Simulated annealing with adaptive neighborhood: A case study in off-line robot path planning

Simulated annealing (SA) is an optimization technique that can process cost functions with degrees of nonlinearities, discontinuities and stochasticity. It can process arbitrary boundary conditions and constraints imposed on these cost functions. The SA technique is applied to the problem of robot path planning. Three situations are considered here: the path is represented as a polyline; as a Bezier curve; and as a spline interpolated curve. In the proposed SA algorithm, the sensitivity of each continuous parameter is evaluated at each iteration increasing the number of accepted solutions. The sensitivity of each parameter is associated to its probability distribution in the definition of the next candidate. (C) 2010 Elsevier Ltd. All rights reserved.

Robust integration of real time optimization with linear model predictive control

Here, we study the stable integration of real time optimization (RTO) with model predictive control (MPC) in a three layer structure. The intermediate layer is a quadratic programming whose objective is to compute reachable targets to the MPC layer that lie at the minimum distance to the optimum set points that are produced by the RTO layer. The lower layer is an infinite horizon MPC with guaranteed stability with additional constraints that force the feasibility and convergence of the target calculation layer. It is also considered the case in which there is polytopic uncertainty in the steady state model considered in the target calculation. The dynamic part of the MPC model is also considered unknown but it is assumed to be represented by one of the models of a discrete set of models. The efficiency of the methods presented here is illustrated with the simulation of a low order system. (C) 2010 Elsevier Ltd. All rights reserved.

Real time optimization (RTO) with model predictive control (MPC)

This paper studies a simplified methodology to integrate the real time optimization (RTO) of a continuous system into the model predictive controller in the one layer strategy. The gradient of the economic objective function is included in the cost function of the controller. Optimal conditions of the process at steady state are searched through the use of a rigorous non-linear process model, while the trajectory to be followed is predicted with the use of a linear dynamic model, obtained through a plant step test. The main advantage of the proposed strategy is that the resulting control/optimization problem can still be solved with a quadratic programming routine at each sampling step. Simulation results show that the approach proposed may be comparable to the strategy that solves the full economic optimization problem inside the MPC controller where the resulting control problem becomes a non-linear programming problem with a much higher computer load. (C) 2010 Elsevier Ltd. All rights reserved.

Optimizing model predictive control of an industrial distillation column

The main scope of this work is the implementation of an MPC that integrates the control and the economic optimization of the system. The two problems are solved simultaneously through the modification of the control cost function that includes an additional term related to the economic objective. The optimizing MPC is based on a quadratic program (QP) as the conventional MPC and can be solved with the available QP solvers. The method was implemented in an industrial distillation system, and the results show that the approach is efficient and can be used, in several practical cases. (C) 2011 Elsevier Ltd. All rights reserved.

Stable Model Predictive Control for Integrating Systems with Optimizing Targets

This paper concern the development of a stable model predictive controller (MPC) to be integrated with real time optimization (RTO) in the control structure of a process system with stable and integrating outputs. The real time process optimizer produces Optimal targets for the system inputs and for Outputs that Should be dynamically implemented by the MPC controller. This paper is based oil a previous work (Comput. Chem. Eng. 2005, 29, 1089) where a nominally stable MPC was proposed for systems with the conventional control approach where only the outputs have set points. This work is also based oil the work of Gonzalez et at. (J. Process Control 2009, 19, 110) where the zone control of stable systems is studied. The new control for is obtained by defining ail extended control objective that includes input targets and zone controller the outputs. Additional decision variables are also defined to increase the set of feasible solutions to the control problem. The hard constraints resulting from the cancellation of the integrating modes Lit the end of the control horizon are softened,, and the resulting control problem is made feasible to a large class of unknown disturbances and changes of the optimizing targets. The methods are illustrated with the simulated application of the proposed,approaches to a distillation column of the oil refining industry.

Robust model predictive control with zone control

Model predictive control (MPC) is usually implemented as a control strategy where the system outputs are controlled within specified zones, instead of fixed set points. One strategy to implement the zone control is by means of the selection of different weights for the output error in the control cost function. A disadvantage of this approach is that closed-loop stability cannot be guaranteed, as a different linear controller may be activated at each time step. A way to implement a stable zone control is by means of the use of an infinite horizon cost in which the set point is an additional variable of the control problem. In this case, the set point is restricted to remain inside the output zone and an appropriate output slack variable is included in the optimisation problem to assure the recursive feasibility of the control optimisation problem. Following this approach, a robust MPC is developed for the case of multi-model uncertainty of open-loop stable systems. The controller is devoted to maintain the outputs within their corresponding feasible zone, while reaching the desired optimal input target. Simulation of a process of the oil re. ning industry illustrates the performance of the proposed strategy.

A stable MPC with zone control

Several MPC applications implement a control strategy in which some of the system outputs are controlled within specified ranges or zones, rather than at fixed set points [J.M. Maciejowski, Predictive Control with Constraints, Prentice Hall, New Jersey, 2002]. This means that these outputs will be treated as controlled variables only when the predicted future values lie outside the boundary of their corresponding zones. The zone control is usually implemented by selecting an appropriate weighting matrix for the output error in the control cost function. When an output prediction is inside its zone, the corresponding weight is zeroed, so that the controller ignores this output. When the output prediction lies outside the zone, the error weight is made equal to a specified value and the distance between the output prediction and the boundary of the zone is minimized. The main problem of this approach, as long as stability of the closed loop is concerned, is that each time an output is switched from the status of non-controlled to the status of controlled, or vice versa, a different linear controller is activated. Thus, throughout the continuous operation of the process, the control system keeps switching from one controller to another. Even if a stabilizing control law is developed for each of the control configurations, switching among stable controllers not necessarily produces a stable closed loop system. Here, a stable M PC is developed for the zone control of open-loop stable systems. Focusing on the practical application of the proposed controller, it is assumed that in the control structure of the process system there is an upper optimization layer that defines optimal targets to the system inputs. The performance of the proposed strategy is illustrated by simulation of a subsystem of an industrial FCC system. (C) 2008 Elsevier Ltd. All rights reserved.

Control charts for individual observations of a bivariate Poisson process

In this paper, three single-control charts are proposed to monitor individual observations of a bivariate Poisson process. The specified false-alarm risk, their control limits, and ARLs were determined to compare their performances for different types and sizes of shifts. In most of the cases, the single charts presented better performance rather than two separate control charts ( one for each quality characteristic). A numerical example illustrates the proposed control charts.

Diagnostic errors and repetitive sequential classifications in on-line process control by attributes

The procedure of on-line process control by attributes, known as Taguchi`s on-line process control, consists of inspecting the mth item (a single item) at every m produced items and deciding, at each inspection, whether the fraction of conforming items was reduced or not. If the inspected item is nonconforming, the production is stopped for adjustment. As the inspection system can be subject to diagnosis errors, one develops a probabilistic model that classifies repeatedly the examined item until a conforming or b non-conforming classification is observed. The first event that occurs (a conforming classifications or b non-conforming classifications) determines the final classification of the examined item. Proprieties of an ergodic Markov chain were used to get the expression of average cost of the system of control, which can be optimized by three parameters: the sampling interval of the inspections (m); the number of repeated conforming classifications (a); and the number of repeated non-conforming classifications (b). The optimum design is compared with two alternative approaches: the first one consists of a simple preventive policy. The production system is adjusted at every n produced items (no inspection is performed). The second classifies the examined item repeatedly r (fixed) times and considers it conforming if most classification results are conforming. Results indicate that the current proposal performs better than the procedure that fixes the number of repeated classifications and classifies the examined item as conforming if most classifications were conforming. On the other hand, the preventive policy can be averagely the most economical alternative rather than those ones that require inspection depending on the degree of errors and costs. A numerical example illustrates the proposed procedure. (C) 2009 Elsevier B. V. All rights reserved.

Effects of the preventive and corrective adjustments in economical designs for online process control for attributes with misclassification errors

The procedure for online process control by attributes consists of inspecting a single item at every m produced items. It is decided on the basis of the inspection result whether the process is in-control (the conforming fraction is stable) or out-of-control (the conforming fraction is decreased, for example). Most articles about online process control have cited the stoppage of the production process for an adjustment when the inspected item is non-conforming (then the production is restarted in-control, here denominated as corrective adjustment). Moreover, the articles related to this subject do not present semi-economical designs (which may yield high quantities of non-conforming items), as they do not include a policy of preventive adjustments (in such case no item is inspected), which can be more economical, mainly if the inspected item can be misclassified. In this article, the possibility of preventive or corrective adjustments in the process is decided at every m produced item. If a preventive adjustment is decided upon, then no item is inspected. On the contrary, the m-th item is inspected; if it conforms, the production goes on, otherwise, an adjustment takes place and the process restarts in-control. This approach is economically feasible for some practical situations and the parameters of the proposed procedure are determined minimizing an average cost function subject to some statistical restrictions (for example, to assure a minimal levelfixed in advanceof conforming items in the production process). Numerical examples illustrate the proposal.

Adaptive Carrier Tracking for Mars to Earth Communications During Entry, Descent, and Landing

We propose a robust and low complexity scheme to estimate and track carrier frequency from signals traveling under low signal-to-noise ratio (SNR) conditions in highly nonstationary channels. These scenarios arise in planetary exploration missions subject to high dynamics, such as the Mars exploration rover missions. The method comprises a bank of adaptive linear predictors (ALP) supervised by a convex combiner that dynamically aggregates the individual predictors. The adaptive combination is able to outperform the best individual estimator in the set, which leads to a universal scheme for frequency estimation and tracking. A simple technique for bias compensation considerably improves the ALP performance. It is also shown that retrieval of frequency content by a fast Fourier transform (FFT)-search method, instead of only inspecting the angle of a particular root of the error predictor filter, enhances performance, particularly at very low SNR levels. Simple techniques that enforce frequency continuity improve further the overall performance. In summary we illustrate by extensive simulations that adaptive linear prediction methods render a robust and competitive frequency tracking technique.

Transient and Steady-State Analysis of the Affine Combination of Two Adaptive Filters

In this paper, we propose an approach to the transient and steady-state analysis of the affine combination of one fast and one slow adaptive filters. The theoretical models are based on expressions for the excess mean-square error (EMSE) and cross-EMSE of the component filters, which allows their application to different combinations of algorithms, such as least mean-squares (LMS), normalized LMS (NLMS), and constant modulus algorithm (CMA), considering white or colored inputs and stationary or nonstationary environments. Since the desired universal behavior of the combination depends on the correct estimation of the mixing parameter at every instant, its adaptation is also taken into account in the transient analysis. Furthermore, we propose normalized algorithms for the adaptation of the mixing parameter that exhibit good performance. Good agreement between analysis and simulation results is always observed.

Distributed Estimation Over an Adaptive Incremental Network Based on the Affine Projection Algorithm

We study the problem of distributed estimation based on the affine projection algorithm (APA), which is developed from Newton`s method for minimizing a cost function. The proposed solution is formulated to ameliorate the limited convergence properties of least-mean-square (LMS) type distributed adaptive filters with colored inputs. The analysis of transient and steady-state performances at each individual node within the network is developed by using a weighted spatial-temporal energy conservation relation and confirmed by computer simulations. The simulation results also verify that the proposed algorithm provides not only a faster convergence rate but also an improved steady-state performance as compared to an LMS-based scheme. In addition, the new approach attains an acceptable misadjustment performance with lower computational and memory cost, provided the number of regressor vectors and filter length parameters are appropriately chosen, as compared to a distributed recursive-least-squares (RLS) based method.

Improving the tracking capability of adaptive filters via convex combination

As is well known, Hessian-based adaptive filters (such as the recursive-least squares algorithm (RLS) for supervised adaptive filtering, or the Shalvi-Weinstein algorithm (SWA) for blind equalization) converge much faster than gradient-based algorithms [such as the least-mean-squares algorithm (LMS) or the constant-modulus algorithm (CMA)]. However, when the problem is tracking a time-variant filter, the issue is not so clear-cut: there are environments for which each family presents better performance. Given this, we propose the use of a convex combination of algorithms of different families to obtain an algorithm with superior tracking capability. We show the potential of this combination and provide a unified theoretical model for the steady-state excess mean-square error for convex combinations of gradient- and Hessian-based algorithms, assuming a random-walk model for the parameter variations. The proposed model is valid for algorithms of the same or different families, and for supervised (LMS and RLS) or blind (CMA and SWA) algorithms.

The Policy Iteration Algorithm for Average Continuous Control of Piecewise Deterministic Markov Processes

The main goal of this paper is to apply the so-called policy iteration algorithm (PIA) for the long run average continuous control problem of piecewise deterministic Markov processes (PDMP`s) taking values in a general Borel space and with compact action space depending on the state variable. In order to do that we first derive some important properties for a pseudo-Poisson equation associated to the problem. In the sequence it is shown that the convergence of the PIA to a solution satisfying the optimality equation holds under some classical hypotheses and that this optimal solution yields to an optimal control strategy for the average control problem for the continuous-time PDMP in a feedback form.