Auxiliary signal design for robust multimodel identification

Under the assumption that one of two given linear models is the real underlying model of the system, a proper auxiliary signal is defined as an input signal that allows the selection of the correct model. Under the assumption that model noises have bounded energy, the separability index is defined as the inverse of the energy of the proper auxiliary signal of least energy. A method for the computation of this index and the construction of the auxiliary signal is presented. Finally, an efficient procedure for online identification, called the "hyperplane test", is developed     

Information induced multimodel solutions in multiple decisionmaker problems

This paper is concerned with modeling and control strategy interaction in a multimodel context. The role of the observability structure in multiple decisionmaker (DM) problems is examined. A procedure is developed for generating multimodel solutions based on certain deterministic information patterns. This is achieved by first explicitly identifying the state space structure induced by the observation sets of the DM'S, and then overlapping appropriately the input space structure of each DM. Such a representation is used to identify the class of admissible strategies which generate multimodel solutions. Conditions, which depend on the information pattern, are obtained under which these multimodel solutions admit partial noninteraction among the DM's.     

A multimodel approach to stochastic team problems

This paper develops decentralized team strategies for decision makers using different models of the same large-scale system. Multiparameter singular perturbations are employed to capture the multimodel nature of the fast dynamic subsystems interconnected through slow dynamic variables. The small parameters are appropriately scaled so that the variables in both time scales are well defined. The system considered is linear and the cost criterion is quadratic. First, a multimodel solution is obtained when the decision makers make different noisy linear observations of the random initial state only. Then the solution to this static team problem is utilized to obtain a multimodel solution to the dynamic team problem with sampled observations under the one-step-delay observation sharing pattern. In both cases, the well-posedness of the multimodel solution is demonstrated.     

Menu planning via computer simulation

This paper presents a simulation model for determining a detailed menu for daily meals that satisfies specified nutritional and variety requirements for a sequence of days.The model was built for a mental health center where patients are hospitalized for longer periods than in the usual hospitals; therefore, the variety issue is very important.     

A multimodel approach to stochastic nash games

A decentralized filtering and control scheme is presented for obtaining low-order Nash equilibrium strategies for decision makers using different models of the same large-scale system. Multiparameter singular perturbations are employed to capture the multimodel nature of the fast dynamic subsystems interconnected through slow dynamic variables. The small parameters are appropriately scaled so that the variables in both time scales are well defined. The decision makers have decentralized information structures and are constrained to use only finite dimensional compensators of a specified dimension. It is shown that the proposed scheme is in fact the asymptotic limit of the exact solution as the small parameters go to zero.     

Die-cavity pocketing via cutting simulation

For die-cavity pocketing, the cavity volume is sliced into a number of cutting-layers by horizontal cutting-planes, and each layer is pocket-machined using the contour-parallel offset method in which the tool-paths are obtained by repeatedly offsetting the boundary-pocketing curve. The major challenges in die-cavity pocketing include: 1) finding a method for obtaining the boundary-pocketing curve, 2) generating evenly spaced contour-parallel offset toolpaths, 3) detecting and removing uncut-regions, and 4) estimating chip-loads for an adaptive feed control. No systematic solution for these problems has been offered in the literature, except the curve offsetting methods for computing contour-parallel offset curves. Presented in the article is a straightforward approach to die-cavity pocketing, in which all the four challenges are handled successfully by using the existing cutting-simulation methods.     

A hybrid neural-genetic multimodel parameter estimation algorithm

We introduce a hybrid neural-genetic multimodel parameter estimation algorithm. The algorithm is applied to structured system identification of nonlinear dynamical systems. The main components of the algorithm are: 1) a recurrent incremental credit assignment neural network which computes a credit function for each member of a generation of models; and 2) a genetic algorithm which uses the credit functions as selection probabilities for producing new generations of models. The neural network and genetic algorithm combination is applied to the task of finding the parameter values which minimize the total square output error: the credit function reflects the closeness of each model's output to the true system output and the genetic algorithm searches the parameter space by a divide-and-conquer technique. The algorithm is evaluated by numerical simulations of parameter estimation for a planar robotic manipulator and a waste water treatment plant.     

Optimization of stochastic simulation models

An algorithm called SAMOPT is developed for optimizing the response function of simulation models that describe systems exhibiting stochastic behavior. Because of the stochastic nature of these simulated systems, the result of each evaluation of response by simulation is only a noisy (i.e., uncertain) observation of the true response. The SAMOPT algorithm uses these noisy responses to find a set of values for decision variables of the system such that the true response is optimized. Principles of the Stochastic Approximation Method have been used in developing this algorithm. The SAMOPT algorithm also allows for the case where the decision variables are subject to a set of linear constraints. Comparison of results between applications of SAMOPT and another well-known method are given for problems and a simulation model.     

Robust synthesis of a PID controller by uncertain multimodel approach

This paper presents an effective method to design a PID (or PI) controller for nonlinear systems where desirable robustness and performance properties must be maintained across a large range of operating conditions. For this purpose, an uncertain multimodel of the original nonlinear system is used. The uncertainties affecting the system are treated as stochastic matrices. Based on this multimodel representation a robust PID controller can be designed in order to obtain acceptable performance for all operating conditions. Numerical examples show the practical applicability of the proposed method.     

Min-max sliding-mode control for multimodel linear time varying systems

An original linear time-varying system with unmatched disturbances and uncertainties is replaced by a finite set of dynamic models such that each one describes a particular uncertain case including exact realizations of possible dynamic equations as well as external bounded disturbances. Such a tradeoff between an original uncertain linear time varying dynamic system and a corresponding higher order multimodel system with a complete knowledge leads to a linear multi-model system with known bounded disturbances. Each model from a given finite set is characterized by a quadratic performance index. The developed min-max sliding-mode control strategy gives an optimal robust sliding-surface design algorithm, which is reduced to a solution of an equivalent linear quadratic problem that corresponds to the weighted performance indices with weights from a finite dimensional simplex. An illustrative numerical example is presented.     

Mini-max integral sliding-mode control for multimodel linear uncertain systems

An original linear time-varying system with matched and unmatched disturbances and uncertainties is replaced by a finite set of dynamic models such that each one describes a particular uncertain case including exact realizations of possible dynamic equations as well as external unmatched bounded disturbances. Such a tradeoff between an original uncertain linear time varying dynamic system and a corresponding higher order multimodel system containing only matched uncertainties leads to a linear multi-model system with known unmatched bounded disturbances and unknown matched disturbances as well. Each model from a given finite set is characterized by a quadratic performance index. The developed minimax integral sliding mode control strategy gives an optimal minimax linear quadratic (LQ)-control with additional integral sliding mode term. The design of this controller is reduced to a solution of an equivalent mini-max LQ problem that corresponds to the weighted performance indices with weights from a finite dimensional simplex. The additional integral sliding mode controller part completely dismisses the influence of matched uncertainties from the initial time instant. Two numerical examples illustrate this study.     

Consistent Shape Matching via Coupled Optimization

We propose a new method for computing accurate point‐to‐point mappings between a pair of triangle meshes given imperfect initial correspondences. Unlike the majority of existing techniques, we optimize for a map while leveraging information from the inverse map, yielding results which are highly consistent with respect to composition of mappings. Remarkably, our method considers only a linear number of candidate points on the target shape, allowing us to work directly with high resolution meshes, and to avoid a delicate and possibly error‐prone up‐sampling procedure. Key to this dimensionality reduction is a novel candidate selection process, where the mapped points drift over the target shape, finalizing their location based on intrinsic distortion measures. Overall, we arrive at an iterative scheme where at each step we optimize for the map and its inverse by solving two relaxed Quadratic Assignment Problems using off‐the‐shelf optimization tools. We provide quantitative and qualitative comparison of our method with several existing techniques, and show that it provides a powerful matching tool when accurate and consistent correspondences are required.     

Parallel simulation of DEDS via event synchronization

In this paper we use the event synchronization scheme to develop a new method for parallel simulation of many discrete event dynamic systems simultaneously. Though a few parallel simulation methods have been developed during the last several years, such as the well-known Standard Clock method, most of them are largely limited to Markovian systems. The main advantage of our method is its applicability to non-Markovian systems. For Markovian systems a comparison study on efficiency between our method and the Standard Clock method is done on Connection Machine CM-5. CM-5 is a parallel machine with both SIMD (Single Instruction, Multiple Data) and MIMD (Multiple Instruction Multiple Data) architectures. The simulation results show that if event rates of Markovian systems do not differ by much then both methods are compatible but the Standard Clock method performs better in most cases. For Markovian systems with very different event rates, our method often yields better results. Most importantly, our simulation results also show that our method works as efficiently for non-Markovian systems as for Markovian systems.     

Developing cost-optimization production control model via simulation

This research is a further development of our recent papers 2, 3. A production system produces a given target amount by a given due date and has several possible speeds which are subject to random disturbances. The system's output can be measured only at present inspection (control) points. The average manufacturing costs per time unit for each production speed and the average cost of performing a single inspection at the control point to observe the actual output at that point, are given. The least permissible probability of meeting the target on time, i.e. the system's chance constraint, is pre-given too. The problem is to determine both, control points and speeds to be introduced at those points, in order to minimize the system's expenses within the planning horizon. A stochastic optimization problem is formulated, followed by a heuristic solution via simulation. A numerical example is given. Extensive experimentation has been undertaken to illustrate the efficiency of the presented algorithm. The algorithm has been used in practice on a real man–machine plant.     

Stabilization via Nonsmooth, Nonconvex Optimization

Nonsmooth variational analysis and related computational methods are powerful tools that can be effectively applied to identify local minimizers of nonconvex optimization problems arising in fixed-order controller design. We support this claim by applying nonsmooth analysis and methods to a challenging "Belgian chocolate" stabilization problem posed in 1994: find a stable, minimum phase, rational controller that stabilizes a specified second-order plant. Although easily stated, this particular problem remained unsolved until 2002, when a solution was found using an eleventh-order controller. Our computational methods find a stabilizing third-order controller without difficulty, suggesting explicit formulas for the controller and for the closed loop system, which has only one pole with multiplicity 5. Furthermore, our analytical techniques prove that this controller is locally optimal in the sense that there is no nearby controller with the same order for which the closed loop system has all its poles further left in the complex plane. Although the focus of the paper is stabilization, once a stabilizing controller is obtained, the same computational techniques can be used to optimize various measures of the closed loop system, including its complex stability radius or H_infin performance     

Material-aware cloth simulation via constrained geometric deformation

Most real-world cloth consists of nonlinear material and exhibits anisotropic behavior. This paper proposes an efficient and expressive mesh deformation method to obtain realistic cloth shapes with various cloth materials. The key idea in this work is to model the cloth using a mesh-based deformation energy that is composed of several energy terms and to fit the weighting coefficients of the terms from real data. We first develop a direct geometrical material measurement method for testing the recovery, stretching and bending behaviors of different real cloth samples. Then, we separate the geometric deformation energy into three terms related to the vertex position, edge length and bending of the dihedral angle, respectively, and the weights for the three energy terms are learned from the data measured with real cloth. Reusing the weights for the geometric deformation by a numerical solution in the least square sense can model similar cloth behavior. The experiments show that our method effectively provides rich cloth simulation results that are able to capture distinctive material effects.     

Hybrid cutting simulation via discrete vector model

Geometric cutting simulation and verification play an important role in detecting NC machining errors in mold and die manufacturing, thereby reducing the correcting time and cost on the shop floor. According to workpiece model, current researches may be categorized into view-based, solid-based, and discrete vector-based methods. Each methodology has its own strengths and weaknesses in terms of computing speed, representation accuracy, and its ability to perform numerical inspection. This paper proposes a cutting simulation methodology via a hybrid workpiece model which consists of the general discrete vector model and its simplified model. Workpiece modeling scheme, cutting simulation via tool swept surface modeling and vector intersection, and some case studies of mold and die machining are presented in this paper.     

The Rochester checkers player: multimodel parallel programming foranimate vision

It is maintained that to exploit fully the parallelism inherent in animate vision systems, an integrated vision architecture must support multiple models of parallelism. To support this claim, the hardware base of a typical animate vision laboratory and the software requirements of applications are described. A brief overview is then given of the Psyche operating system, which was designed to support multimodel programming. A complex animate vision application, checkers, constructed as a multimodel program under Psyche, is also described. Checkers demonstrates the advantages of decomposing animate vision systems by function and independently selecting an appropriate parallel-programming model for each function