Generic properties and control of linear structured systems: a survey

In this survey paper, we consider linear structured systems in state space form, where a linear system is structured when each entry of its matrices, like A,B,C and D, is either a fixed zero or a free parameter. The location of the fixed zeros in these matrices constitutes the structure of the system. Indeed a lot of man-made physical systems which admit a linear model are structured. A structured system is representative of a class of linear systems in the usual sense. It is of interest to investigate properties of structured systems which are true for almost any value of the free parameters, therefore also called generic properties. Interestingly, a lot of classical properties of linear systems can be studied in terms of genericity. Moreover, these generic properties can, in general, be checked by means of directed graphs that can be associated to a structured system in a natural way. We review here a number of results concerning generic properties of structured systems expressed in graph theoretic terms. By properties we mean here system-specific properties like controllability, the finite and infinite zero structure, and so on, as well as, solvability issues of certain classical control problems like disturbance rejection, input-output decoupling, and so on. In this paper, we do not try to be exhaustive but instead, by a selection of results, we would like to motivate the reader to appreciate what we consider as a wonderful modelling and analysis tool. We emphasize the fact that this modelling technique allows us to get a number of important results based on poor information on the system only. Moreover, the graph theoretic conditions are intuitive and are easy to check by hand for small systems and by means of well-known polynomially bounded combinatorial techniques for larger systems.     

Computational adaptive optimal control for continuous-time linear systems with completely unknown dynamics

This paper presents a novel policy iteration approach for finding online adaptive optimal controllers for continuous-time linear systems with completely unknown system dynamics. The proposed approach employs the approximate/adaptive dynamic programming technique to iteratively solve the algebraic Riccati equation using the online information of state and input, without requiring the a priori knowledge of the system matrices. In addition, all iterations can be conducted by using repeatedly the same state and input information on some fixed time intervals. A practical online algorithm is developed in this paper, and is applied to the controller design for a turbocharged diesel engine with exhaust gas recirculation. Finally, several aspects of future work are discussed.     

Multipartitioning linear estimation algorithms: Continuous systems

The partitioned estimation algorithms of Lainiotis for the linear continuous-time state estimation problem have been generalized in this paper in two important ways. First, the initial condition of the estimation problem can, using the results of this paper, be partitioned into the sum of an arbitrary number of jointly Gaussian random variables; and second, these jointly Gaussian random variables may be statistically dependent. The form of the resulting algorithm consists of an imbedded Kalman filter with partial initial conditions and one correction term for each other partition or subdivision of the initial state vector. Emphasis in this paper is on ways in which this approach, called multipartitioning, can be used to provide added insight into the estimation problem. One significant application is in the parameter identification problem where identification algorithms can be formulated in which the inversion of the information matrix of the parameters is replaced by simple division by scalars. A second use of multipartitioning is to show the specific effects on the filtered state estimate of off-diagonal terms in the initial-state covariance matrix.     

Computational algorithms for linear balance models of intersectoral ecological-economic interaction

Linear balance models of intersectorial ecological-economical interaction are analyzed and new computer algorithms for solving them are proposed. The efficiency of these algorithms and the possibility of using them in practice are substantiated.     

Diagonalization algorithms for linear time-varying dynamic systems

On the basis of a mode-vector representation, we show that its time-varying amplitudes and frequencies can be obtained by diagonalizing the system matrix. Next, we reformulate an explicit diagonalizing algorithm that was earlier proposed by Wu. Then, the missing convergence proof is given. Moreover, we present a new and implicit iteration scheme that is closely related to that given by Wu. In both algorithms, the time-varying system matrix is gradually diagonalized by successive algebraic similarity transformations. It is proved that the convergence conditions are essentially the same. Although the class of systems for which the algorithms are applicable is still not fully known, the results of this paper may be of theoretical and practical interest.     

Computational complexity of randomized algorithms for solving parameter-dependent linear matrix inequalities

Randomized algorithms are proposed for solving parameter-dependent linear matrix inequalities and their computational complexity is analyzed. The first proposed algorithm is an adaptation of the algorithms of Polyak and Tempo [(Syst. Control Lett. 43(5) (2001) 343)] and Calafiore and Polyak [(IEEE Trans. Autom. Control 46 (11) (2001) 1755)] for the present problem. It is possible however to show that the expected number of iterations necessary to have a deterministic solution is infinite. In order to make this number finite, the improved algorithm is proposed. The number of iterations necessary to have a probabilistic solution is also considered and is shown to be independent of the parameter dimension. A numerical example is provided.     

Chandrasekhar algorithms for linear time varying distributed systems

Generalized Chandrasekhar type algorithms are obtained that are applicable to linear time varying as well as time invariant distributed systems. Utilizing the framework of J. L. Lions for quadratic control and the framework of A. Bensoussan for filtering of linear distributed systems, we analyze the implications of these algorithms.     

Optimal state reconstruction algorithms for linear discrete-time systems

This paper deals with optimal time-invariant reconstruction of the state of a linear time-invariant discrete-time system from output measurements. The problem is analysed in two settings, depending on whether or not the present output measurement is available for the estimation of the present state. The results prove complete separation of observer and controller design for the optimal dynamic output feedback control with respect to a quadratic cost.     

Genetic algorithms: a survey

Genetic algorithms provide an alternative to traditional optimization techniques by using directed random searches to locate optimal solutions in complex landscapes. We introduce the art and science of genetic algorithms and survey current issues in GA theory and practice. We do not present a detailed study, instead, we offer a quick guide into the labyrinth of GA research. First, we draw the analogy between genetic algorithms and the search processes in nature. Then we describe the genetic algorithm that Holland introduced in 1975 and the workings of GAs. After a survey of techniques proposed as improvements to Holland's GA and of some radically different approaches, we survey the advances in GA theory related to modeling, dynamics, and deception     

A minimal residual class of algorithms for linear systems

A family of rapidly convergent algorithms to solve linear systems of equations are described. These methods are easy to implement. In an empirical comparison over a class of problems the presented algorithms were superior to several commonly used methods.     

Two-grid algorithms for some linear and nonlinear elliptic systems

In this paper, several two-grid algorithms are presented. For nonsymmetric linear systems, we propose a two-grid algorithm by using the information of the adjoint operator. The solution of the original systems is mainly reduced to a solution of symmetric positive definite (SPD) systems. For nonlinear systems, we present a two-grid algorithm based on the modified Newton method. The solution of the original systems on the fine space is reduced to the solution of two small systems on the coarse space and two similar linear systems (with same stiffness matrix) on the fine space. It is shown that the accuracy ( ${\mathcal{L}^2}$ norm) obtained by this algorithm is as same as the optimal accuracy derived by using two full Newton steps. Additionally, for more practically applications, the ideas of these algorithms can be also extended to the multilevel case. Numerical experiments are given for these new algorithms.     

Error encoding algorithms for networked control systems

A networked control system is characterized by having a feedback loop closed through a local area network. This paper considers methods for scheduling the use of the network to guarantee both stability and controller performance. We propose and validate algorithms for choosing message identifiers for dynamically scheduled networked control systems. Two schemes for selecting priority levels are proposed: a fixed arbitrary grid and an auto-scaling grid. We prove that the system is uniformly ultimately bounded in the case of the fixed encoding scheme, and asymptotically stable with auto-scaling. An inverted pendulum is used to illustrate the encoding methods.     

Minimum attention control for linear systems

In this paper, we present a novel solution to the minimum attention control problem for linear systems. In minimum attention control, the objective is to minimise the ‘attention’ that a control task requires, given certain performance requirements. Here, we interpret ‘attention’ as the inverse of the interexecution time, i.e., the inverse of the time between two consecutive executions. Instrumental for our approach is a particular extension of the notion of a control Lyapunov function and the fact that we allow for only a finite number of possible interexecution times. By choosing this extended control Lyapunov function to be an ∞-norm-based function, the minimum attention control problem can be formulated as a linear program, which can be solved efficiently online. Furthermore, we provide a technique to construct a suitable ∞-norm-based (extended) control Lyapunov function. Finally, we illustrate the theory using a numerical example, which shows that minimum attention control outperforms an alternative ‘attention-aware’ control law available in the literature.     

Adaptive control for input-constrained linear systems

This paper proposes a direct model reference adaptive control method for linear systems with unknown parameters in the presence of input constraints. First, we used the well-known linear quadratic regulator (LQR) technique to develop a modified reference model, which is the optimal model under input constraints. Second, a model reference adaptive controller, which tracked the modified reference model instead of the reference model, was designed to compensate for parametric uncertainties. Using Lyapunov stability theory, we proved that the modified reference model tracking error converges to zero. Simulation results demonstrate the effectiveness of the proposed controller.     

Adaptive stochastic control for a class of linear systems

The problem considered in this paper deals with the control of linear discrete-time stochastic systems with unknown (possibly time-varying and random) gain parameters. The philosophy of control is based on the use of an open-loop feedback optimal (OLFO) control using a quadratic index of performance. It is shown that the OLFO system consists of 1) an identifier that estimates the system state variables and gain parameters and 2) a controller described by an "adaptive" gain and correction term. Several qualitative properties and asymptotic properties of the OLFO adaptive system are discussed. Simulation results dealing with the control of stable and unstable third-order plants are presented. The key quantitative result is the precise variation of the control system adaptive gains as a function of the future expected uncertainty of the parameters; thus, in this problem the ordinary "separation theorem" does not hold.     

Networked control design for linear systems

In this paper we study a systematic networked control method designed specifically to handle the constraints of the networked realization of a linear time invariant control system. The general structure of the proposed controller requires switching between the open loop and closed loop subsystems of the controller which is dictated by the behaviour of the communication network.     

Computational methods for Traditional Chinese Medicine: a survey

Traditional Chinese Medicine (TCM) has been actively researched through various approaches, including computational techniques. A review on basic elements of TCM is provided to illuminate various challenges and progresses in its study using computational methods. Information on various TCM formulations, in particular resources on databases of TCM formulations and their integration to Western medicine, are analyzed in several facets, such as TCM classifications, types of databases, and mining tools. Aspects of computational TCM diagnosis, namely inspection, auscultation, pulse analysis as well as TCM expert systems are reviewed in term of their benefits and drawbacks. Various approaches on exploring relationships among TCM components and finding genes/proteins relating to TCM symptom complex are also studied. This survey provides a summary on the advance of computational approaches for TCM and will be useful for future knowledge discovery in this area.