Noninteracting control with stability for Hamiltonian systems

The problem of noninteraction with stability via dynamic state feedback is addressed and solved for a class of nonlinear Hamiltonian systems. A simple way to check necessary and sufficient conditions is proposed. It is well known that to decide if the problem is solvable, and which class of state feedback has to be used, the stability properties of some special dynamics are to be investigated. For this reason, on the way to the main result, it is shown that such dynamics are not necessarily Hamiltonian. Several examples, clarifying the role of different classes of state-feedback control laws (either static or dynamic) in the solution of the problem, are proposed     

Optimal control of 2-D systems

Two-dimensional (2-D) optimal control theory that parallels one-dimensional (1-D) optimal control is developed. A generalized performance measure suited to 2-D systems is introduced. The canonical equations associated with this performance measure and a general nonlinear model are obtained. The 2-D linear quadratic regulator problem is formulated, and its canonical equations are derived for the Roesser model. An earlier result by T. Kaczorek and J. Klamka (1986) for the solution of the minimum-energy problem with fixed-final local state is rederived using this approach. A new problem, minimum-energy with fixed-final-pass local states is formulated and solved, and a numerical example is given     

Noninteracting control with stability for a class of nonlinear systems

In this paper we address the problem of noninteracting control with stability for the class of nonlinear square systems for which noninteraction can be achieved (without stability) by means of invertible static state-feedback. The use of both static state-feedback and dynamic state-feedback is investigated. We prove that in both cases the asymptotic stabilizability of certain subsystems is necessary to achieve noninteraction and stability. We use this and some recent results to state a complete set of necessary and sufficient conditions in order to solve the problem.     

Noninteracting control via static measurement feedback fornonlinear systems with relative degree

In this paper the author gives a necessary and sufficient geometric condition for achieving noninteraction via static measurement feedback for nonlinear systems with vector relative degree. The analysis relies on the theory of connections and as a result gives systematic procedures for constructing a decoupling feedback law     

Minimum energy control for general model of 2-D linear systems

A new definition of the straight line controllability for the general model of 2-D linear systems is presented. Necessary and sufficient conditions for the straight line controllability of the general model are established. The minimum energy control problem for the general model of 2-D systems with constant coefficients is formulated and solved.     

Controllability of 2-D systems

The concept of controllability of 2-D systems is introduced in a behavioral framework. This property is defined as a systems concept and is characterized in terms of system representations. State-space realizations for controllable 2-D systems are presented. The structure of state-space systems is analyzed, and the notions of trimness, reachability, and observability are introduced and characterized. These realizations do not depend on any assumptions concerning causality     

Noninteracting control by output feedback and dynamic compensation

The design of noninteracting multivariable control systems by slate feedback has received considerable attention recently, and an extensive theory is now available. One area, however, that requires further clarification concerns the case where the state vector is not accessible to measurement, and feedback of output is inadequate for the purpose of decoupling. In this paper a new technique is described by means of which it is possible to decouple a system which is not olherwise decouplable by proportional feedback of the output vector. The technique is based on the addition of a dynamic controller in the forward path, and is analogous to cascade compensation in single-loop systems. It is shown that a necessary and sufficient condition for the success of this method of decoupling control is that the Original system should satisfy the condition for state feedback decoupling.     

Decomposition of 2-D linear systems into 1-D systems in thefrequency domain

A method is presented for the decomposition of the frequency domain of 2-D linear systems into two equivalent 1-D systems having dynamics in different directions and connected by a feedback system. It is shown that under some assumptions the decomposition problem can be reduced to finding a realizable solution to the matrix polynomial equation X(z₁)P(z₂ )+Q(z₁)Y(z₂ )=D(z₁, z₂). A procedure for finding a realizable solution X(z₁ ), Y(z₂) to the equation is given     

Exact model matching of 2-D systems

In this note the 2-D model mathing problem is considered. The purpose of this note is not to present a complete solution to this problem but rather to indicate some possible solutions. By using a generalized dynamic cover (GDC) [5] a first level realization, [1] is constructed for the desired compensator.     

General response formula and minimum energy control for the generalsingular model of 2-D systems

The general response formula for the general singular model of 2-D linear systems is derived. The concepts of local reachability and local controllability are extended to the singular model. Necessary and sufficient conditions for local reachability and local controllability are established. The minimum energy control problem for the singular model is formulated and solved     

State-space discrete systems: 2-D eigenvalues

A correction is given to a proof of the fact, presented in a paper by Roesser [1], that every partitioned matrixAnot only satisfies the two-dimensional characteristic equation, but it must also satisfy an additional set of equations. A new definition of 2-D eigenvalues is proposed.     

On robust stability of 2-D discrete systems

Presents a study on robust stability of two-dimensional (2-D) discrete systems in the Fornasini-Marchesini (F-M) state space setting. A measure of stability robustness of a stable F-M model is defined. The relation of this measure to its counterpart in the Roessor state space and related computational issues are addressed. Three lower bounds of the stability-robustness measure defined are derived using a one-dimensional parameterization approach and a 2-D Lyapunov approach. A numerical example is included to illustrate the main results obtained     

Stability of nonlinear parameter-varying digital 2-D systems

A general state-space model for nonlinear parameter-varying digital two-dimensional (2-D) systems is proposed. Sufficient conditions for system stability are given. Presented theorem can be considered as a generalization of the Lyapunov stability theorem for one-dimensional nonlinear systems. Given results can be useful in stability analysis for systems described by 2-D models     

3-D imaging systems and high-speed processing for robot control

Bin picking by a robot in real time requires the performance of a series of tasks that are beyond the capabilities of commercially available state-of-the-art robotic systems. In this paper, a laser-ranging sensor for real-time robot control is described. This sensor is incorporated into a robot system that has been applied to the bin-picking or random-parts problem. This system contains new technological components that have been developed recently at the Environmental Research Institute of Michigan (ERIM). These components (the 3-D imaging scanner and a recirculating cellular-array pipeline processor) make generalized real-time robot vision a practical and viable technology. This paper describes these components and their implementation in a typical real-time robot vision system application.     

Duality of 2-D singular systems of Roesser models

In this paper, the properties and concepts of dual systems of the two-dimensional singular Roesser models （2-D SRM） are studied. Two different concepts of the dual systems are proposed for the 2-D SRM. One is derived from the duality defined for two-dimensional singular general models （2-D SGM）-called the S-dual systems; the other one is defined based on 2-D SRM in a traditional sense-called the T-dual systems. It is shown that if a 2-D SRM is jump-mode free or jump-mode reachable, then it can be equivalently transformed into a canonical form of a 2-D SRM, for which the T-duality and the S-duality are equivalent. This will be of some perspective applications in the robust control of 2-D SRM.