Optimal Control Methodology Research Articles

Design of an intelligent optimal neural network-based tracking controller for nonholonomic mobile robot systems

This paper addresses the trajectory-tracking control problem of mobile robot systems with nonholonomic constraints, in the presence of time-varying parametric uncertainties and external disturbances. This necessitates an accurate controller to meet as much control objectives, as possible. Therefore, this paper deals with an artificial intelligence control technique to design a robust controller to meet the control objectives. The design of the intelligent controller is based on the optimal control theory, the adaptive neural network system, and the robust control technique. The trajectory-tracking problem is solved using the optimal control methodology. Since the nonholonomic wheeled mobile robot is strongly nonlinear, the neural network system is applied to approximate the nonlinear function in the optimal control law. The robust controller, for his part, is then applied to adaptively estimate an unknown upper bound of the time-varying parametric uncertainties, external disturbances and approximation error of the neural network system. The stability of the closed-loop robot system is proven using the optimal control theory and Lyapunov stability analysis. The results of the simulation studies on three typical nonholonomic mobile robots are provided to demonstrate the effectiveness of the proposed controller. In addition, a comparative study with a recent robust adaptive controller shows that our proposed intelligent controller gives better results, in the sense that the output trajectory converges to the steady state faster with smaller tracking error.

Open-loop optimal control of batch chromatographic separation processes using direct collocation

This contribution presents a novel model-based methodology for open-loop optimal control of batch high-pressure liquid chromatographic (HPLC) separation processes. The framework allows for simultaneous optimization of target component recovery yield and production rate with respect to a parameterization of the input elution trajectory and fractionating interval endpoints. The proposed methodology implies formulating and solving a large-scale dynamic optimization problem (DOP) constrained by partial differential equations (PDEs) governing the multi-component system dynamics. It is based on a simultaneous method where both the control and state variables are fully discretized in the temporal domain, using direct local collocation on finite elements, and the state variables are discretized in the spatial domain, using an adaptive finite volume weighted essentially non-oscillatory (WENO) scheme. The direct transcription of the DOP described by Modelica, and its extension Optimica, code into a sparse nonlinear programming problem (NLP) is thoroughly presented. The NLP was subsequently solved using CasADi's (Computer algebra system with Automatic Differentiation) interface to the primal-dual interior point method IPOPT. The advantages of the open-loop optimal control strategy are highlighted through the solution of a challenging ternary complex mixture separation problem of human insulin analogs, with the intermediately eluting component as the target, for a hydrophobic interaction chromatography system. Moreover, the high intercorrelation between the shape of the optimal elution trajectories and the fractionation interval endpoints is thoroughly investigated. It is also demonstrated that the direct transcription methodology enabled accurate and efficient computation of optimal cyclic-steady-state solutions, which govern that state and control variables conform to periodicity constraints imposed on column re-generation and re-equilibration. By these means, the generic methods and tools developed here are applicable to continuous chromatographic separation technologies, including the continuous simulated moving bed (SMB) and the multicolumn counter-current solvent gradient purification (MCSGP) process.

Optimizing production while reducing machinery lockout/tagout circumvention possibilities

Purpose – The optimization of production imposes a review of facility maintenance policies. Accidents during maintenance activities are frequent, sometimes fatal and often associated with deficient or absent machinery lockout/tagout. Lockout/tagout is often circumvented in order to avoid what may be viewed as unnecessary delays and increased production costs. To reduce the dangers inherent in such practice, the purpose of this paper is to propose a production strategy that provides for machinery lockout/tagout while maximizing manufacturing system availability and minimizing costs. Design/methodology/approach – The joint optimization problem of production planning, maintenance and safety planning is formulated and studied using a stochastic optimal control methodology. Hamilton-Jacobi-Bellman equations are developed and studied numerically using the Kushner approach based on finite difference approximation and an iterative policy improvement technique. Findings – The analysis leads to a solution that suggests increasing the “comfortable” inventory level in order to provide the time required for lockout/tagout activities. It is also demonstrated that the optimization of lockout/tagout procedures is particularly important when the equipment is relatively new and the inventory level is minimal. Research limitations/implications – This paper demonstrates that it is possible to integrate production, maintenance and lockout/tagout procedures into production planning while keeping manufacturing system cost objectives attainable as well as ensuring worker safety. Originality/value – This integrated production and maintenance policy is unique and complements existing procedures by explicitly accounting for safety measures.

On the nature of motor planning variables during arm pointing movement: Compositeness and speed dependence

The purpose of this study was to investigate the nature of the variables and rules underlying the planning of unrestrained 3D arm reaching. To identify whether the brain uses kinematic, dynamic and energetic values in an isolated manner or combines them in a flexible way, we examined the effects of speed variations upon the chosen arm trajectories during free arm movements. Within the optimal control framework, we uncovered which (possibly composite) optimality criterion underlays at best the empirical data. Fifteen participants were asked to perform free-endpoint reaching movements from a specific arm configuration at slow, normal and fast speeds. Experimental results revealed that prominent features of observed motor behaviors were significantly speed-dependent, such as the chosen reach endpoint and the final arm posture. Nevertheless, participants exhibited different arm trajectories and various degrees of speed dependence of their reaching behavior. These inter-individual differences were addressed using a numerical inverse optimal control methodology. Simulation results revealed that a weighted combination of kinematic, energetic and dynamic cost functions was required to account for all the critical features of the participants’ behavior. Furthermore, no evidence for the existence of a speed-dependent tuning of these weights was found, thereby suggesting subject-specific but speed-invariant weightings of kinematic, energetic and dynamic variables during the motor planning process of free arm movements. This suggested that the inter-individual difference of arm trajectories and speed dependence was not only due to anthropometric singularities but also to critical differences in the composition of the subjective cost function.

Optimal control of a class of pseudo Euler‐Lagrange systems

SummaryThis paper presents a solution of the optimal control problem for a class of pseudo Euler‐Lagrange systems and proposes a systematic approach to find a Lyapunov function for stability analysis and controller synthesis for such systems. There are three main contributions of the paper. First, a systematic procedure is proposed and proved to construct a Lyapunov function for pseudo Euler‐Lagrange system directly from the mathematical structure of the differential equations, without the need to determine any kinetic or potential energy of the system first. Second, control methodologies for pseudo Euler‐Lagrange systems are also developed. In particular, an optimal controller is found for the case of second order dynamics yielding the same structure for the closed‐loop Lyapunov function as the one derived from the systematic procedure outlined as the first contribution. Finally, the optimal control methodology is extended to systems with order higher than two for a class of triangular systems. The method proposed here works for any mathematical model in the class of pseudo Euler‐Lagrange systems and is therefore not restricted to models of physical systems. Several examples illustrate the application of the novel approach, including mass‐spring‐damper systems and Van der Pol oscillators. Copyright © 2016 John Wiley & Sons, Ltd.

Modeling of Optimal Targeted Therapies Using Drug-Loaded Magnetic Nanoparticles for Liver Cancer.

To enhance locoregional therapies for liver cancer treatment, we propose in this study a mathematical model to optimize the transcatheter arterial delivery of therapeutical agents. To maximize the effect of the treatment and minimize adverse effects on the patient, different mathematical models of the tumor growth are considered in this study to find the optimal number of the therapeutic drug-loaded magnetic nanoparticles to be administered. Three types of therapy models are considered, e.g., angiogenesis inhibition therapy, chemotherapy and radiotherapy. We use state-dependent Riccati equations (SDRE) as an optimal control methodology framework to the Hahnfeldt's tumor growth formulation. Based on this, design optimal rules are derived for each therapy to reduce the growth of a tumor through the administration of appropriate dose of antiangiogenic, radio- and chemo-therapeutic agents. Simulation results demonstrate the validity of the proposed optimal delivery approach, leading to reduced intervention time, low drug administration rates and optimal targeted delivery.

A two-agent model applied to the biological control of the sugarcane borer (Diatraea saccharalis) by the egg parasitoid Trichogramma galloi and the larvae parasitoid Cotesia flavipes

The paper is aimed at a methodological development in biological pest control. The considered one pest two-agent system is modelled as a verticum-type system. Originally, linear verticum-type systems were introduced by one of the authors for modelling certain industrial systems. These systems are hierarchically composed of linear subsystems such that a part of the state variables of each subsystem affect the dynamics of the next subsystem. Recently, verticum-type system models have been applied to population ecology as well, which required the extension of the concept a verticum-type system to the nonlinear case.In the present paper the general concepts and technics of nonlinear verticum-type control systems are used to obtain biological control strategies in a two-agent system. For the illustration of this verticum-type control, these tools of mathematical systems theory are applied to a dynamic model of interactions between the egg and larvae populations of the sugarcane borer (Diatraea saccharalis) and its parasitoids: the egg parasitoid Trichogramma galloi and the larvae parasitoid Cotesia flavipes.In this application a key role is played by the concept of controllability, which means that it is possible to steer the system to an equilibrium in given time. In addition to a usual linearization, the basic idea is a decomposition of the control of the whole system into the control of the subsystems, making use of the verticum structure of the population system. The main aim of this study is to show several advantages of the verticum (or decomposition) approach over the classical control theoretical model (without decomposition). For example, in the case of verticum control the pest larval density decreases below the critical threshold value much quicker than without decomposition. Furthermore, it is also shown that the verticum approach may be better even in terms of cost effectiveness. The presented optimal control methodology also turned out to be an efficient tool for the “in silico” analysis of the cost-effectiveness of different biocontrol strategies, e.g. by answering the question how far it is cost-effective to speed up the reduction of the pest larvae density, or along which trajectory this reduction should be carried out.

Preview Controller Design for Vehicle Stability With V2V Communication

This paper presents a design method of a preview controller for vehicle stability with vehicle-to-vehicle (V2V) communication. Using V2V communication technology, a driver's steering input of a preceding vehicle is obtained on a following vehicle for preview control. To cope with changes in speed and intervehicle distance in a real situation, a position-based sampling is used. With the position-based sampling data, the time-based preview data are resampled by interpolation. For the controller design, linear vehicle modes describing yaw and roll motions are used. To design a preview controller on the following vehicle with the previewed steering input, a linear optimal preview control methodology is adopted. To validate the preview control with V2V communication in terms of vehicle stability, a simulation is conducted using a vehicle simulation package.

A Global Optimal Control Methodology and its Application to a Mobile Robot Model

Abstract: A global optimal control algorithm is developed and applied to an omni-directional mobile robot model. The aim is to search and find the most intense signal source among other signal sources in the operation region of the robot. In other words, the control problem is to find the global extremum point when there are local extremas. The locations of the signal sources are unknown and it is assumed that the signal magnitudes are maximum at the sources and their magnitudes are decreasing away from the sources. The distribution characteristics of the signals are unknown, i.e. the gradients of the signal distribution functions are unknown. The control algorithm also doesn’t need any position measurement of the robot itself. Only the signal magnitude should be measured via a sensor mounted on the robot. The simulation study shows the performance of the controller.

GUIDANCE LAW FOR IMPACT TIME AND ANGLE CONTROL WITH CONTROL COMMAND RESHAPING

In this article, a more generalized form of the impact time and angle control guidance law is proposed based on the linear quadratic optimal control methodology. For the purpose on controlling an additional constraint such as the impact time, we introduce an additional state variable that is defined to be the jerk (acceleration rate). Additionally, in order to provide an additional degree of freedom in choosing the guidance gains, the performance index that minimizes the control energy weighted by an arbitrary order of time-to-go is considered in this work. First, the generalized form of the impact angle control guidance law with an additional term which is used for the impact time control is derived. And then, we also determine the additional term in order to achieve the desired impact time. Through numbers of numerical simulations, we investigate the superiority of the proposed guidance law compared to previous guidance laws. In addition, a salvo attack scenario with multiple missile systems is also demonstrated.

Optimal reactive power and voltage control in distribution networks with distributed generators by fuzzy adaptive hybrid particle swarm optimisation method

A new and efficient methodology for optimal reactive power and voltage control of distribution networks with distributed generators based on fuzzy adaptive hybrid particle swarm optimisation (PSO) is proposed. The objective is to minimise comprehensive cost, consisting of power loss and operation cost of transformers and capacitors, and subject to constraints such as minimum and maximum reactive power limits of distributed generators, maximum deviation of bus voltages and maximum allowable daily switching operation number. PSO is used to solve the corresponding mixed integer non-linear programming problem and the hybrid PSO (HPSO) method, consisting of three PSO variants, is presented. In order to mitigate the local convergence problem, fuzzy adaptive inference is used to improve the searching process and the final fuzzy adaptive inference-based HPSO is proposed. The proposed algorithm is implemented in VC++ 6.0 program language and the corresponding numerical experiments are finished on the modified version of the IEEE 33-node distribution system with two newly installed distributed generators and eight newly installed capacitors banks. The numerical results prove that the proposed method can search a more promising control schedule of all transformers, all capacitors and all distributed generators with less time consumption, compared with other listed artificial intelligent methods.

Torque and Center of Combustion Evaluation Through a Torsional Model of the Powertrain

The continuous development of modern internal combustion engine (ICE) management systems is mainly aimed at combustion control improvement. Nowadays, performing an efficient combustion control is crucial for drivability improvement, efficiency increase (critical for spark ignited engines), and pollutant emissions reduction (critical in compression ignited engines). The most important quantities used for combustion control are engine load (indicated mean effective pressure (IMEP) or torque delivered by the engine) and center of combustion, i.e., the angular position in which 50% of fuel burned within the engine cycle is reached. Both quantities can be directly evaluated starting from in-cylinder pressure measurement, which could be performed using the newly developed piezoresistive pressure sensors for on-board applications. However, the use of additional sensors would increase the cost of the whole engine management system. Due to these reasons, over the past years, a methodology that allows evaluating both engine load and the center of combustion with no extra cost has been developed. This approach is based on engine speed fluctuation measurement, which can be performed using the same speed sensor already mounted on-board. The methodology is general and can be applied to different engine–driveline systems with different architectures and combustion orders. Furthermore, it is compatible with on-board requirements, since the evaluation of only one specific harmonic component of interest is required (depending on the engine–driveline configuration under investigation). In order to clarify all the issues related to the application of the presented approach, it has been applied to some different engines, both compression ignited and spark ignited, taking also into account the case of combustion not evenly spaced. For all the analyzed configurations, the results obtained using the estimation algorithm seemed to be adequate to feedback a closed-loop methodology for optimal combustion control.

Adaptive Inverse Optimal Control of a Novel Fractional-Order Four-Wing Hyperchaotic System with Uncertain Parameter and Circuitry Implementation

An efficient approach of inverse optimal control and adaptive control is developed for global asymptotic stabilization of a novel fractional-order four-wing hyperchaotic system with uncertain parameter. Based on the inverse optimal control methodology and fractional-order stability theory, a control Lyapunov function (CLF) is constructed and an adaptive state feedback controller is designed to achieve inverse optimal control of a novel fractional-order hyperchaotic system with four-wing attractor. Then, an electronic oscillation circuit is designed to implement the dynamical behaviors of the fractional-order four-wing hyperchaotic system and verify the satisfactory performance of the controller. Comparing with other fractional-order chaos control methods which may have more than one nonlinear state feedback controller, the inverse optimal controller has the advantages of simple structure, high reliability, and less control effort that is required and can be implemented by electronic oscillation circuit.

Active vibration control of a cylindrical structure using flexible piezoactuators: experimental work in air and water environments

In the present work, the modal characteristics and vibration control performance of a cylindrical structure in air and water are experimentally investigated, and the results are presented in time and frequency domains. In order to achieve this goal, an end-capped cylindrical shell structure is considered as a host structure, and MFC (macro fiber composite) actuators, which are flexible, are bonded on the surface of the structure. After manufacturing a cylindrical shell structure with aluminum, a modal test is carried out, and the natural frequencies of the proposed structure are obtained and analyzed. To verify the modal test results, a finite element analysis is also performed, and the results are compared with the modal test results. By using the experimentally obtained modal characteristics, a state space control model is established. An optimal controller is then designed in order to control the unwanted vibration and is experimentally realized. It has been shown that the structural vibration can be effectively decreased with the optimal control methodology in both air and water environmental conditions.

Minimized Tracking Error Randomness Control for Nonlinear Multivariate and Non-Gaussian Systems Using the Generalized Density Evolution Equation

In this technical note, a new stochastic control algorithm is presented for nonlinear and non-Gaussian continuous-time systems. Based on the recently developed generalized density evolution equation, which is more tractable than the classical Liouville equation, the relationship is established among the probability density function (PDF) of tracking error, control input and disturbances. An improved performance index is then constructed for this stochastic control strategy, which includes quadratic information potential of the tracking error, mean value of squared tracking error and constraints on the control input energy. By minimizing the performance index, a recursive optimal control algorithm is obtained using the gradient descent method. Moreover, the statistical linearization technique is adopted to formulate the boundedness condition of the closed-loop system. An illustrative example is given to demonstrate the validity and efficiency of the proposed stochastic optimal control methodology.

A new multistage dynamic model for biological control exemplified by the host–parasitoid system Spodoptera exigua–Chelonus oculator

Over the last few decades, important advances have been made in understanding of host–parasitoid relations and their applications to biological pest control. Not only has the number of agent species increased, but new manipulation techniques for natural enemies have also been empirically introduced, particularly in greenhouse crops. This makes biocontrol more complex, requiring a new mathematical modeling approach appropriate for the optimization of the release of agents. The present paper aimed at filling this gap by the development of a temperature- and stage-dependent dynamic mathematical model of the host–parasitoid system with an improved functional response. The model is appropriate not only for simulation analysis of the efficiency of biocontrol agents, but also for the application of optimal control methodology for the optimal timing of agent releases, and for the consideration of economic implications. Based on both laboratory and greenhouse trials, the model was validated and fitted to the data of Chelonus oculator (F.) (Hym.: Braconidae) as a biological control agent against the beet armyworm, Spodoptera exigua Hubner (Lep.: Noctuidae). We emphasize that this model can be easily adapted to other interacting species involved in biological or integrated pest control with either parasitoid or predator agents.

Optimal tracking control with feedforward compensation for offshore steel jacket platforms with active mass damper mechanisms

This paper presents the optimal tracking control methodology for an offshore steel jacket platform subject to external wave force. Based on a dynamic model of an offshore steel jacket platform with an active mass damper mechanism and a linear exogenous system model of the external wave force on the offshore platform, an optimal tracking control scheme with feedforward compensation is proposed to attenuate the wave-induced vibration of the offshore platform. A feedforward and feedback optimal tracking controller (FFOTC) can be obtained by solving an algebraic Riccati equation and a Sylvester equation, respectively. It is demonstrated that the wave-induced vibration amplitudes of the offshore platform under the FFOTC are much smaller than the ones under the feedback optimal tracking controller (FOTC) and the feedforward and feedback optimal controller (FFOC). Furthermore, the required control force under the FFOTC is smaller than the ones under the FOTC and the FFOC.

Optimal Sizing Design and Energy Management of Stand-alone Photovoltaic/Wind Generator Systems

Presently, the photovoltaic (PV) and the wind energies are the most important energetic alternative resources. So far, a lot of researches are developed and conducted concerning the cost-optimally design and energy management for the stand-alone hybrid PV-wind generator (WG) systems. In this study, a methodology for optimal sizing design and strategy control based on differential flatness approach is applied to the hybrid stand-alone PV-WG systems. The purpose is to find the optimal number of units ensuring that the 20 years round total system cost is minimized subject to the constraint that the load energy requirements are completely covered. The optimization methodology, using the genetic algorithm and the formulation of the problem are detailed. Finally, an optimal configuration is obtained with a lifetime of 20 years; also the results of the control algorithm based on the flatness properties obtained under Matlab/Simulink are given.

Optimal Control for Superharmonic Vibration of Intelligent Structures

A piezoelectric optimal feedback control methodology is provided to mitigate the superharmonic resonance of a flexible intelligent structure. Relationships among the feedback gains and the coefficients of vibration system and amplitude of excitation are obtained by using the stable conditions of superharmonic response for nonlinear vibration system. The regions of the feedback gain are obtained by using the stability conditions of eigenvalue equation. Attenuation rate is used to evaluate the performance of vibration control by taking the proportion of peak amplitude of free vibration for the suspension system with and without control. Taking the attenuation rate and energy function as objective functions and the regions of the feedback gain as constraint conditions, the control parameters of velocity and displacement feedback gains are worked out by using optimal method. It is found that a big feedback gain of velocity can lead to a small attenuation rate and has a good performance. The energy of the vibration system can be minimum by using the optimal feedback gains. The controller is designed to control the amplitude of super-harmonic vibration of intelligent structures. A experimental control system is designed to control the amplitude of nonlinear harmonic vibration and the research of control experiment is carried out.

Optimal Operation of Heavy-Haul Trains Equipped With Electronically Controlled Pneumatic Brake Systems Using Model Predictive Control Methodology

An optimal control methodology for heavy-haul trains with the objective to optimize the train's operation in terms of energy consumption, velocity tracking, and operation safety is introduced. Rather than optimize the operation of the train at a specific position, this approach tries to schedule the train during a long period of travel in a model predictive control (MPC) framework; therefore, an effort is made so that the operation strategy of the train is optimal during a track section rather than at a specific position, as is done in existing literature. With this purpose, the cascade mass point model of the train is first simplified and transformed to facilitate the controller design. Then, an optimal controller is presented taking advantage of the MPC concept with the future behavior of the train and all operational constraints considered. Simulations demonstrate the feasibility as well as the advantages of the proposed approach.