Optimal robust disturbance attenuation for continuous time‐varying systems

In this paper we consider the Optimal robust disturbance attenuation problem (ORDAP) for continuous time‐varying systems subject to time‐varying unstructured uncertainty. We show that for causal (possibly time‐varying) continuous systems, ORDAP is equivalent to finding the smallest fixed point of a ‘two‐disc’ type optimization problem under time‐varying feedback control laws. Duality is applied in the context of nest algebra of causal stable systems, to prove existence of optimal continuous time‐varying controllers. We also show that for time‐invariant nominal plants, time‐varying control laws offer no improvement over time‐invariant feedback control laws. Copyright © 2003 John Wiley & Sons, Ltd.     

Synthesis of dissipative systems using quadratic differentialforms: part II

For pt.1 see ibid., p.53-69 (2002). The authors discuss several important special cases of the problem solved in Part I. These are: disturbance attenuation and passivation, the full information case, the filtering problem, and the case that the to-be-controlled plant is given in input-state-output representation. An interesting aspect is the notion of full information, which we define in terms of the observability of the to-be-controlled variables from the control variables. When the system is given in state space form, we obtain conditions for the existence of a controller that renders a system dissipative in terms of two coupled algebraic Riccati inequalities. The controller turns out to be a feedback system with a transfer function that is proper, but, in general, not strictly proper. Another issue that we study in this paper is feedback implementability. We find conditions under which, in the context of synthesis of dissipative systems, a controlled behavior can implemented by a feedback controller     

含有不确定性的非线性互联系统的鲁棒分散H∞控制

讨论了含有不确定性非线性互联系统的鲁棒分散Ｈ∞控制问题,建立了鲁棒Ｈ∞控制之间的联系,在这种联系基础上,基于Ｈａｍｉｌｔｏｎ－Ｊａｃｏｂｉ不等式给出了含有不确定性互联系统的鲁棒分散Ｈ∞控制问题存在的充分条件,分别构造出状态反 输出反发散控制器以确保闭环系统从外部干扰输入到控制输出的Ｌ２增益小于或等于一预先给定的正数。     

On the control of asynchronous machines with races

The problem of eliminating the effects of critical races on asynchronous machines is considered in a control theoretic context. State feedback controllers that eliminate the effects of critical races are developed. The results include necessary and sufficient conditions for the existence of such controllers and algorithms for their design. When the controllers exist, they eliminate the race effects and control the machine to match a given race-free model.     

Remarks on smooth feedback stabilization of nonlinear systems

We investigate the problem of smooth feedback stabilization of nonlinear systems with stable uncontrolled dynamics. We present sufficient conditions for the existence of a smooth feedback stabilizing control that are also necessary in the case of linear systems. Analogous results are established for discrete time systems.     

An optimal quantized feedback strategy for scalar linear systems

We give an optimal (memoryless) quantized feedback strategy for stabilization of scalar linear systems, in the case of integral eigenvalue. As we do not require the quantization subsets to be intervals, this strategy has better performances than allowed by the lower bounds recently proved by Fagnani and Zampieri. We also describe a general setting, in which we prove a necessary and sufficient condition for the existence of a memoryless quantized feedback to achieve stability, and provide an analysis of Maxwell's demon in this context.     

Almost fault‐tolerant tracking

A new formulation of the problem of almost fault‐tolerant perfect tracking in presence of disturbances is presented, and necessary and sufficient existence conditions are found, as well as a controller, which consists of a feedback block and two feedforward blocks. The feedback block is aimed for almost disturbance and fault decoupling, and the feedforward blocks are aimed for almost perfect tracking. A two‐step control design procedure such that the feedback block is designed independently of the feedforward blocks is presented. In order to simplify the necessary and sufficient existence conditions, as well as to present a physical interpretation of the existence conditions, the dimension of disturbance and fault vectors is reduced. In order to find a feedback controller, the physical interpretation of the existence conditions is used so that the four‐block‐type problem is transformed to a two‐block‐type problem. Examples are given, which illustrate that the controller of the article is practically realizable.     

Robust nonlinear H∞-output feedback control

This paper investigates the problem of robust H_∞-output feedback control for nonlinear systems with time-varying parameter uncertainty satisfying some integral functional constraints. We address the problem of designing a compensator such that the L₂-gain of the mapping from the exogenous input noise to the penalty output is minimized or guaranteed to be less than or equal to a prescribed value. We establish the interconnection between the robust nonlinear H_∞-control problem and the nonlinear H _∞-control problem, Based on this connection, a sufficient condition for the existence of a solution to the robust nonlinear H_∞-output feedback control problem is derived in terms of a “scaled” Hamilton-Jacobi inequality     

Rigid body attitude control with inclinometer and low-cost gyro measurements

In our paper, we consider the state regulation problem for the nonlinear kinematic equations and Euler equations of a rigid body observed under low-pass sensors. This problem is motivated by the corresponding state estimation problem covered in recent literature on walking robots and virtual reality gadgets. We show the existence of an asymptotically stabilizing feedback controller for the dynamics that provides reliable performance.     

Pole assignment for linear periodic systems by memoryless outputfeedback

We consider linear periodic discrete-time systems. We are interested in the problem of placing the poles of the monodromy map by means of periodic output feedback of the same or multiple period. It is well known that, in general, the poles of time-invariant systems cannot be assigned by constant output feedback. This is in contrast with what can be obtained in the context of time-variant systems. The main contribution of this paper is that periodic output feedback suffices for pole placement of periodic systems     

Stationary policies for lower bounds on the minimum average cost of discrete‐time nonlinear control systems

The paper deals with the control problem of discrete‐time nonlinear systems. The main contribution of this note is to present conditions that assure the existence of stationary policies that generate lower bounds for the minimal long‐run average cost. These lower bounds coincide with the optimal solution when a mild convergence assumption holds. To illustrate the results, the paper presents an application for the simultaneous state‐feedback control problem, and the derived strategy is used to design a real‐time simultaneous control for two direct current motor devices. The dynamics of these two devices are written in terms of a nonlinear algebraic matrix recurrence, which in turn represents a particular case for our general nonlinear approach. The optimal gain for the corresponding simultaneous state‐feedback problem is obtained, and such a gain was implemented in a laboratory testbed to control simultaneously the two direct current motors. Copyright © 2013 John Wiley & Sons, Ltd.     

Asymptotic feedback stabilization: A sufficient condition for the existence of control Lyapunov functions

In this paper we study the feedback stabilization problem for a wide class of nonlinear systems that are affine in the control. We offer sufficient conditions for the existence of ‘Control Lyapunov functions’ that according to [3,23] and [28–30] guarantee stabilization at a specified equilibrium by means of a feedback law, which is smooth except possibly at the equilibrium. We note that the results of the paper present a local nature.     

On output feedback pole assignability

The problem of assigning all the system poles by means of output feedback is considered. This problem was studied by Munro and Vardulakis (1973) who obtained a necessary and sufficient condition for the existence of such an output feedback. In this paper it is shown that satisfaction of the condition obtained by Munro and Vardulakis (1973) is equivalent to the existence of an incomplete state feedback law which achieves the desired pole configuration. A coordinate transformation is used to test this condition, and it is shown that when the condition is satisfied the required output feedback matrix is obtained directly.     

On the control of asynchronous sequential machines with infinite cycles

The problem of eliminating the effects of infinite cycles on asynchronous sequential machines is considered in a control theoretic context. The main objective is to develop state feedback controllers that stop infinite cycles in an existing asynchronous machine, while controlling the machine to match a prescribed model. Necessary and sufficient conditions for the existence of such controllers are derived in terms of an inequality condition between two numerical matrices. The results include an algorithm for the characterization of all infinite cycles of a given machine as well as an algorithm for the construction of appropriate controllers, whenever they exist.     

Proper,denominator assigning feedback compensators equivalent to state variable feedback

For linear, time-invariant, stabilizable multivariable systems, we examine the problem of the existence and computation of proper denominator assigning and internally stabilizing feedback compensators, which give rise to a closed-loop system, whose transfer function matrix is equal to one that can be obtained by the action of state variable feedback. We establish a sufficient condition for the solution of this problem for the class of systems with the same number of inputs and outputs and non-singular transfer function matrix with all its zeros located in the open left half of the complex plane.     

On periodic solutions of adaptive systems in the presence of periodic forcing terms

We consider a discrete-time system consisting of a linear plant and a periodically forced feedback controller whose parameters are slowly adapted. Using degree theory, we give sufficient conditions for the existence of periodic solutions. Using linearization methods, we give sufficient conditions for their (in)stability provided the adaptation is slow enough. We then study when the degree theoretic conditions for the existence are satisfied byd-steps-ahead adaptive controllers in the presence of unmodeled dynamics and a persistently exciting periodic reference output.     

Stabilization of Arbitrary Switched Linear Systems With Unknown Time-Varying Delays

We consider continuous time switched systems that are stabilized via a computer. Several factors (sampling, computer computation, communications through a network, etc.) introduce model uncertainties produced by unknown varying feedback delays. These uncertainties can lead to instability when they are not taken into account. Our goal is to construct a switched digital control for continuous time switched systems that is robust to the varying feedback delay problem. The main contribution of this note is to show that the control synthesis problem in the context of unknown time varying delays can be expressed as a problem of stabilizability for uncertain systems with polytopic uncertainties.     

Characterization of feedback Nash equilibria for multi-channel systems via a set of non-fragile stabilizing state-feedback solutions and dissipativity inequalities

We consider the problem of state-feedback stabilization for a multi-channel system in a game-theoretic framework, where the class of admissible strategies for the players is induced from a solution set of the individual objective functions that are associated with certain dissipativity properties of the system. In such a framework, we characterize the feedback Nash equilibria via a set of non-fragile stabilizing state-feedback solutions corresponding to a family of perturbed multi-channel systems. Moreover, we show that the existence of a weak-optimal solution to a set of constrained dissipativity problems is a sufficient condition for the existence of a feedback Nash equilibrium, whereas the set of non-fragile stabilizing state-feedbacks solutions is described in terms of a set of dilated linear matrix inequalities.     

Name disambiguation in scientific cooperation network by exploiting user feedback

Name disambiguation is a very critical problem in scientific cooperation network. Ambiguous author names may occur due to the existence of multiple authors with the same name. Despite much research work has been conducted, the problem is still not resolved and becomes even more serious. In this paper, we focus ourselves on such problem. A method of exploiting user feedback for name disambiguation in scientific cooperation network is proposed, which can make use of user feedback to enhance the performance. Furthermore, to make the user feedback more effective, we divide user feedback into three types and assign different weights to them. To evaluate the effectiveness of our proposed method, experiments are conducted with standard public collections. We compare the performance of our proposal with baseline methods. Results show that the proposed algorithm outperforms the previous methods without introducing user interactions. Besides, we investigate into how different types of user feedback can affect the disambiguation results.     

Relevance feedback in image retrieval: A comprehensive review

We analyze the nature of the relevance feedback problem in a continuous representation space in the context of content-based image retrieval. Emphasis is put on exploring the uniqueness of the problem and comparing the assumptions, implementations, and merits of various solutions in the literature. An attempt is made to compile a list of critical issues to consider when designing a relevance feedback algorithm. With a comprehensive review as the main portion, this paper also offers some novel solutions and perspectives throughout the discussion. RID="*" ID="*" Work was done while at the University of Illinois.