Hajime Akashi

Brief paper: Random sampling approach to state estimation in switching environments

This paper deals with the state estimation for the systems under measurement noise whose mean and covariance change with Markov transition probabilities. The minimum variance estimate for the state involves consideration of a prohibitively large number of sequences, so that the usual computation method becomes impractical. In the algorithm proposed here, the estimate is calculated with a relatively small number of sequences sampled at random from the set of a large number of sequences. The average risk of the algorithm is shown to converge to the optimal average risk as the number of sampled sequences increases. An ideal sampling probability yielding a very fast convergence is found. The probability is approximated in a minimum mean squared sense by a probability according to which sequences can be sampled sequentially and with great ease. This policy of determination of sampling probability makes it possible to design practical and efficient algorithms. Digital simulation results show a good performance of the proposed algorithm.

Disturbance localization and output deadbeat control through an observer in discrete-time linear multivariable systems

This paper considers the problem of disturbance localization for the system x(i + 1) = Ax(i) + Bu(i) + Dd(i), y(i) = Cx(i), w(i) = Ex(i) , with disturbance d(i) , measurement output y(i) , and controlled output w(i) . It is shown that the problem is solvable by using an observer if and only if V^{\ast} \supset 2^{\ast} where V*is the largest ( A,B )-invariant subspace in \ker E and 2*is the least ( A,\ker C )-conditioned invariant subspace containing Im D . Also, it is shown that there exists a controller using an observer that achieves simultaneous disturbance localization and output deadbeat control if and only if the system is controllable modulo \ker E and, in addition, V^{\ast} \supset O^{\ast} where O*is the unknown input unconstructible subspace. A simple algorithm is proposed to design such a controller. This algorithm comprises those of designing the optimal output deadbeat state feedback controller and an unknown input observer.

Interactive Optimization of System Reliability Under Multiple Objectives

This paper considers a multiobjective reliability allocation problem for a series system with time-dependent reliability. The method determines the most preferable reliability allocation and preventive maintenance schedule. The problem is multiobjective nonlinear mixed-integer. The decision making procedure is based on interactive optimization and a nonlinear programming algorithm. The method is illustrated by a numerical example.

Sensitivity approaches to optimization of linear systems with time delay

This paper presents two different sensitivity approaches to synthesis problems of optimal control for linear systems with small time delays. In the first part, the optimal control considering sensitivity is discussed for a minimum energy problem to make up for the undesirable effect caused by a small time delay. In this sensitivity synthesis of optimal control, the central role is played by a combined system which consists of the model neglecting the delay time and the sensitivity model with respect to it. In order to ensure the optimal control with zero-sensitive terminal constraints, the controllability property of the combined system is investigated, and the necessary and sufficient condition for it is derived for a linear system. The second part presents a synthesis method of a suboptimal control for a regulator problem, in which the optimal control is expanded into MacLaurin series in terms of the delay time and the first two or more terms are used to yield a sub-optimal control. Another slightly different approach, in which the singular perturbation method is applied, is also discussed and compared with the other one. As shown by the numerical examples, the present sensitivity approaches decrease considerably the computational efforts, while preserving a good performance in the synthesis of time delay systems.

Output deadbeat controllers with stability for discrete-time multivariable linear systems

This short paper Treats the problem of designing output deadbeat controllers having the property that the control input to the system converges to zero as time goes to infinity, for discrete-time multivariable linear systems. Two configurations of controllers are considered: one is of state feedback; the other is a dynamic controller using an observer. The existence of such controllers is examined, and the methods are presented for designing such controllers when they exist. The controller using a state feedback obtained in this paper is optimal in the sense that the controller settles the output in zero for any initial state in the minimum number of steps. On the other hand, the dynamic controller is not optimal in that sense, but it minimizes t , where t is defined as an integer such that the controller drives the output to zero in no more than t steps for any set of initial conditions of the system and the observer.

On time optimal control of linear discrete-time systems by geometric approach

This paper arose from the need for a better understanding of the minimum time state regulation problem of finite-dimensional linear time-invariant discrete systems with an incomplete state observation. For this we used a geometric approach and obtained the following interesting results. First, the necessary and sufficient condition of the existence of controllers which regulate the system from any initial state to the origin in finite steps is that the system is controllable and reconstructable. Secondly, the general minimum regulation time is obtained, which is the maximum value of the minimum regulation time. Thirdly, two typical controllers which drive the system from any initial state to the origin in the general minimum regulation time are designed. One is a time-variant system taking the systems input and output of each time as input. The other is a time-invariant system. Fourthly, it is shown that the controller does not necessarily exist which transfers the system to the origin in the minimum reg...

Minimum time output regulation problem of linear discrete-time systems

This paper deals with the minimum time output regulation problem of finite-dimensional linear time-invariant discrete-time systems with an incomplete state observation. First, the necessary and sufficient condition is obtained for the existence of controllers which regulate the system for any arbitrary initial state to a certain given subspace in finite steps. Then, the minimum time is obtained in which the system satisfying the above conditions can be regulated, and a minimum time regulating controller is designed. These are obtained by the geometric approach which is a powerful tool for the investigation of the structural property of linear systems.

Optimal Reliability Allocation Under Preventive Maintenance Schedule

This paper considers a series system of components with time-dependent reliability and gives a new formulation of an optimal reliability allocation problem where an optimal preventive maintenance (PM) schedule is determined simultaneously. The importance of this formulation is shown in comparison with a conventional formulation where PM schedule is not taken into account. The optimization problem becomes a nonlinear mixed-integer programming problem. A simple approximate solution algorithm is given on the basis of a nonlinear programming (NLP) algorithm. The procedure is illustrated by use of a numerical example. Though we restrict our attention to the case where a preventive replacement is adopted as a PM policy, a similar discussion is possible for the as-good-as-new repair.

Analysis of decisions under risk with incomplete knowledge

The application of decision theory on the basis of the expected utility criterion is discussed. Cases are considered where the form of the utility function is not known except for certain of its characteristics such as increasing concavity or increasing concavity with positive third derivatives, and/or the probability of the individual state of nature is not known exactly, and only certain relations between the probabilities of different states are available. First the reformulation of statistical dominance is carried out by assuming a limited amount of information on the probability of the state. Then a new method of dominance relation, referred to as S-S dominance, is introduced; here limited information on both the utility function and the probability of the state is assumed to be available, as is complete knowledge of the conditional probability distribution of the consequences for each state. Finally, the feasibility of S-S dominance is demonstrated through examples.

Improvement of Supervision Schedules for Protective Systems

Improvement of supervision schedule is considered for protective-systems of multiple components. Each component is periodically supervised. Our improvement procedure consists of two steps. 1) Determine the time length of supervision and duration of successive supervisions which maximize the minimum point availability for simultaneous supervision schedule where all components are supervised simultaneously. 2) Improve the supervision schedule of Step 1 by constructing a staggered supervision schedule. In this schedule components are divided into subgroups, and supervisions of subgroups are staggered while components in the same subgroup are supervised simultaneously. A systematic method is given to optimize allocating components into subgroups for a specified number of subgroups and staggering of supervisions. An example illustrates the method.