Distributed optimal consensus control for nonlinear multiagent systems based on DISOPE algorithm

In this note, a distributed dynamic integrated system optimization and parameter estimation (DISOPE) algorithm for nonlinear multiagent system with general local finite time horizon performance index is proposed, which integrates the model optimization and parameter estimation techniques. Two difficult issues for optimal consensus problem, nonlinear multiagent system and nonlinear quadratic performance index, are considered. With the help of DISOPE algorithm, a distributed optimal control policy is designed to minimize the local performance index in finite time horizon. Furthermore, the convergence of distributed DISOPE algorithm is given, such that the convergence solution satisfies the optimality conditions. Finally, a simulation is employed to show the effectiveness of the distributed DISOPE algorithm.     

Optimal topology design and distributed formation control of multiagent systems with complex-weights directed networks

In this article, we consider the optimal topology design and distributed formation control problem of multiagent systems (MAS) with complex-weighted directed topology. First, a framework is proposed to associate optimal topology of MAS to a constrained optimization problem with a complex Laplacian matrix, which is independent of the agent dynamics. The main contribution of the proposed approach compared with existing results is that the proposed approach does not require the calculation of the stabilizing matrix such that the closed-loop system is asymptotically stable, and a unique set of complex weights that satisfy associated cooperative conditions can be chosen. Then, a distributed formation control protocol is proposed to enable all agents to achieve the control goal. Finally, some numerical example results are provided to demonstrate the effectiveness of the proposed scheme.     

Design and optimization of a novel fast distributed Kalman consensus filtering algorithm

A new type of fast distributed Kalman consensus filtering algorithm based on local information feedback is presented to tackle filtering problems in wireless sensor networks. First, this fast filtering issues are transformed into a stochastic stability problem of the dynamic estimation errors, which can be solved by Lyapunov's second method and matrix theory. Then, two sufficient conditions about the proportional-like feedback (double gains regulation) method and incremental Proportional-Integral-Derivative (PID) feedback method for the asymptotical stability of the systems are presented, respectively. Moreover, to achieve a faster convergence rate, a novel optimal method is given by combing a genetic algorithm and incremental PID. Finally, an illustrative example is presented to give a comparison of the convergence speed between the three filtering algorithms in the same condition, and verify the effectiveness and advantage of the proposed theoretical results in this article.     

Optimal control of discrete-time nonlinear heterogeneous multi-agent systems via a distributed DISOPE algorithm

A distributed offline DISOPE algorithm for optimal state synchronization of leader-follower systems with nonlinear discrete-time dynamics is considered, which integrates the model optimization idea and parameter estimation technique together. It can be seen that the convergent solutions of modified linear optimal control problems satisfy the optimality conditions of the original nonlinear optimization problem with non-LQ performance indices. The heterogeneous agents can cooperate and exchange information via network communication. Based on DISOPE algorithm, a distributed optimal control policy is obtained to assure state synchronization and minimize performance indices in finite time horizon. Finally, a simulation example is provided to illustrate the effectiveness of the distributed DISOPE algorithm.     

Hybrid BOA-GWO-PSO algorithm for mitigation of congestion by optimal reactive power management

The generation of power with load optimization, particularly in the current deregulated electricity market conditions, is a very important process for improved planning and operation of the grid. In addition, it is very important for the system not to experience problems due to congestion, have tensile stability, and protection to increase the share of electricity from renewable sources with the current supply system. This article presents load balancing with the butterfly optimization algorithm (BOA) in a hybridized form to minimize and maximize loads when used in pool and hybrid markets. The methods have been designed to prevent the drawbacks of BOA and generate a better trade-off between exploration and exploitation abilities by hybridizing it with particle swarm optimization (PSO) and gray wolf optimizer (GWO). Empirical research on other algorithms shows that proposed hybrid BOA-GWO-PSO algorithm performs better and shows potential in diverse problems. These studies give it a significant advantage over BOA in general, and when it is employed to solve complex optimization problems validated on benchmark IEEE 30 bus system. A comparative analysis has been conducted to validate the potency of the hybrid BOA-GWO-PSO approach with some conventional meta-heuristic algorithms. Analysis of results by mathematical validation on 23 benchmark functions and application in congestion management by optimal reactive power management (RPM) reveal that the proposed technique has the potent to solve real world optimization problems and is competitive with recent methods reported in state-of- art literature.     

An algorithm for optimal scheduling of a class of cascade water supply systems

The problem of determining overall optimized control schedules for a class of cascade water supply systems containing only fixed speed pumps is examined. The system control is by nature an on-off type. The optimal scheduling problem can be formulated as dynamical optimal control problems with purely discrete symbols, discrete controls and also with continuous intermediate variables interrelated in a highly non-linear way. An efficient problem solver is proposed. Its high efficiency is achieved by exploiting, through a suitable decomposition, certain structural properties of the problem. Lagrange relaxation is applied in order to break down the time structure of discrete control variables. The decomposition also enables consideration of mixed integer optimization on purely static grounds. The dynamical optimization constitutes only that part of the solver which deals with entirely continuous variables. There is a duality gap in the problem. However, certain, but not complete, information obtained through solving the dual problem (dual optimal information) is close to that which corresponds to the true (primal) optimal solution. This is an important property of the scheduling problem, which together with the problem structure creates a basis for the solver design.     

A novel continuous genetic algorithm for the solution of optimal control problems

In this paper, the Continuous Genetic Algorithm (CGA), previously developed by the principal author, is applied for the solution of optimal control problems. The optimal control problem is formulated as an optimization problem by the direct minimization of the performance index subject to constraints, and is then solved using CGA. In general, CGA uses smooth operators and avoids sharp jumps in the parameter values. This novel approach possesses two main advantages when compared to other existing direct and indirect methods that either suffer from low accuracy or lack of robustness. First, our method can be applied to optimal control problems without any limitation on the nature of the problem, the number of control signals, and the number of mesh points. Second, high accuracy can be achieved where the performance index is globally minimized while satisfying the constraints. The applicability and efficiency of the proposed novel algorithm for the solution of different optimal control problems is investigated. Copyright © 2010 John Wiley & Sons, Ltd.     

A gradient algorithm for solution of the optimal control problem for hybrid switching systems

In this article, an algorithm is presented for solving the optimal control problem for the general form of a hybrid switching system. The cost function comprises terminal, running and switching costs. The controlled system is an autonomous hybrid switching system with jumps either at some switching times or some time varying switching manifolds. The proposed algorithm is an extension of the first-order gradient method for the conventional optimal control problem. The algorithm requires a low computational effort. The system's dynamical equations together with a set of algebraic equations are solved at each iteration in order to find the descent direction. The convergence of algorithm is proved and examples are provided to demonstrate the efficiency of the algorithm for different types of hybrid switching system optimal control problems.     

Prediction for global African swine fever outbreaks based on a combination of random forest algorithms and meteorological data

African swine fever (ASF) is a virulent infectious disease of pigs. As there is no effective vaccine and treatment method at present, it poses a great threat to the pig industry once it breaks out. In this paper, we used ASF outbreak data and the WorldClim database meteorological data and selected the CfsSubset Evaluator‐Best First feature selection method combined with the random forest algorithms to construct an African swine fever outbreak prediction model. Subsequently, we also established a test set for data other than modelling, and the accuracy accuracy value range of the model on the independent test set was 76.02%–84.64%, which indicated that the modelling effect was better and the prediction accuracy was higher than previous estimates. In addition, logistic regression analysis was conducted on 12 features used for modelling and the ROC curves were drawn. The results showed that the bio14 features (precipitation of driest month) had the largest contribution to the outbreak of ASF, and it was speculated that the outbreak of the epidemic was significantly related to precipitation. Finally, we used this qualitative prediction model to build a global online prediction system for ASF outbreaks, in the hope that this study will help to decision‐makers who can then take the relevant prevention and control measures in order to prevent the further spread of future epidemics of the disease.     

Online identifier–actor–critic algorithm for optimal control of nonlinear systems

In this paper, a novel identifier–actor–critic optimal control scheme is developed for discrete‐time affine nonlinear systems with uncertainties. In contrast to traditional adaptive dynamic programming methodology, which requires at least partial knowledge of the system dynamics, a neural‐network identifier is employed to learn the unknown control coefficient matrix working together with actor–critic‐based scheme to solve the optimal control online. The critic network learns the approximate value function at each step. The actor network attempts to improve the current policy based on the approximate value function. The weights of all neural networks are updated at each sampling instant. Lyapunov theory is utilized to prove the stability of closed‐loop system. It shows that system states and neural network weights are uniformly ultimately bounded. Finally, simulations are provided to illustrate the effectiveness of the developed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Design of robust quadratic‐optimal controllers for uncertain singular systems using orthogonal function approach and genetic algorithm

This paper discusses the robust‐optimal state feedback controller design problems of linear singular systems under the structured (elemental) parameter uncertainties by using the orthogonal function approach (OFA) and the hybrid Taguchi genetic algorithm (HTGA). A sufficient condition is proposed to ensure that the linear singular systems with the structured parameter uncertainties are regular, impulse free, and asymptotically stable. Based on the OFA, an algorithm only involving algebraic computation is derived in this paper and then is integrated with the HTGA to design the robust‐optimal state feedback controller of linear uncertain singular systems subject to robust stability constraint and the minimization of a quadratic performance index. A design example of a two degree of freedom mass–spring–damper system is given to demonstrate the applicability of the proposed approach. Copyright © 2008 John Wiley & Sons, Ltd.     

Multiobjective optimization of tibial locking screw design using a genetic algorithm: Evaluation of mechanical performance.

Breakage or loosening of locking screws may impair fracture fixation or bone healing in locked nailing of tibial fractures. Bending strength and bone holding power, two important design objectives of locking screws, may conflict with each other. The present study used multiobjective optimization with a genetic algorithm to investigate the optimal designs with respect to these two objectives. Three-dimensional finite element models for analyzing bending strength and bone holding power of locking screws were created first. Through use of a Taguchi L25 orthogonal array, two objective functions were developed by least-squares regression analyses. Then, the trade-off solutions between the two objectives known as Pareto optima were explored by a weighted-sum aggregating approach under geometric constraints. The objective functions, reliably reflecting the finite element results, were valid for multiobjective studies. The Pareto fronts of the screws with 4.5-mm and 5.0-mm outer diameters were similar. The "knee" region of the Pareto front, characterized by the fact that a small improvement in either objective will cause a large deterioration in the other objective, might be the favored choice of optimal designs. The commercially available locking screws compared with the Pareto optima were found to be dominated designs and could be improved. In conclusion, the multiobjective optimization with a genetic algorithm was useful for optimization of locking screw design with many variables and conflicting objectives. Choosing an optimal design requires a thorough knowledge of the inherent problems. This method could reduce the time, cost, and labor associated with the screw development process.     

A novel projected Fletcher‐Reeves conjugate gradient approach for finite‐time optimal robust controller of linear constraints optimization problem: Application to bipedal walking robots

For finite‐time optimal robust control problem of bipedal walking robot, a class of global and feasible projected Fletcher‐Reeves conjugate gradient approach is proposed based on an online convex optimization algorithm. The optimal robust controllers are solved by projected Fletcher‐Reeves conjugate gradient approach. The approach can rapidly converge to a stable gait cycle by selecting an initial gait. Under some suitable conditions, we provide a rigorous proof of global convergence and well‐defined properties for projected Fletcher‐Reeves conjugate gradient approach. To demonstrate the effectiveness of the bipedal walking robot, we will conduct numerical simulations on the model of 3‐link robot with nonlinear, impulsive, and underactuated dynamics. Furthermore, to indicate the availability of high‐dimensional robotic system, the main result is illustrated on a nonlinear impulsive model of a bipedal walking robot through simulations via finite‐time optimal robust controller. Numerical results show that the projected Fletcher‐Reeves conjugate gradient approach is feasible and effective for bipedal walking robots. Therefore, it is reasonable to infer that the optimal robust control approach can be used in practical systems.     

Assessment of in-shoe pressure: Development of a clinical user guide based on a DELPHI-derived consensus

BackgroundThe F-Scan (F-Scan System by Tekscan, Boston, USA) is an in-shoe pressure measurement device used to provide dynamic pressure, force and timing information to guide appropriate offloading of plantar foot ulcers. Despite the clinical utility of an in-shoe pressure measuring device there are some limitations in the validity and reliability of the output of the F-Scan. The aim of this study was to develop a consensus-based guideline following information provided by experienced clinicians, synthesis of research evidence and manufacturer’s guidelines on the most appropriate use and interpretation of the data generated by the F-Scan to manage plantar foot ulceration.MethodsUsing the Delphi method a series of sixteen consensus statements were developed following a two-step questionnaire utilising clinicians feedback, a review of evidence and the manufacturer’s guidelines.FindingsSeventeen clinicians responded to the first questionnaire and 11 to the second, that included 8 podiatrists and 9 pedorthists working in the public and private sectors. Of the sixteen statements there was strong consensus for ten and moderate consensus for a further four. Only two statements failed to reach consensus and the feedback from the respondents was of great value providing sound clinical rationale for their rejection.InterpretationThe objective of this study has been achieved in developing a clear and concise set of guiding statements (Table 1) to standardise use of the F-Scan. The application of the guiding statements will encourage standardisation of practice with the aim of highlighting the limitations of the system and reducing potential systematic error in measurement from output produced.     

Semi‐decentralized approximation of optimal control of distributed systems based on a functional calculus

This paper discusses a new approximation method for operators that are solution to an operational Riccati equation. The latter is derived from the theory of optimal control of linear problems posed in Hilbert spaces. The approximation is based on the functional calculus of self‐adjoint operators and the Cauchy formula. Under a number of assumptions, the approximation is suitable for implementation on a semi‐decentralized computing architecture in view of real‐time control. Our method is particularly applicable to problems in optimal control of systems governed by partial differential equations with distributed observation and control. Some relatively academic applications are presented for illustration. More realistic examples relating to microsystem arrays have already been published. Copyright © 2014 John Wiley & Sons, Ltd.     

Design of robust‐optimal controllers with low trajectory sensitivity for uncertain Takagi–Sugeno fuzzy model systems using differential evolution algorithm

By integrating the robust stabilizability condition, the orthogonal‐function approach (OFA) and the Taguchi‐sliding‐based differential evolution algorithm (TSBDEA), an integrative computational approach is presented in this paper to design the robust‐optimal fuzzy parallel‐distributed‐compensation (PDC) controller with low trajectory sensitivity such that (i) the Takagi–Sugeno (TS) fuzzy model system with parametric uncertainties can be robustly stabilized, and (ii) a quadratic finite‐horizon integral performance index for the nominal TS fuzzy model system can be minimized. In this paper, the robust stabilizability condition is proposed in terms of linear matrix inequalities (LMIs). Based on the OFA, an algebraic algorithm only involving the algebraic computation is derived for solving the nominal TS fuzzy feedback dynamic equations. By using the OFA and the LMI‐based robust stabilizability condition, the robust‐optimal fuzzy PDC control problem for the uncertain TS fuzzy dynamic systems is transformed into a static constrained‐optimization problem represented by the algebraic equations with constraint of LMI‐based robust stabilizability condition; thus, greatly simplifying the robust‐optimal PDC control design problem. Then, for the static constrained‐optimization problem, the TSBDEA has been employed to find the robust‐optimal PDC controllers with low trajectory sensitivity of the uncertain TS fuzzy model systems. A design example is given to demonstrate the applicability of the proposed new integrative approach. Copyright © 2011 John Wiley & Sons, Ltd.     

dsoa: The implementation of a dynamic system optimization algorithm

This paper describes the ANSI C/C++ computer program dsoa , which implements an algorithm for the approximate solution of dynamics system optimization problems. The algorithm is a direct method that can be applied to the optimization of dynamic systems described by index‐1 differential‐algebraic equations (DAEs). The types of problems considered include optimal control problems and parameter identification problems. The numerical techniques are employed to transform the dynamic system optimization problem into a parameter optimization problem by: (i) parameterizing the control input as piecewise constant on a fixed mesh, and (ii) approximating the DAEs using a linearly implicit Runge‐Kutta method. The resultant nonlinear programming (NLP) problem is solved via a sequential quadratic programming technique. The program dsoa is evaluated using 83 nontrivial optimal control problems that have appeared in the literature. Here we compare the performance of the algorithm using two different NLP problem solvers, and two techniques for computing the derivatives of the functions that define the problem. Copyright © 2009 John Wiley & Sons, Ltd.     

The spectral linear filter method for a stochastic optimal control problem of partially observable systems

In this paper, two spectral methods are presented to solve a stochastic optimal control problem of a partially observable system. These two methods work together to solve such problems. In fact, solving such problems involves two cases: obtaining the control function and simulating the partially observable system. At first, a spectral linear filter is defined as a function of time to obtain an appropriate solution for a partially observable system. This linear filter is equipped with an orthogonal basis and it is made to predict the future behavior of this system. In this method, the goal is to approximate the trend of the partially observable system. The second method is suggested to achieve the optimal control corresponding to each sample path. In this method, the spectral Fourier transform is used. These two methods are used together to solve linear and nonlinear cases. In fact, the innovative contents of this paper are both the spectral linear filter and the suggested spectral optimal control method.