinary differential and difference equations of the form $A_r (x)\xi ^r y(x) + \ldots + A_1 (x)\xi y(x) + A_0 (x)y(x) = 0,\xi \in \left\{ {\frac{d} {{dx}},E} \right\}$ , where E is the shift operator, Ey(x) = y(x + 1), are considered. The coefficients A _i (x), i = 0, ..., r, are square matrices of order m, and their entries are polynomials in x over a number field K, with A _r (x) and A ₀(x) being nonzero matrices. The equations are assumed to be independent over K[x, ξ]. For any system S of this form, algorithms EG_δ (in the differential case) and EG_σ (in the difference case) construct, in particular, the l-embracing system $\bar S$ of the same form. The determinant of the leading matrix $\bar A_r (x)$ of this system is a nonzero polynomial, and the set of solutions of system $\bar S$ contains all solutions of system S. (Algorithm EG_δ provides also a number of additional possibilities.) Examples of problems that can be solved with the help of EG_δ and EG_σ are given. The package EG implementing the proposed algorithms in Maple is described.     

On performance sensitivity of optimal control systems†

Formulae for the differential, with respect to plant parameters of an optimized performance index (performance sensitivity), are extended to include hard (instantaneous) as well as soft (isoperimetric) constraints on the control. In particular, this extends to discontinuous and bang-bang controls the Pagurek-Witscnhausen result on the equality of such differentials for open and closed-loop optimal systems     

On the controllability of distributed parameter systems†

The reachable states of distributed parameter systems where the magnitude of the control energy is constrained are found. The systems considered are described by linear partial differential equations on a bounded domain. The controls may be either distributed or at the boundary and are required to satisfy a constraint in the magnitude of their norm. The results are then used to find conditions for null controllability.     

On the α-migrativity of multivariate semi-copulas

In this paper we introduce and study the α-migrative property for the class of multivariate semi-copulas. In particular, a characterization of α-migrative copulas is provided.     

Order-k α-hulls and α-shapes

We introduce order-k α-hulls and α-shapes – generalizations of α-hulls and α-shapes. Being also a generalization of k-hull (known in statistics as “k-depth contour”), order-k α-hull provides a link between shape reconstruction and statistical depth. As a generalization of α-hull, order-k α-hull gives a robust shape estimation by ignoring locally up to k outliers in a point set. Order-k α-shape produces an “inner” shape of the set, with the amount of “digging” into the points controlled by k. As a generalization of k-hull, order-k α-hull is capable of determining “deep” points amidst samples from a multimodal distribution: it correctly identifies points which lie outside clusters of samples.The order-k α-hulls and α-shapes are related to order-k Voronoi diagrams in the same way in which α-hulls and α-shapes are related to Voronoi diagrams. This implies that order-k α-hull and α-shape can be readily built from order-k Voronoi diagram, and that the number of different order-k α-shapes for all possible values of α is proportional to the complexity of order-k Voronoi diagram.     

On various types of decoupling for time-varying systems†

This paper deals with the problem of decoupling a class of linear time-varying multi-variable systems, based on the defining property that the impulse response matrix of a decoupled system is diagonal. Depending on the properties of the coefficient matrices of the vector differential equation of the open-loop system, the system may be uniformly or totally decoupled. The necessary and sufficient conditions that permit a system to be uniformly or totally decoupled by state variable feedback are given. The main contribution of this paper is the precise definition of these two classes of decoupling and a rigorous derivation of the necessary and sufficient conditions which show the necessity of requiring that the system be of constant ordered rank with respect to observability. A simple example illustrates the importance of having several definitions of decoupling. Finally, the results are specialized to the case of time invariant systems.     

On the state estimation for non-linear dynamic systems †

The object of this paper is to present an approximate technique for state estimation of non-linear dynamical systems under noisy observations. The conditional cumulant is introduced, by which the conditional probability density can be characterized. A set of dynamical equations satisfied by conditional cumulants is derived, and an approximate method is proposed for computing the cumulants. The relation of the cumulant method to the stochastic linearization technique is also discussed. Finally the state estimation problem for linear stochaatic system with state-dependent disturbance is solved to illustrate the use of the Gaussian approximation.     

On the 45° -Region and the uniform asymptotic stability of classes of second order parameter-varying and switched systems

In this paper we present sufficient conditions for the stability of a number of classes of time-varying systems. These results are of interest for two reasons. Firstly, the conditions presented take the form of matrix pencil eigenvalue criteria, and are therefore co-ordinate independent and easily verifiable. Secondly, we show a direct relationship between the form of our criteria, and the choice of Lyapunov function used to demonstrate stability (quadratic or unic). These results indicate the importance of the region of the complex plane known as the 45°-Region.     

Predictive control,embedded cyberphysical systems and systems of systems – A perspective

Today’s world is changing rapidly due to advancements in information technology, computation and communication. Actuation, communication, sensing, and control are becoming ubiquitous. These technological advancements have led to the widespread availability of information and the possibility to connect systems in unforeseen manner. There is a strong desire for smart(er) cities, buildings, devices, factories, health monitoring – a smarter world. However, designing such a smarter world requires addressing also many challenges resulting from the emerging complex interactions and interoperation of systems. How is it possible to handle the increasing complexity during design and maintenance of such systems? How can one guarantee safety and performance of systems operating over networks which are subject to erroneous communication, delays, and failures of sensors and actuators? Is it possible to design control systems which allow for easy reconfiguration or even self-organization, for example by letting subsystems join and leave larger systems via plug and play strategies? Can one guarantee privacy of the controlled subsystems while exchanging information, which is necessary for maintaining overall system performance? We believe that predictive control is a well suited control approach to tackle some of these challenges due to its flexibility with respect to the formulation of the problem and the possibility to directly take constraints, preview information, as well as models of different complexity of the physical world into account. In this perspective we limit our attention to three areas we believe predictive control methods can provide a basis to tackle the appearing challenges: the efficient and easy implementation of predictive control on omnipresent embedded computation hardware, the question of resource and network aware control, as well as control on the network level of systems of systems. We briefly summarize results from these fields and outline some ideas on challenges, which arise.     

On improving resource utilization and system throughput of master slave job scheduling in heterogeneous systems

The rapid advances of network technologies shed light on many aspects of the practicability of large scale ubiquitous computing. Grid technology has been recognized as an efficient solution to coordinate large-scale shared resources and execute complex applications in heterogeneous network environments. The problem of resource management and task allocation has always been one of the main challenges. In this paper, we present an efficient task allocation strategy for distributing tasks onto computing nodes in the underlying heterogeneous networks. The contribution of the proposed technique is to minimize average turnaround time by dispatching tasks to processors with smallest communication ratio. System throughput could be also enhanced by dispersing processor idle time. The proposed technique can be applied to heterogeneous cluster systems as well as computational grid environments, in which the communication costs vary in different clusters. Experimental results show that the proposed scheme outperforms other previous algorithms in terms of throughput and turnaround time.