Solving multi‐objective dynamic optimization problems with fuzzy satisfying method

This article proposes a novel algorithm integrating iterative dynamic programming and fuzzy aggregation to solve multi‐objective optimal control problems. First, the optimal control policies involving these objectives are sequentially determined. A payoff table is then established by applying each optimal policy in series to evaluate these multiple objectives. Considering the imprecise nature of decision‐maker's judgment, these multiple objectives are viewed as fuzzy variables. Simple monotonic increasing or decreasing membership functions are then defined for degrees of satisfaction for these linguistic objective functions. The optimal control policy is finally searched by maximizing the aggregated fuzzy decision values. The proposed method is rather easy to implement. Two chemical processes, Nylon 6 batch polymerization and Penicillin G fed‐batch fermentation, are used to demonstrate that the method has a significant potential to solve real industrial problems. Copyright © 2003 John Wiley & Sons, Ltd.     

A second‐order optimization algorithm using quadric control updates for multistage optimal control problems

This paper describes a trajectory optimization algorithm that generates a quadric control update, which satisfies the constraints and necessary conditions to the second order. The algorithm is designed to solve multistage optimization problems. The algorithm is tested against a commercially available Sequential Quadratic Programming algorithm on problems with linear dynamics and linear and nonlinear constraints. This algorithm is a departure from previous methods because it explicitly satisfies the constraints to the second order. Copyright © 2009 John Wiley & Sons, Ltd.     

A trajectory‐based sampling strategy for sequentially refined metamodel management of metamodel‐based dynamic optimization in mechatronics

Dynamic optimization problems based on computationally expensive models that embody the dynamics of a mechatronic system can result in prohibitively long optimization runs. When facing optimization problems with static models, reduction in the computational time and thus attaining convergence can be established by means of a metamodel placed within a metamodel management scheme. This paper proposes a metamodel management scheme with a dedicated sampling strategy when using computationally demanding dynamic models in a dynamic optimization problem context. The dedicated sampling strategy enables to attain dynamically feasible solutions where the metamodel is locally refined during the optimization process upon satisfying a feasibility‐based stopping condition. The samples are distributed along the iterate trajectories of the sequential direct dynamic optimization procedure. Algorithmic implementation of the trajectory‐based metamodel management is detailed and applied on two case studies involving dynamic optimization problems. These numerical experiments illustrate the benefits of the presented scheme and its sampling strategy on the convergence properties. It is shown that the acceleration of the solution time of the dynamic optimization problem can be achieved when evaluating the metamodel that is lower than 90% compared to the computationally expensive model.     

A reinforcement learning‐based scheme for direct adaptive optimal control of linear stochastic systems

Reinforcement learning where decision‐making agents learn optimal policies through environmental interactions is an attractive paradigm for model‐free, adaptive controller design. However, results for systems with continuous state and action variables are rare. In this paper, we present convergence results for optimal linear quadratic control of discrete‐time linear stochastic systems. This work can be viewed as a generalization of a previous work on deterministic linear systems. Key differences between the algorithms for deterministic and stochastic systems are highlighted through examples. The usefulness of the algorithm is demonstrated through a nonlinear chemostat bioreactor case study. Copyright © 2009 John Wiley & Sons, Ltd.     

A multiphase DMOC‐based trajectory optimization method

Discrete mechanics and optimal control (DMOC) is a methodology that takes advantage of variational structure to solve certain optimal control problems for mechanical systems. This paper proposes to combine a multiphase strategy with the original DMOC method, resulting in a new multiphase DMOC (MDMOC) method and making optimal trajectory generation more efficient. The advantages of the proposed method are demonstrated mathematically, and in addition, a quadrotor, unmanned aerial vehicle, simulation example is presented to show its superiority over the DMOC method. Furthermore, to show its potential application, an arbitrarily chosen controller was used to track the desired trajectory generated by MDMOC. This new MDMOC methodology can also be applied to other mechanical systems such as mobile robots and underwater gliders.     

Low‐order multi‐rate linear time‐invariant decentralized trackers using the new observer‐based sub‐optimal method for unknown sampled‐data nonlinear time‐delay system with closed‐loop decoupling

This paper presents the low‐order multi‐rate linear time‐invariant decentralized trackers using the new observer‐based sub‐optimal method for a class of unknown sampled‐data nonlinear time‐delay system with closed‐loop decoupling. For the unknown sampled‐data nonlinear time‐delay system, we assume that the inner time delay is clearly known. Under this prerequisite, the appropriate (low‐) order decentralized linear observer for the unknown sampled‐data nonlinear system is determined by the off‐line observer/Kalman filter identification (OKID) method with artificial delay input and actual delay output. Then, the above observer has been further improved based on the proposed new observer‐based sub‐optimal approach. Sequentially, the decentralized tracker with the high gain property is proposed, so that the closed‐loop system has the decoupling property. The proposed approach constructs complete mathematics method including the concept of optimal control theory and state‐matching digital redesign technique and is quite useful for the complicated interconnected large‐scale sampled‐data nonlinear time‐delay system with unknown system equation. Copyright © 2010 John Wiley & Sons, Ltd.     

Solving mixed‐integer optimal control problems by branch&bound: a case study from automobile test‐driving with gear shift

The article discusses the application of the branch&bound method to a mixed integer non‐linear optimization problem (MINLP) arising from a discretization of an optimal control problem with partly discrete control set. The optimal control problem has its origin in automobile test‐driving, where the car model involves a discrete‐valued control function for the gear shift. Since the number of variables in (MINLP) grows with the number of grid points used for discretization of the optimal control problem, the example from automobile test‐driving may serve as a benchmark problem of scalable complexity. Reference solutions are computed numerically for two different problem sizes. A simple heuristic approach suitable for optimal control problems is suggested that reduces the computational amount considerably, though it cannot guarantee optimality anymore. Copyright © 2005 John Wiley & Sons, Ltd.     

Linear multi‐model time‐optimization

A linear optimization problem with unknown parameters from a given finite set is tackled. The problem is to find the robust time‐optimal control transferring a given initial point to a convex terminal compact set M for all unknown parameters in a shortest time. The robust maximum principle for this minimax problem is formulated. It gives a necessary and sufficient condition of robust optimality. Under natural conditions, the existence and uniqueness of robust optimal controls are proven when the resource set is a convex polytope. Several illustrating examples, including a bang–bang robust optimal control, are considered in detail. Copyright © 2002 John Wiley & Sons, Ltd.     

Modified whale optimization algorithm for fractional‐order multi‐input SSSC‐based controller design

In this paper, the design of a fractional‐order (FO) multi‐input–single‐output (MISO)–type static synchronous series compensator (SSSC) is proposed with a goal to improve the power system stability using modified whale optimization algorithm (MWOA). The proposed MWOA achieves an appropriate balance between exploitation and exploration stages of the original whale optimization algorithm. The performance of MWOA is validated by employing the benchmark test functions and further contrasted with whale optimization algorithm and other heuristic algorithms like gravitational search algorithm, particle swarm optimization, differential evolution, and fast evolutionary programming algorithms to demonstrate its strength. The proposed FO MISO SSSC controller is optimized by the MWOA technique and tested under single‐machine infinite bus system and further extended to a multi‐machine framework. To demonstrate the superiority of MISO‐type SSSC controller, the results obtained from it are compared with particle swarm optimization and differential evolution–based conventional single‐input–single‐output structured SSSC controllers. The comparison of results of MWOA with that of other methods validates its superiority in the present context.     

Robust reliability method and reliability‐based performance optimization for non‐fragile robust control design of dynamic system with bounded parametric uncertainties

An efficient robust reliability method for non‐fragile robust control design of dynamic system with bounded parametric uncertainties is presented systematically, in which the uncertainties existing in the controlled plant and controller realization are taken into account simultaneously in an integrated framework. Reliability‐based design optimization of non‐fragile robust control for parametric uncertain systems is carried out by optimizing the H₂ and H_∞ performances of the closed‐loop system, with the constraints on robust reliabilities. The non‐fragile robust controller obtained by the presented method may possess a coordinated optimum performance satisfying the precondition that the system is robustly reliable with respect to the uncertainties existing in controlled plant and controller. Moreover, the robustness bounds of uncertain parameters can be provided. The presented formulations are within the framework of linear matrix inequality and thus can be carried out conveniently. It is demonstrated by a numerical example that the presented method is effective and feasible. Copyright © 2016 John Wiley & Sons, Ltd.     

Relaxation methods for hyperbolic PDE mixed‐integer optimal control problems

The convergence analysis for methods solving partial differential equations constrained optimal control problems containing both discrete and continuous control decisions based on relaxation and rounding strategies is extended to the class of first order semilinear hyperbolic systems in one space dimension. The results are obtained by novel a priori estimates for the size of the relaxation gap based on the characteristic flow, fixed‐point arguments, and particular regularity theory for such mixed‐integer control problems. Motivated by traffic flow problems, a relaxation model for optimal flux switching control in conservation laws is considered as an application.     

A new optimal linear quadratic observer‐based tracker under input constraint for the unknown system with a direct feed‐through term

This paper develops a new optimal linear quadratic observer‐based tracker with input constraint for the linear unknown system with a direct transmission term from input to measured output. The off‐line observer/Kalman filter identification method is used to determine the linear sampled‐data model with a direct feed‐through term. On the basis of this model, a high‐gain optimal linear quadratic analog observer‐based tracker is proposed, so that it can effectively induce a high quality performance on the state estimation and the trajectory tracking design. Besides, the prediction‐based digital redesign method is utilized to obtain a relatively low‐gain and implementable observer and digital tracker from the theoretically well‐designed high‐gain analog observer and tracker for the linear system with a direct transmission term from input to output. To reduce the magnitude of control input, which is caused by the high‐gain property to fit the requirement of the input constraint, the modified linear quadratic analog tracker is proposed. Thus, the control input can be compressed effectively without losing the original high performance of tracking much. Copyright © 2014 John Wiley & Sons, Ltd.     

Optimal control of sugarscape agent‐based model via a PDE approximation model

There is no standard framework for solving optimization problems for systems described by agent‐based models (ABMs). We present a method for constructing individual‐level controls that steer the population‐level dynamics of an ABM towards a desired state. Our method uses a system of partial differential equations (PDEs) with control functions to approximate the dynamics of the ABM with control. An optimal control problem is formulated in terms of the PDE model to mimic the optimization goal of the ABM. Mathematical theory is used to derive optimal controls for the PDE model, which are numerically approximated and transformed for use in the ABM. We use the Sugarscape ABM, a prototype ABM that includes agent and environmental heterogeneity and accumulation of agent resources over time. We present a PDE model that approximates well the spatial, temporal, and resource dynamics of the Sugarscape ABM. In both models, control represents taxation of agent wealth with the goal to maximize total taxes collected while minimizing the impact of taxation on the population over a finite time. Solutions to the optimal control problem yield taxation rates specific to an agent's location and current wealth. The use of optimal controls (generated by the PDE model) within the ABM performed better than other controls we evaluated, even though some error was introduced between the ABM and PDE models. Our results demonstrate the feasibility of using a PDE to approximate an ABM for control purposes and illustrate challenges that can arise in applying this technique to sophisticated ABMs. Copyright © 2016 John Wiley & Sons, Ltd.     

Study of wind-solar based combined heat and power economic dispatch problem using quasi-oppositional-based whale optimization technique

Source of fossil fuel is impoverishing in the upcoming future. Renewable energy sources (RESs) are becoming challenging conventional energy substitutes in the present scenario. In this article, an attempt has been made to utilize RESs such as wind and solar energy with combined heat and power economic dispatch problems. The intention of this presentation is to minimize conflict objectives such as fuel cost accomplished with load demand along with transmission losses while satisfying all the constraints. A new optimization technique, namely a quasi-oppositionalbased whale optimization algorithm (QOWOA) is adopted to cope up with the non-linearities of the chosen systems. The proposed technique is tested on two different nonlinear realistic power systems to achieve the satisfactory performances. The superiority of the proposed QOWOA algorithm is judged by comparing it with some recently developed metaheuristic optimization techniques.     

Intensity‐based 2D‐3D registration for an ACL reconstruction navigation system

To improve the positioning accuracy of tunnels for anterior cruciate ligament (ACL) reconstruction, we proposed an intensity‐based 2D‐3D registration method for an ACL reconstruction navigation system. Methods for digitally reconstructed radiograph (DRR) generation, similarity measurement, and optimization are crucial to 2D‐3D registration. We evaluated the accuracy, success rate, and processing time of different methods: (a) ray‐casting and splating were compared for DRR generation; (b) normalized mutual information (NMI), Mattes mutual information (MMI), and Spearman's rank correlation coefficient (SRC) were assessed for similarity between registrations; and (c) gradient descent (GD) and downhill simplex (DS) were compared for optimization. The combination of splating, SRC, and GD provided the best composite performance and was applied in an augmented reality (AR) ACL reconstruction navigation system. The accuracy of the navigation system could fulfill the clinical needs of ACL reconstruction, with an end pose error of 2.50 mm and an angle error of 2.74°.     

Coordinated optimal target realization for linear systems allowing choice‐based actions

This paper studies target‐reaching problems for systems controlled by multiple agents in which every agent implements control based on the choice selected independently from a private choice set. The agents' choices jointly determine the system target to be reached, and all the possible choice combinations define a set of targets to be reached. Without exchanging choice information among the agents, the existence of a set of control laws to realize all the targets in a given target set is a nontrivial question. For linear systems, the necessary and sufficient condition is shown hinged on a compatibility condition on the target set. Under the compatible condition, coordinated optimal control laws are derived such that any target in the target set can be achieved. Copyright © 2015 John Wiley & Sons, Ltd.     

A bread‐based lyophilized C‐strain CSF virus vaccine as an oral vaccine in pigs

A live attenuated cereal‐based classical swine fever (CSF) vaccine for oral application, a form of vaccine that farmers can use themselves, demonstrated the improvement of CSF control in backyard production systems in endemic areas. Due to the dependency on very low storage temperature (−20°C) of the cereal‐based oral CSF vaccine, a lyophilized cereal‐based oral vaccine has been developed and tested. Although some studies showed total protection against a virulent virus strain, the production procedure is still considered complex. In this study, the lyophilized oral CSF virus, which is easy to produce and could be kept in the form of a bread‐based vaccine at 4°C for an extended time, was tested for the ability to induce a humoral immune response in pigs. Among the materials tested as a base for the CSF virus vaccine, plain sliced bread was considered the most appropriate base because of its absorbing ability and virus titre maintenance. Titres of bread‐based lyophilized CSF virus vaccine were stable at around 3.67 log₁₀ TCID₅₀ per ml for 7 months at 4°C. Pigs aged 5 and 8 weeks that orally received five bread‐based lyophilized CSF virus vaccine showed seroconversion of over 90% at 14 dpv. At 28 dpv, both age groups showed 100% seroconversion. In conclusion, the bread‐based lyophilized CSF virus vaccine can be an alternative choice for oral vaccination of pigs. Due to the simple process of production and the need for less virus titre, vaccine prices could be lowered. However, vaccine thermostability has to be improved to allow the vaccine delivery to be less dependent on functioning cool chains.     

Rejection of persistent‐bounded disturbances in continuous time‐delay systems using observer‐based feedback

In this paper, the problem of persistent‐bounded disturbance rejection of linear continuous‐time systems with time‐varying delays is investigated using the tools of invariant set analysis and Lyapunov‐function methodology. We derive less conservative sufficient conditions on robust attractor for time‐delay systems in terms of strict linear matrix inequalities (LMIs) to guarantee the desired ??₁‐performance. A robust output‐feedback controller is designed and the associated gain is determined using strict LMIs. The developed results are tested on two representative time‐delay examples. Copyright © 2009 John Wiley & Sons, Ltd.     

Self‐tuning control of electrical machines using gradient descent optimization

This paper presents a new approach toward the design of a self‐tuning proportional‐integral (PI) control for induction motors. By using the method of gradient descent optimization to the parameter space, the controller gains developed in this study are adjusted automatically online. Therefore, the proposed PI control is robust to the changes of induction motor parameters and achieves the performance of global asymptotic speed tracking. Theoretical analysis and simulation results are presented to show the effectiveness of the approach. Copyright © 2006 John Wiley & Sons, Ltd.     

Incorporation of CT‐based measurements of trunk anatomy into subject‐specific musculoskeletal models of the spine influences vertebral loading predictions

We created subject‐specific musculoskeletal models of the thoracolumbar spine by incorporating spine curvature and muscle morphology measurements from computed tomography (CT) scans to determine the degree to which vertebral compressive and shear loading estimates are sensitive to variations in trunk anatomy. We measured spine curvature and trunk muscle morphology using spine CT scans of 125 men, and then created four different thoracolumbar spine models for each person: (i) height and weight adjusted (Ht/Wt models); (ii) height, weight, and spine curvature adjusted (+C models); (iii) height, weight, and muscle morphology adjusted (+M models); and (iv) height, weight, spine curvature, and muscle morphology adjusted (+CM models). We determined vertebral compressive and shear loading at three regions of the spine (T8, T12, and L3) for four different activities. Vertebral compressive loads predicted by the subject‐specific CT‐based musculoskeletal models were between 54% lower to 45% higher from those estimated using musculoskeletal models adjusted only for subject height and weight. The impact of subject‐specific information on vertebral loading estimates varied with the activity and spinal region. Vertebral loading estimates were more sensitive to incorporation of subject‐specific spinal curvature than subject‐specific muscle morphology. Our results indicate that individual variations in spine curvature and trunk muscle morphology can have a major impact on estimated vertebral compressive and shear loads, and thus should be accounted for when estimating subject‐specific vertebral loading. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:2164–2173, 2017.