IEEE Transactions on Automatic Control

Vital physiological behaviors exhibited daily by bacteria, plants, and animals are governed by endogenous oscillators called circadian clocks. The most salient feature of the circadian clock is its ability to change its internal time (phase) to match that of the external environment. The circadian clock, like many oscillators in nature, is regulated at the cellular level by a complex network of interacting components. As a complementary approach to traditional biological investigation, we utilize mathematical models and systems theoretic tools to elucidate these mechanisms. The models are systems of ordinary differential equations exhibiting stable limit cycle behavior. To study the robustness of circadian phase behavior, we use sensitivity analysis. As the standard set of sensitivity tools are not suitable for the study of phase behavior, we introduce a novel tool, the parametric impulse phase response curve (pIPRC).

The exponential synchronization rate is addressed for Kuramoto oscillators in the presence of a pacemaker. When natural frequencies are identical, we prove that synchronization can be ensured even when the phases are not constrained in an open half-circle, which improves the existing results in the literature. We derive a lower bound on the exponential synchronization rate, which is proven to be an increasing function of pacemaker strength, but may be an increasing or decreasing function of local coupling strength. A similar conclusion is obtained for phase locking when the natural frequencies are non-identical. An approach to trapping phase differences in an arbitrary interval is also given, which ensures synchronization in the sense that synchronization error can be reduced to an arbitrary level.

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An optimisation problem arising in the design of circuits and control systems is formulated, and an outer approximation algorithm for solving it is presented. The problem is characterized by constraints that must be satisfied for all functions in a given subset of a function space. It is shown that an outer-approximation-type algorithm increases the number of variables and constraints at each iteration. A practical algorithm will require a constraint dropping scheme

This paper begins with a discussion of the properties of the noise occurring in the structures considered. This noise is taken to be generated by a stationary, ergodic, purely nondeterministic process. In case the observed vector sequence is generated by an autoregressive-moving average process then (a little more than) the additional requirement that the best predictor be the best linear predictor suffices for the development of an asymptotic inference theory. Signal measurement problems are considered, first where the signal is directly observed except for some unknown parameters and second where the signal is not directly observable and some characteristics, such as the velocity of propagation, have to be measured. Finally nonstationary models, nonlinear models for prediction, transient signals, and irregularly spaced samples are briefly discussed. Throughout, the methods are based on the use of the fast Fourier transforms of the data and their relation to the use of quasimaximum likelihoods in terms of those transforms is discussed.

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This paper investigates the problem of designing a compensating control for a linear multivariable system so that the impulse response matrix of the resulting closed-loop system coincides with the impulse response matrix of a prespecified linear model; this is the model following problem. A new formulation of the problem is developed, and necessary and sufficient conditions for a solution to exist are given. An upper bound is determined for the number of integrators needed to construct the compensating control and, if the open-loop plant in question possesses a left-invertible transfer matrix, this bound is shown to be as small as possible. The relationship between the internal structure of a model following system and the model being followed is explained, and a description is given of the possible distributions of system eigenvalues which can be achieved while maintaining a model following configuration. This leads to a statement of necessary and sufficient conditions for the existence of a solution to the problem which results in a stable compensated system.

The results in the above titled paper (ibid., vol. 52, no. 11, pp. 2019-2028, Nov. 07), are contradicted slightly by those found in two others cited here. The results are explained here.

The notion of a "numerator" of a rational transfer matrix is defined. The fact that any two numerators of the same transfer matrix are equivalent is then formally established and employed in the development of a number of equivalent definitions of the zeros of a rational transfer matrix.

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In this paper two topics are explored. A new approach to the problem of obtaining an estimate of the state of a nonlinear system is proposed. The moving horizon observer produces an estimate of the state of the nonlinear system at time t either by minimizing, or approximately minimizing, a cost function over the preceding interval (horizon) [t-T,t]; as t advances, so does the horizon. Convergence of the estimator is established under the assumption that the corresponding global optimization problem can be (approximately) solved and a uniform reconstructability condition is satisfied; the latter condition is automatically satisfied for linear observable systems. The utility of the estimator for receding horizon control is explored. In particular, stability of a composite moving horizon system, comprising a moving horizon regulator and a moving horizon observer, is established

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Motivated by control Lyapunov functions and Razumikhin theorems on stability of time delay systems, we introduce the concept of control Lyapunov-Razumikhin functions (CLRF). The main reason for considering CLRFs is construction of robust stabilizing control laws for time delay systems. Most existing universal formulas that apply to CLFs, are not applicable to CLRFs. It turns out that the domination redesign control law applies, achieving global practical stability and, under an additional assumption, global asymptotic stability. This additional assumption is satisfied in the practically important case when the quadratic part of a CLRF is itself a CLRF for the Jacobian linearization of the system. The CLRF based domination redesign possesses robustness to input unmodeled dynamics including an infinite gain margin. While, in general, construction of CLRFs is an open problem, we show that for several classes of time delay systems a CLRF can be constructed in a systematic way

In this paper, a unified framework is proposed to study the exponential stability of discrete-time switched linear systems and, more generally, the exponential growth rates of their trajectories under three types of switching rules: arbitrary switching, optimal switching, and random switching. It is shown that the maximum exponential growth rates of system trajectories over all initial states under these three switching rules are completely characterized by the radii of convergence of three suitably defined families of functions called the strong, the weak, and the mean generating functions, respectively. In particular, necessary and sufficient conditions for the exponential stability of the switched linear systems are derived based on these radii of convergence. Various properties of the generating functions are established, and their relations are discussed. Algorithms for computing the generating functions and their radii of convergence are also developed and illustrated through examples.

The model reference adaptive control system has proved very popular on account of a ready-made, but heuristically based, rule for synthesizing the adaptive loops-the so-called "M.I.T. rule." A theoretical analysis of loops so designed is generally very difficult, but analyses of quite simple systems do show that instability is possible for certain system inputs. An alternative synthesis based on Liapunov's second method is suggested here, and is applied to the redesign of adaptive loops considered by some other authors who have all used the M.I.T, rule. Derivatives of model-system error are sometimes required, but may be avoided in gain adjustment schemes if the system transfer function is "positive real," using a lemma due to Kalman. This paper amplifies and extends the work of Butchart and Shackcloth reported at the IFAC (Teddington) Symposium, September, 1965.

Stable direct and indirect decentralized adaptive radial basis neural network controllers are presented for a class of interconnected nonlinear systems. The feedback and adaptation mechanisms for each subsystem depend only upon local measurements to provide asymptotic tracking of a reference trajectory. Due to the functional approximation capabilities of radial basis neural networks, the dynamics for each subsystem are not required to be linear in a set of unknown coefficients as is typically required in decentralized adaptive schemes. In addition, each subsystem is able to adaptively compensate for disturbances and interconnections with unknown bounds

This paper studies sampled-data control of nonlinear systems using high-gain observers. The observer is designed in continuous time, then discretized using three different discretization methods. Closed-loop analysis shows that the sampled-data controller recovers the performance of the continuous time controller as the sampling frequency and observer gain become sufficiently large. The theory is illustrated by experimental results

This paper reports on the use of the stochastic automaton theory to configure control algorithms for high precision assembly operations performed with a force-sensing robot. The basic principle of the stochastic automation, i.e., its variable structure, has been extended to the dimensionality of the automaton by gradually optimizing the resolution of the input variables.

The problem of preserving stability of discrete-time adaptive controllers in spite of reduced-order modeling and output disturbances is addressed in this paper. Conditions for global stability (convergence of the tracking error with bounded signals) are derived for a discrete-time pole-zero placement adaptive controller where the parameter estimator is modified in terms of normalized signals. Following an input-output perpective, the overall system is decomposed into two subsystems reflecting the parameter estimation and modeling errors, respectively, and its stability is studied using the sector stability and passivity theorems. First the analysis is carried for the class of disturbances and reference inputs that are either decaying or can be exactly hulled by a linear controller of the chosen structure. In this L 2 -framework, it is shown that the only substantive assumption to assure stability is the existence of a linear controller such that the closed-loop transfer function verifies certain conicity conditions. The convergence speed and alertness properties of various parameter adaptation algorithms regarding this condition are discussed. The results are further extended to a broader class of L_{infty} disturbances and reference inputs.

Recently, methods in stochastic control are used to study the synchronization properties of a nonautonomous discrete-time linear system x(k+1)=G(k)x(k) where the matrices G(k) are derived from a random graph process. The purpose of this note is to extend this analysis to directed graphs and more general random graph processes. Rather than using Lyapunov type methods, we use results from the theory of inhomogeneous Markov chains in our analysis. These results have been used successfully in deterministic consensus problems and we show that they are useful for these problems as well. Sufficient conditions are derived that depend on the types of graphs that have nonvanishing probabilities. For instance, if a scrambling graph occurs with nonzero probability, then the system synchronizes.

An algorithm is given for designing discrete-time controllers which are robust with respect to parameter variations and which also guarantee specified l ₂ performance constraints for stochastic inputs and l _∞ performance constraints for deterministic inputs. This is not an analysis but a design method guaranteeing the specified robust performances. Also an upper bound on the covariance matrix is provided

Nonlinear passivity-based control (PBC) algorithms for power converters have proved to be an interesting alternative to other, mostly linear, control techniques. The control objective is usually achieved through an energy reshaping process and by injecting damping to modify the dissipation structure of the system. However, a key question that arises during the implementation of the controller is how to tune the various control parameters. From a circuit theoretic perspective, a PBC forces the closed-loop dynamics to behave as if there are artificial resistors-the control parameters-connected in series or in parallel to the real circuit elements. In this paper, a solution to the tuning problem is proposed that uses the classical Brayton-Moser equations. The method is based on the study of a certain "mixed-potential function" which results in quantitative restrictions on the control parameters. These restrictions seem to be practically relevant in terms stability, overshoot and nonoscillatory responses. The theory is exemplified using the elementary single-switch buck and boost converters.

We present a globally stable nonlinear dynamic output feedback controller for torque tracking and flux regulation of induction motors. The control law is globally defined, requires only measurement of stator variables and rotor speed, and does not rely on cancellation of the systems nonlinearities. Our work extends the result of the paper by Ortega et al.(1993), where the torque tracking problem was solved for a model and the variables are expressed in a frame rotating at an arbitrary angular frequency (dq model). First, we obviate the need to transfer the dq control signals of the paper by Ortega et al., to the physical input variables in the stator frame, hence providing a directly implementable control law. Second, besides the torque tracking objective, we include the practically important rotor flux regulation task. Third, by choosing a more suitable representation of the motor model, we simplify the controller structure and provide a better understanding of its derivation and behavior

In this paper we analyze numerical methods for the solution of the large scale dynamical system Edot{y}(t)=Ay(t)+g(t),Y(t_{0})=y_{0} , where E and A are matrices, possibly singular. Systems of this type have been referred to as implicit systems and more recently as descriptor systems since they arise from formulating system equations in physical variables. Special cases of such systems are algebraic-differential systems. We discuss the numerical advantages of this formulation and identify a class of numerical integration algorithms which have accuracy and stability properties appropriate to descriptor systems and which preserve structure, detect nonsolvable systems, resolve initial value consistency problems, and are applicable to "stiff" descriptor systems. We also present an algorithm for the control of the local truncation error on only the state variables.

We consider the problem of optimizing the steady-state mean of a controlled regenerative process using a stochastic optimization algorithm driven by infinitesimal perturbation analysis (IPA) derivative estimates. We derive IPA derivative estimates for our problem and prove almost sure convergence of the algorithm. The generality of our formulation should encompass a wide variety of practical systems. We illustrate our framework and results via several examples

An adaptive H^∞ tracking control equipped with a VSC algorithm is proposed for a class of nonlinear multiple-input-multiple-output (MIMO) systems that are represented by input-output models involving parametric uncertainties, unmodeled perturbations and external disturbances. In order to counteract the effect due to the unmodeled perturbation in the input weighting gain the H^∞ tracking control requires to solve a modified algebraic Riccati-like matrix equation. The derived hybrid adaptive-robust tracking control schemes guarantee that all the signals and states are bounded, the tracking error is uniformly and ultimately bounded and an H^∞ tracking performance is achieved. Compared with the conventional H^∞ tracking control design the developed adaptive-robust H^∞ tracking control scheme can be applied to a broader class of nonlinear MIMO systems in the presence of high-degree uncertainties

Two different optimal feedback laws are derived for state-space systems parametrized through an independent identically distributed vector sequence. Both feedback laws are obtained by minimizing the expectation of a multistep quadratic loss function at each time step. They differ on the assumptions made about the future inputs. The properties and implementability of the feedback laws are discussed for the infinite horizon case

An adaptive control scheme for manipulators with redundant degrees of freedom is presented. The control purpose is to achieve a desired interaction force between the end-effector and the environment as well as to regulate the robot tip position in the Cartesian space. This control approach does not require measurement of the joint acceleration or the force derivative

We present serial and parallel algorithms for solving a system of equations that arises from the discretization of the Hamilton-Jacobi equation associated to a trajectory optimization problem of the following type. A vehicle starts at a prespecified point x_o and follows a unit speed trajectory x(t) inside a region in ℛ^m until an unspecified time T that the region is exited. A trajectory minimizing a cost function of the form ∫₀^T r(x(t))dt+q(x(T)) is sought. The discretized Hamilton-Jacobi equation corresponding to this problem is usually solved using iterative methods. Nevertheless, assuming that the function r is positive, we are able to exploit the problem structure and develop one-pass algorithms for the discretized problem. The first algorithm resembles Dijkstra's shortest path algorithm and runs in time O(n log n), where n is the number of grid points. The second algorithm uses a somewhat different discretization and borrows some ideas from a variation of Dial's shortest path algorithm (1969) that we develop here; it runs in time O(n), which is the best possible, under some fairly mild assumptions. Finally, we show that the latter algorithm can be efficiently parallelized: for two-dimensional problems and with p processors, its running time becomes O(n/p), provided that p=O(√n/log n)

The synthesis of discrete model reference adaptive systems is discussed from the hyperstability point of view. The results included here are an extension of previous results obtained by the author for the continuous case [1].

A class of network topological optimization problems is formulated as a nonlinear mixed integer programming model, which can be used to design transportation and computer communication networks subject to a budget constraint. The approach proposed for selecting an optimal network consists of separating the continuous part of the model from the discrete part by generalized Benders decomposition. One then solves a sequence of master and subproblems. The subproblems of the minimal convex cost multicommodity flow type are used to generate cutting planes for choosing potential topologies by means of the master problems. Computational techniques suited to solving the master and subproblems are suggested, and very encouraging experimental results are reported.

This note establishes global boundedness and control tracking properties of a continuous-time direct adaptive controller subject to an input saturation constraint. Under a finite gain stability condition on a nonadaptive controller using the true plant parameters, global stability of the adaptive version of the controller is established. It is also shown that the adaptive controller can account for modeling uncertainties and limited disturbances, hence providing a certain degree of robustness

Presents an adaptive control scheme for flexible joint robot manipulators. Asymptotic stability is insured regardless of the joint flexibility value, i.e., the results are not restricted to weak joint elasticity. Moreover, the joint flexibility is not assumed to be known. Joint position and velocity tracking errors are shown to converge to zero with all the signals in the system remaining bounded

During the last seven years, while structural changes have been taking place in the industrial sector of the U.S. and questions of technological leadership and technology transfer have been debated widely, new areas for research have been developing. This led the leadership of the IEEE Control Systems Society to recommend that a workshop be organized to assess the state of the art of the field and outline directions of research. An Organizing Committee, consisting of D. D. Siljak (Chairman), G. F. Franklin, A. H. Levis, and W. R. Perkins, submitted a proposal to the Systems Theory and Operations Research Program of the National Science Foundation to hold such a workshop at the University of Santa Clara, in Santa Clara, CA, on September 18-19, 1986. As part of the proposal effort, a Steering Committee was constituted to assist the organizers in selecting workshop participants and to carry out the preparalory work for the meeting. The twelve-member Steering Committee consisted of the four organizers and eight other individuals: R. W. Brockett, E. J. Davison, Y.-C. Ho, P. Kokotovic, A. J. Laub, S. 1. Marcus, W. F. Powers, and S. S. Sastry. In early 1986, the organizers issued an open call for participation in the workshop that was published in the April issue of the IEEE CONTROL SYSTEMS MAGAZINE. in addition, more than 150 letters were sent to leaders in the field, inviting them to apply for participation in the workshop. The Steering Committee was also asked to identify individuals who could provide unique perspectives. The cut-off date for applications, that included a statement of proposed contribution, was May 31. In June, during the 1986 American Control Conference, the Steering Committee met for many hours to select the participants from the many applicants and to decide on the final structure of the program. One of the decisions was to invite all the Presidential Young Investigator awardees who had applied, another was to limit the total number of participants to fifty. In addition to the Steering Committee, the following persons attended and contributed to the deliberations: K. J. Astrom, M. Athans, D. Auslander, J. S. Baras, T. Basar, G. Blankenship, S. P. Boyd, A. E. Bryson, Jr., J. Burns, J. Cassidy, J. B. Cruz, D. F. Delchamps, C. A. Desoer, R. F. - Drenick, T. Edgar, J. S. Freudenberg, D. Gangsaas, J. Grizzle, A. H. Haddad, W. E. Hopkins, Jr., M. Ilí-Spong, P. loannou, T. L. Johnson, T. Kailath, A. J. Krener, R. E. Larson, W. S. Levine, J. L. Melsa, J. M. Mendel, G. Meyer, J. B. Pearson, H. E. Rauch, G. N. Saridis, J. L. Speyer, J. N. Tsitsiklis, P. Varaiya, G. C. Verghese, M. Vidyasagar, A. S. Willsky, and M. Wonham. The National Science Foundation was represented by Dr. M. P. Polis, Program Director of the Systems Theory and Operations Research Program, and by Dr. G. Hazelrig, Acting Program Director of the Instrumentation, Sensing, and Measurement Systems Program. The workshop was organized into plenary sessions and breakout sessions, during which Working Groups discussed and wrote the material that forms the basis of this report. Seven keynote talks addressed the main themes of the workshop: accomplishments in the past twenty five years and definition of important current and future research problems drawn from the needs of the industrial and service sectors of the economy. The Working Groups were structured so that, while discussions could take place with few constraints, written materials could be produced by the end of each session. To that effect, each group had one or two persons designated as recorders, with the primary responsibility of keeping notes during the discussion and assisting the group leaders in preparing the Working Group draft reports. In order to provide some focus in the deliberations of the Working Groups,eight persons were asked to prepare position statements based on their own perspectives. Seven of these position papers are being published concurrently in the April 1987

This note describes the modeling of the power and voltage control loop of a thermal power plant of 180 MW. The modeling is based upon full-scale measurements at the Flevo power plant of the PGEM. A relatively simple ninth-order mathematical model of one unit for several working points has been developed. Based on this model the existing controller structure has been analyzed and an improved voltage control system designed. The design method is based on a state-feedback technique and pole placement. By means of computer simulations in an extended nonlinear model of this unit, including the grid, the existing and the newly developed control algorithms are compared. Field tests have been carried out to verify the results of the designed control algorithms.

This paper presents a method for assigning the poles in a specified disk by state feedback for a linear discrete or continuous time uncertain system, the uncertainty being norm bounded. For this the “quadratic d stabilizability” concept which is the counterpart of quadratic stabilizability in the context of pole placement is defined and a necessary and sufficient condition for quadratic d stabilizability derived. This condition expressed as a parameter dependent discrete Riccati equation enables one to design the control gain matrix by solving iteratively a discrete Riccati equation

The subject of this paper is open multiclass queueing networks, which are common models of communication networks, and complex manufacturing systems such as wafer fabrication facilities. We provide sufficient conditions for the existence of bounds on long-run average moments of the queue lengths at the various stations, and we bound the rate of convergence of the mean queue length to its steady-state value. Our work provides a solid foundation for performance analysis either by analytical methods or by simulation. These results are applied to several examples including re-entrant lines, generalized Jackson networks, and a general polling model as found in computer networks applications

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