A. P. Roberts

The Luenberger canonical form in the state/parameter estimation of linear systems

The use of the Luenberger canonical form in the state model allows the non-linear state/parameter estimation problem to be separated into two linear problems. This is illustrated for ‘a’ a deterministic system and ‘6’ a system with equal state and measurement noises. Computational results are presented. An on-line state/ parameter estimator for the innovations model of the discrete-time, linear, stochastic system is outlined.

Polynomial optimization of stochastic feedback control for unstable plants

ABSTRACT The role of Kuceras two diophantine equations is explored in the optimization of a discrete-time feedback controller for a multivariate unstable plant subject to stochastic reference and disturbance, but it is usually only necessary to solve one of the equations. However, with an unstable plant, an extra diophantine equation must be solved when there is output measurement noise.

Polynomial optimization of stochastic discrete-time control for unstable plants

The matrix polynomial method of optimization of linear multivariable discrete-time control for unstable plants with stationary stochastic inputs is derived in a constructive manner. New sufficient conditions are obtained and Kuceras second diophantine equation is found directly from the requirement that the system be stable. Although the second equation must be satisfied, it is proved that it need not be used in the optimization when a certain coprimeness exists.

Simpler polynomial solutions in stochastic feedback control

This paper is an exact parallel to the solution of the stochastic feedback control problem in discrete time given in Kuceras book (1979). The difference is that here it is shown that usually it is only necessary to solve one, rather than two, diophantine equations. The resulting reduction in dimension will be particularly important in large-scale systems.

Lagging Filtering and Progressive Interpolation

ABSTRACT Mediteh (1967) has solved the problems of lagging filtering and progressive interpolation in discrete-time when message and noise are independent. His results are now extended to continuous-time. A solution is also found for progressive interpolation in both discrete and continuous-time when message and noise are correlated. The latter is used to find the progressive interpolator when the noise is coloured instead of white. The error covariance is examined in all of these cases.

Generalized polynomial optimization of stochastic feedback control

A purely algebraic polynomial approach is used to optimize the discrete-time feedback controller for a multivariable plant subject to stochastic reference and disturbance and coloured output measurement noise. A quadratic cost criterion with dynamic weightings is used that includes sensitivity and complementary sensitivity as well as tracking error and control input. The method involves the solution of only one diophantine equation.

Polynomial optimization of stochastic continuous-time control for unstable plants

The matrix polynomial method of optimization of linear multivariable continuous-time control for unstable plants with stationary stochastic inputs is derived in a constructive manner. New sufficient conditions are included but certain extra conditions imposed previously for continuous-time optimization are shown to be unnecessary. Kuceras second diophantine equation is derived directly from the requirement that the system be stable. As in discrete time, the second equation need not be used in the optimization when a certain coprimeness exists.

An analogue technique for solving trajectory optimization problems

Analogue or hybrid computer methods for solving trajectory optimization problems usually require the solution of a two-point boundary value problem. A method of solving this problem is presented which does not require a good initial approximation to ensure convergence of the iteration. Analogue computer results are given with the method applied to a double integrator plant. Two different forms of performance index are considered.

Optimal linear filtering and lagging filtering of coloured noise

The Kalman filtering problem is reformulated for coloured noise. This allows solution of the corresponding lugging filtering problem. Different methods of solution are found by using statistical orthogonality and maximum likelihood, and the two methods are compared. All rosults nro givon in continuous-time.

A variational approach to the polynomial optimization of multivariabie control with coloured measurement noise

Polynomial optimization has been applied to multivariabie control in the presence of stochastic inputs including coloured measurement noise. The method has been derived using the calculus of variations, which is thought to be a simpler formulation than completing squares. Both discrete-time and continuous-time systems are considered.