Suboptimal Regulator Research Articles

Combined identification of the input-output and noise dynamics of a closed-loop controlled linear system

The open-loop input-output dynamics and the noise dynamics of a feedback controlled linear system perturbed by coloured noise admitting a Markov representation are identified in state variable form using a two-stage algorithm. This system is equivalent to an augmented system driven by white noise. First the input-output dynamics are identified through a stochastic approximation algorithm using superimposed white noise. Subtracting the model output from the system output yields correlated residuals which are then used to identify the noise dynamics using stochastic realization theory. An innovations representation is obtained that is equivalent to the above defined augmented system. The two stages are combined by a judicious coordinate transformation. The method can be applied on an operating feedback controlled process, regardless of the structure of the unknown suboptimal regulator.

量子化操作量を利用した準最適レギュレータ問題

量子化操作量を利用した準最適レギュレータ問題

A method for construction of suboptimal non-linear regulators by minimax algorithm†

A method is proposed for an approximate construction of the optimal state regulator for an autonomous non-linear system with quadratic performance index. The method is bused upon the instantaneous linearization technique developed by Pearson. In the method of instantaneous linearization, the non-linear system is approximated by a state-dependent linear model. However, the solution is not optimal in general because of the arbitrariness of the linearized model. The purpose of the present paper is to correct the shortcomings of this method. First, an optimality condition for the control law obtained by the method of instantaneous linearization is derived. Secondly, by making use of this condition, a systematic procedure is presented to determine a suboptimal feedback control for a second-order system. A minimax algorithm is used to design the linearized model closely approximating the original system within a prescribed region in the state space. The validity of the present method is shown by examining typic...

Discrete-time Regulator of an Infinite-dimensional System

The recurrence relations which are satisfied by optimal controllers and state estimators are given in Part I. These relations are extensions of the work of Tou ( 1, 2 . The extensions could be heuristically achieved by changing finite-dimensional matrices with infinite-dimensional ones (operators) and conjugate matrices with normed conjugate operators. The definitions of Falb ( 3 ) are used as the covariance operator of infinite- dimensional random vectors. By using the functional analysis approach, it is shown that the relations obtained heuristically are correct. In Part II, the infinite-dimensional system is approximated by the finite-dimensional system in order to calculate the suboptimal regulator. If the infinite-dimensional system is approximated by the n-dimensional system, the optimal regulator of the latter can be easily calculated by Tou's formulae. The solution of this may not be necessarily a suboptimal regulator, because there remains an important question as to whether this regulator tends to the optimal one of the infinite-dimensional system when n tends to infinity. This convergence is shown in the operator topology by making use of the facts that the suboptimal feedback controllers and state estimators are uniformly bounded in n. By this convergence the suboptimal regulator can be obtained as exactly as desired by choosing n appropriately large.

Three-term controller parameter selection using suboptimal regulator theory

The classical problem of parameter selection of three-term controllers within the framework of suboptimal linear regulator theory is viewed. Iterative techniques are used to determine the controller parameters so that the expected value of a quadratic loss type performance index is minimized, with the initial states of the system a random variable uniformly distributed over a unit sphere.

Suboptimal linear regulators with incomplete state feedback

A method of designing linear regulators with incomplete state feedback has been suggested by Rekasius [1]. Ramar and Ramaswami [2] have pointed out the difficulties encountered in applying this method. This correspondence presents, briefly, an alternative approach to this problem in two cases of a) unknown initial state and b) known initial state statistics, viz., mean and covariance matrix. Solution for the control law utilizing only the available states is obtained by minimizing an upper bound on the ratio of the suboptimal to optimal cost in case a). In case b) the expected value of the suboptimal cost is minimized. It is assumed that the available states are sufficient to make the feedback system stable. The solution is in the form of necessary conditions and results in a set of simultaneous polynomial equations, but the solution to the optimal control problem is not required.

Suboptimal linear regulators with incomplete state feedback

Suboptimal linear regulators with incomplete state feedback