Disturbance attenuation of linear quadratic OL-Nash games on repetitive processes with smoothing on the gas dynamics

This article presents necessary and sufficient results for existence and uniqueness of an equilibrium of a N-player disturbed Nash game with quadratic performance criteria and an affine repetitive process with smoothing describing the two dimensional 2D-system dynamics, under open loop information pattern. The gas dynamics in a single pipeline is modelled in this theoretical framework, and an algorithm withdrawn from the exposed procedure to calculate the equilibrium point is applied to a simple network example.     

Robust control with finite frequency specification for uncertain discrete linear repetitive processes

This paper is dedicated to the study of robust stability and controller synthesis for discrete linear repetitive processes with polytopic uncertainty. In the robust control domain, conditions based on parameter dependent Lyapunov functions are proposed in order to reduce the conservatism related to uncertainty problems. The solution is a class of Lyapunov functions that depends in a polytopic way on the uncertain parameters and that can be derived from linear matrix inequality conditions. Nevertheless, in many cases in practice, the frequency range of reference signals, noises and disturbances are known beforehand. Therefore, performing controller synthesis in the full frequency range is not practically suited and may introduce conservatism to some extent. Based on generalized Kalman–Yakubovich–Popov Lemma, a finite frequency controller is derived for uncertain discrete linear repetitive processes which are the most investigated class of 2D systems. Hence, the designer can specify a frequency range where the prescribed control performance is required, where, for example, this range could be determined by inspection of frequency spectrums of the available signals.     

On control laws for discrete linear repetitive processes with dynamic boundary conditions

Repetitive processes are characterized by a series of sweeps, termed passes, through a set of dynamics defined over a finite duration known as the pass length. On each pass an output, termed the pass profile, is produced which acts as a forcing function on, and hence contributes to, the dynamics of the next pass profile. This can lead to oscillations in the sequence of pass profiles produced which increase in amplitude in the pass-to-pass direction and cannot be controlled by application of standard control laws. Here we give new results on the design of physically based control laws for so-called discrete linear repetitive processes which arise in applications areas such as iterative learning control.     

Decoupling and iterative approaches to the control of discrete linear repetitive processes

This paper reports new results on the analysis and control of discrete linear repetitive processes which are a distinct class of 2D discrete linear systems of both systems theoretic and applications interest. In particular, we first propose an extension to the basic state-space model to include a coupling term previously neglected but which arises in some applications and then proceed to show how computationally efficient control laws can be designed for this new model.     

Simple proof of unconditional controllability and observability

A direct proof using a frequency-domain argument is given of Chu's theorem on complete controllability and observability for every nonzero input and output matrix.     

Strong practical stability and stabilization of discrete linear repetitive processes

This paper considers two-dimensional (2D) discrete linear systems recursive over the upper right quadrant described by well known state-space models. Included are discrete linear repetitive processes that evolve over subset of this quadrant. A stability theory exists for these processes based on a bounded-input bounded-output approach and there has also been work on the design of stabilizing control laws, elements of which have led to the assertion that this stability theory is too strong in many cases of applications interest. This paper develops so-called strong practical stability as an alternative in such cases. The analysis includes computationally efficient tests that lead directly to the design of stabilizing control laws, including the case when there is uncertainty associated with the process model. The results are illustrated by application to a linear model approximation of the dynamics of a metal rolling process.

Hankel-type model reduction for linear repetitive processes: differential and discrete cases

This paper investigates a Hankel-type model reduction problem for linear repetitive processes. Both differential and discrete cases are considered. For a given stable along the pass process, our attention is focused on the construction of a reduced-order stable along the pass process, which guarantees the corresponding error process to have a specified Hankel-type error performance. The Hankel-type performances are first established for differential and discrete linear repetitive processes, respectively, and the corresponding model reduction problems are solved by using the projection approach. Since these obtained conditions are not expressed in linear matrix inequality (LMI) form, the cone complementary linearization (CCL) method is exploited to cast them into sequential minimization problems subject to LMI constraints, which can be solved efficiently. Three numerical examples are provided to demonstrate the proposed theory. This work was partially supported by RGC HKU 7028/04P.     

Decentralized control via disturbance attenuation and eigenstructure assignment

In this brief, a simple approach is proposed for decentralized control of linear large-scale systems. Sufficient conditions for diagonal dominance of closed-loop large-scale systems are derived. Based on these conditions, the interactions between the subsystems can be considered as external disturbances for each isolated subsystem. Then, a previously proposed approach is used to attenuate disturbances via dynamic output compensators based on complete parametric eigenstructure assignment. Through attenuation of the disturbances, the closed-loop poles of the overall system are assigned in the desirable region, by assigning the eigenstructure of each isolated subsystem appropriately. An example is given to show the effectiveness of the proposed method.     

Control law design for discrete linear repetitive processes with non-local updating structures

Repetitive processes are a class of 2D systems where information propagation in one direction is of finite duration. These processes make a series of sweeps, termed passes, through a set of dynamics and on completion of each pass resetting to the starting position occurs ready for the start of the next pass. The control problem is that the previous pass output, termed the pass profile, acts as a forcing function on the current pass and can result in oscillations that increase in amplitude from pass-to-pass. In the case of discrete dynamics, these processes have structural links with 2D systems described by the well known Roesser and Fornasini–Marchesini state-space models but some applications require updating structures that cannot be represented by these models. This requirement arises either in adequately modeling the dynamics or as a result of the control law structure and requires the development of a systems theory for eventual use in applications. In this paper such a theory is advanced through the development of new control law design algorithms.     

On the stability and the stabilization of linear discrete repetitive processes

Multidimensional Systems and Signal Processing - This article deals with stability and stabilization issues for linear two-dimensional (2D) discrete models. More precisely, we focus on repetitive...     

Robust control of robot manipulator by model-based disturbance attenuation

In this letter, a model-based disturbance attenuator (MBDA) for robot manipulators is proposed and the stability of the MBDA in robot positioning problems is proved via Liapunov's direct method. This method does not require an accurate model of a robot manipulator and takes care of disturbances or modeling errors so that the plant output remains relatively unaffected by them. The output error due to the gravity or constant disturbance can be effectively eliminated by this method.     

金属锻造重复过程的输出反馈控制

研究了金属锻造重复过程的输出反馈控制问题.通过设计一个输出反馈控制器使金属锻造重复过程稳定,给出控制器存在的充分条件,并将控制器的设计转化为一个凸优化的求解问题.仿真实例证实了该设计方法的有效性.     

Guaranteed cost control of uncertain differential linear repetitive processes

This paper deals with the problem of designing a control law for differential linear repetitive processes based on minimizing a cost function in the presence of uncertainties in the process model. This control law results in a closed-loop stable process with an associated cost function which is bounded for all admissible uncertainties. Moreover, an optimization algorithm is developed to design this law such that it minimizes the upperbound of the closed-loop cost function.     

Automatic generation of test infrastructures for analog integrated circuits by controllability and observability co-optimization

This paper presents a method to address the automatic testing of analog ICs for catastrophic defects. Based on Design-for-Testability building blocks offering extra controllability and extra observability, a test infrastructure is generated for a targeted circuit. The selection of the extra blocks and their insertion into the circuit is done automatically by a workflow based on DC simulations and optimization algorithms. Adopting a defect-oriented methodology, this approach maximizes the fault coverage while minimizing the silicon area overhead and test time. The proposed method is applied to two industrial circuits in order to generate optimal test infrastructures combining controllability and observability. These case studies show that, with a silicon area overhead of less than 10%, a fault coverage of 94.1% can be reached.     

Just-in-time adaptive disturbance estimation for run-to-run control of semiconductor processes

Run-to-run control is the term used for the application of discrete parts manufacturing control as practiced in the semiconductor industry. This paper presents a new algorithm for use in run-to-run control that has been designed to address some of the challenging issues unique to batch-type manufacturing. Just-in-time adaptive disturbance estimation (JADE) uses recursive weighted least squares parameter estimation to identify the contributions to variation that are dependent upon manufacturing context. The strengths and weaknesses of the JADE algorithm are demonstrated in a series of test cases developed to separate the various disturbances and processing issues a control system would be expected to encounter.     

Maximum principle for optimal control of two-directionally continuous linear repetitive processes

In the paper, maximum principle for a two-directionally continuous variant of a linear autonomous repetitive process with cost functional depending on a fixed “end-function” is obtained. Maximum condition has a pointwise form, a conjugate system has a Fornasini-Marchesini form. The result is derived from the extremum principle for smooth-convex problems, due to Ioffe and Tikhomirov.     

H/sub /spl infin// control of differential linear repetitive processes

Repetitive processes are a distinct class of two-dimensional (2-D) systems (i.e., information propagation in two independent directions) of both systems theoretic and applications interest. They cannot be controlled by direct extension of existing techniques from either standard [termed one-dimensional (1-D) here] or 2-D systems theory. Here, we give new results on the relatively open problem of the design of control laws using an H/sub /spl infin// setting. These results are for the sub-class of so-called differential linear repetitive processes which arise in applications.     

New results in 2-D systems theory, part II: 2-D state-space models—Realization and the notions of controllability, observability, and minimality

In this part, a comparison between the different state-space models is presented. We discuss proper definitions of state, controllability and observability and their relations to minimality of 2-D systems. We also present new circuit realizations and 2-D digital filter hardware implementation of 2-D transfer functions.