A scheme is developed for classifying the types of motion perceived by a humanlike robot. It is assumed that the robot receives visual images of the scene using a perspective system model. Equations, theorems, concepts, clues, etc., relating the objects, their positions, and their motion to their images on the focal plane are presented. >

http://ieeexplore.ieee.org/iel2/815/3148/00100651.pdf

Robot vision

The paper presents a proof of stability of model reference adaptive control systems using direct control. The structure of the adaptive system is similar to that considered by Monopoli [1] and Narendra and Valavani [2] but contains an additional feedback term which ensures that the time derivative of the parameter error vector belongs to the L2space. The output of the plant is shown to be bounded by expressing the plant feedback loop as an exponentially stable system with a time-varying gain \dot{\phi}(\cdot)\in L^{2} in the feedback path.

Stable adaptive controller design, part II: Proof of stability

Single-loop feedback-stabilization of linear multivariable dynamical plants

This survey is concerned with the definition and main properties of sets of specific values of complex frequency, called poles and zeros, which may be associated with a matrix-valued function of a complex frequency variable. The main emphasis is on the physical interpretation of invariant zeros in terms of the general zero-output behaviour of a linear dynamical system. A discussion is given of the relationship between this definition of a zero and the various other forms adopted in the current literature. The relationship is considered between poles and zeros defined by algebraic means and the standard complex variable theory of algebraic functions. It is shown that the poles and zeros of a square matrix-valued function of a complex variable G(s) are the same as the poles and zeros of an associated algebraic function g(s).

Poles and zeros of linear multivariable systems : a survey of the algebraic, geometric and complex-variable theory

Theory of Equations. By J. V. Uspensky. Pp. vii, 353. 27s. 1948. (McGraw-Hill)

A computational technique for inverse kinematics

This paper presents an adaptive control structure which can be used to assign all poles and zeros of a continuous-time linear multivariable system represented by an ( m \times m ) strictly proper transfer matrix T(s) , provided T(s) has no right-half plane zeros. The controller parameters can be directly estimated from input-output data. The paper also serves to point out the type of a priori information necessary for multivariable adaptive controller design. This information is a natural extension of that required in the scalar case.

A parameter adaptive control structure for linear multivariable systems

It is shown that the related questions of output tracking and output regulation (with and without input sensor measurement), all with associated internal stability, can be resolved via a single polynomial matrix formulation which employs the recently developed notion of skew prime polynomial matrices. In particular, the primary condition which must be satisfied in all cases is that R(s) , the plant numerator matrix, and a matrix where zeros represent the modes of the exogenous system, be externally skew prime. This observation is then elucidated in light of a new internal model principle.

Output regulation and tracking in linear multivariable systems

A partial resolution to the question of stability of solutions to the minimal design problem is given in terms of transfer matrix factorizations employing the new notions of common system poles and common systems zeros as well as the fixed poles of all solutions and the fixed poles of minimal solutions. The results are employed to more directly and easily resolve questions involving the attainment of stable solutions to the model matching problem and stable minimal-order state observers.

/pdf/on-the-stability-of-solutions-to-minimal-and-nonminimal-1o9g5e1048.pdf

On the stability of solutions to minimal and nonminimal design problems

A pair of polynomial matrices, P(s) and Q(s) , is defined to be "externally skew prime" if and only if a solution, M(s), N(s) , to the polynomial matrix equation P(s)M(s)+N(s)Q(s)=I exists. It is shown that P(s) and Q(s) are externally skew prime if and only if Q(s)P(s)= \bar{P}(s)R(s) with Q(s) and \bar{P}(s) relatively left prime and P(s) and R(s) relatively right prime. This observation implies a new constructive procedure for determining M(s) and N(s) where P(s) and Q(s) are found to be externally skew prime and P(s) is nonsingular. A new procedure for obtaining solutions to the more general polynomial matrix equation, P(s)M(s)+N(s)Q(s)= V(s) , based on the notion of skew-prime polynomial matrices is also presented. A characterization of all solutions when V(s)= I is also given, under appropriate assumptions, and then employed to determine a unique solution to this polynomial matrix equation.

http://ieeexplore.ieee.org/iel5/9/24168/01101854.pdf

William A. Wolovich

Papers

A computational technique for inverse kinematics

A parameter adaptive control structure for linear multivariable systems

Output regulation and tracking in linear multivariable systems

On the stability of solutions to minimal and nonminimal design problems

Skew prime polynomial matrices