Nonparametric multi-step prediction in nonlinear state space dynamic systems

Filtering and smoothing of stochastic state space dynamic systems have benefited from several generations of estimation approaches since the seminal works of Kalman in the sixties. A set of global analytical or numerical methods are now available, such as the well-known sequential Monte Carlo particle methods which offer some theoretical convergence results for both types of problems. However except in the case of linear Gaussian systems, objectives of the third kind i.e. prediction objectives, which aim at estimating k time steps ahead the anticipated probability density function of the system state variables, conditional on past and present system output observations, still raise theoretical and practical difficulties. The aim of this paper is to propose a nonparametric particle multi-step prediction method able to consistently estimate such anticipated conditional pdf of the state variables as well as their expectations.     

Power-of-two sampling in redundancy systems: The impact of assignment constraints

A classical sampling strategy for load balancing policies is power-of-two, where any server pair is sampled with equal probability. This does not cover practical settings with assignment constraints which force non-uniform sampling. While intuition suggests that non-uniform sampling adversely impacts performance, this was only supported through simulations, and rigorous statements have remained elusive. Building on product-form distributions for redundancy systems, we prove the stochastic dominance of uniform sampling for a four-server system as well as arbitrary-size systems in light traffic.     

Tribal particle swarm optimization for neurofuzzy inference systems and its prediction applications

This study presents tribal particle swarm optimization (TPSO) to optimize the parameters of the functional-link-based neurofuzzy inference system (FLNIS) for prediction applications. The proposed TPSO uses particle swarm optimization (PSO) as evolution strategies of the tribes optimization algorithm (TOA) to balance local and global exploration of the search space. The proposed TPSO uses a self-clustering algorithm to divide the particle swarm into multiple tribes, and selects suitable evolution strategies to update each particle. The TPSO also uses a tribal adaptation mechanism to remove and generate particles and reconstruct tribal links. The tribal adaptation mechanism can improve the qualities of the tribe and the tribe adaptation. Finally, the FLNIS model with the proposed TPSO (FLNIS-TPSO) was used in several predictive applications. Experimental results demonstrated that the proposed TPSO method converges quickly and yields a lower RMS error than other current methods.     

Optimal control of continuous-time deterministic systems with incomplete discrete feedback

Sufficient conditions for optimality are obtained for controls that depend on the current time and values of known functions of the state vector at finite points of the time interval. The equations for finding the required control laws are derived. An example is given for which an exact solution of the problem can be obtained.The author is grateful to Professor R. W. Rishel for his support during the preparation of the paper.     

Optimal control of differential-difference systems with intragroup symmetry

A decomposition method of finding the optimal control of differential-difference systems with intragroup symmetry is presented. The introduction of two forms of motions of coordinates of separate groups allows us to reduce the original optimal control problem to the solution of optimal control problems of order less than the order of the initial problem.     

Optimal control of semilinear parabolic systems with state constraint

The aim of this work is to obtain the existence of optimal solution and maximum principle for optimal control problem with pointwise type state constraint governed by semilinear parabolic systems with certain polynomial-like nonlinearity. Application to optimal control problems of the phase transition system is given.     

Generalized Steiner systems with block size three and group size g ≡ 3(mod 6)

Generalized Steiner Systems, GS(2, 3, n, g), are equivalent to maximum constant weight codes over an alphabet of size g + 1 with distance 3 and weight 3 in which each codeword has length n. We construct Generalized Steiner Triple Systems, GS(2, 3, n, g), when g ≡ 3(mod 6). © 1997 John Wiley & Sons, Inc. J Combin Designs 5:417–432, 1997     

Optimal control of time-delay systems with distributed parameters

An optimal control problem with a prescribed performance index for parabolic systems with time delays is investigated. A necessary condition for optimality is formulated and proved in the form of a maximum principle. Under additional conditions, the maximum principle gives sufficient conditions for optimality. It is also shown that the optimal control is unique. As an illustration of the theoretical consideration, an analytic solution is obtained for a time-delayed diffusion system.The author wishes to express his deep gratitude to Professors J. M. Sloss and S. Adali for the valuable guidance and constant encouragement during the preparation of this paper.     

Optimal control of delay systems via block pulse functions

The concept of coefficient shift matrix is introduced to represent delay variables in block pulse series. The optimal control of a linear delay system with quadratic performance index is then studied via block pulse functions, which convert the problems into the minimization of a quadratic form with linear algebraic equation constraints. The solution of the two-point boundary-value problem with both delay and advanced arguments is circumvented. The control variable obtained is piecewise constant.     

Prediction of diameter errors in bar turning: a computationally effective model

Machining accuracy can be considerably affected by the deflections of the machine–workpiece–tool system as well as the thermal expansion of material during machining. An improved model for predicting dimensional errors in turning process is presented. This model uses a geometric analysis in the machine frame, in which the elastic deflections of the machine–workpiece–tool system due to the cutting force are studied. In this paper, our workpiece deflection model [A.-V. Phan, G. Cloutier, J.R.R. Mayer, International Journal of Production Research 37 (1999) 4039–4051; G. Cloutier, J.R.R. Mayer, A.-V. Phan, Computer Modeling and Simulation in Engineering 4 (1999) 133–137] earlier developed is employed. As described in Phan et al. (1999), this deflection model is general, accurate and computationally effective thanks to its closed-form solutions derived from the finite element technique. Also, due to the coupling between the cutting force and actual depth of cut, iterative computations are performed to obtain the coupling value of this force which provides further accuracy to the prediction. Finally, via numerical examples, the predicted diameter error on a workpiece, the ratio between the coupled cutting force and its nominal value along the part axis as well as the influence of the cutting force components on the error prediction are computed using the proposed model. The results provide additional insight into the error formation in the turning process.     

Economic off-line quality control strategy with two types of inspection errors

A commonly used quality control method is to inspect products to identify their quality and to perform the related disposition of acceptance, salvage or rejection based on the findings. While the issue of finding the most economical inspection/disposition policy has been studied for a batch of units produced from an unreliable system, previous studies assumed the inspections to be perfect. In this study, we further extend the inspection/disposition model to consider two types of inspection errors in order to facilitate the adaptation of this economic inspection/disposition model to real world applications. We first describe an inspection/disposition policy for the two types of inspection errors and then obtain the related mathematical formulae. An algorithm is presented for determining the optimal inspection/disposition policy. Finally, numerical examples are given to illustrate the effect of inspection errors on the optimal inspection/disposition policy under the following three quality control policies: cost minimizing, zero-defects and perfect information policy.     

Optimal generation scheduling for constrained multi-area hydrothermal power systems with cascaded reservoirs

The optimization problem in this paper is targeted at large-scale hydrothermal power systems. The thermal part of the system is a multi-area power pool with tie-line constraints, and the hydro part is a set of cascaded hydrostations. The objective is to minimize the operation cost of the thermal subsystem. This is an integer nonlinear optimization process with a large number of variables and constraints. In order to obtain the optimal solution in a reasonable time, we decompose the problem into thermal and hydro subproblems. The coordinator between these subproblems is the system Lagrange multiplier. For the thermal subproblem, in a multi-area power pool, it is necessary to coordinate the area generations for reducing the operation cost without violating tie limits. For the hydro subsystem, network flow concepts are adopted to coordinate water usage over the entire study time span, and the reduced gradient method is used to overcome the linear characteristic of the network flow method in order to obtain the optimal solution. In this study, load forecasting errors and forced outages of generating units are incorporated in system reliability requirements. Three case studies for the proposed method are presented.     

Optimal control problems with state constraints for semilinear distributed-parameter systems

We consider optimal control problems for distributed-parameter systems described by semilinear equations, with constraints on the control and on the state, and an exact pointwise target condition. As an application of a general theory of nonlinear programming problems in Banach spaces, a version of the Pontryagin maximum principle is obtained.This research was partly supported by the National Science Foundation under Grant DMS-92-21819.     

Optimal replacement strategies for repairable systems

This paper considers repair-replacement models introduced by Lam Yeh [6] and [7], and Stadje and Zuckerman [9]. Without imposing reliability theory conditions on the repair and operating distributions, the optimal replacement problem is first solved in a finite horizon setting and then extensions are given to the infinite horizon case.     

Generalized steiner triple systems with group size five

Generalized Steiner triple systems, GS(2, 3, n, g) are used to construct maximum constant weight codes over an alphabet of size g+1 with distance 3 and weight 3 in which each codeword has length n. The existence of GS(2, 3, n, g) has been solved for g=2, 3, 4, 9. In this paper, by introducing a special kind of holey generalized Steiner triple systems (denoted by HGS(2, 3, (n, u), g)), singular indirect product (SIP) construction for GDDs is used to construct generalized Steiner systems. The numerical necessary conditions for the existence of a GS(2, 3, n, g) are shown to be sufficient for g=5.     

Optimal operation of multireservoir power systems

The optimal monthly operating policy of a multireservoir hydroelectric power system is a stochastic nonlinear problem. This paper presents a new method for determining the optimal monthly operating policy of a power system ofn reservoirs in series on a river taking into account the stochasticity of the river flows. Functional optimization techniques and minimum-norm formulation have been used to find the optimal release policy of the system. Results for a numerical example composed of four reservoirs are presented.This work was supported by the National Research Council of Canada, Grant No. A4146.     

Optimal control of impulsive hybrid systems

In this paper, we deal with optimization techniques for a class of hybrid systems that comprise continuous controllable dynamics and impulses (jumps) in the state. Using the mathematical techniques of distributional derivatives and impulse differential equations, we rewrite the original hybrid control system as a system with autonomous location transitions. For the obtained auxiliary dynamical system and the corresponding optimal control problem (OCP), we apply the Lagrange approach and derive the reduced gradient formulas. Moreover, we formulate necessary optimality conditions for the above hybrid OCPs, and discuss the newly elaborated Pontryagin-type Maximum Principle for impulsive OCPs. As in the case of the conventional OCPs, the proposed first order optimization techniques provide a basis for constructive computational algorithms.     

On estimation and control of errors of the Mann iteration process

The purpose of this note is to study the estimation of errors of the Mann iterative process with random errors. It is shown that the accumulative errors in iterative process is bounded and the errors is controllable with some conditions.     

Optimal control for nonlinear systems calculated with small computers

Using Ritz's procedure of representing the control functions of an optimal control problem by a function series with parameters to be optimized, it is shown that, from the well-known gradient procedure for dynamic problems, a simple iteration formula for the optimization of these parameters can be derived. Using an example with a technical background, the effectiveness of the program realization of this approach is demonstrated and is compared with the results of unrestricted dynamic optimization.This work was performed at the Technische Hochschule in Darmstadt, West Germany, with financial support from the DFG (Deutsche Forschungs-Gemeinschaft).