A multi-objective design approach for tuning LQR controllers is proposed.A new reinforced quantum-behaved PSO algorithm is introduced.Comparative studies among nine various techniques are conducted. A novel and generic multi-objective design paradigm is proposed which utilizes quantum-behaved PSO (QPSO) for deciding the optimal configuration of the LQR controller for a given problem considering a set of competing objectives. There are three main contributions introduced in this paper as follows. (1) The standard QPSO algorithm is reinforced with an informed initialization scheme based on the simulated annealing algorithm and Gaussian neighborhood selection mechanism. (2) It is also augmented with a local search strategy which integrates the advantages of memetic algorithm into conventional QPSO. (3) An aggregated dynamic weighting criterion is introduced that dynamically combines the soft and hard constraints with control objectives to provide the designer with a set of Pareto optimal solutions and lets her to decide the target solution based on practical preferences. The proposed method is compared against a gradient-based method, seven meta-heuristics, and the trial-and-error method on two control benchmarks using sensitivity analysis and full factorial parameter selection and the results are validated using one-tailed T-test. The experimental results suggest that the proposed method outperforms opponent methods in terms of controller effort, measures associated with transient response and criteria related to steady-state.
They are a few studies that exploit multi-objective design for tuning LQR controllers. In @cite_4 a multi-objective evolutionary algorithm is presented to control a double inverted pendulum system. They concluded that multi-objective approach results in shorter adjusting time and smaller amplitude value deviating from steady-state in comparison with the pole assignment design approach. @cite_22 also applies a multi-objective evolutionary algorithm to stabilize a double inverted pendulum system. Their results suggest that multi-objective approach results in shorter adjusting time and smaller amplitude value deviating from steady-state in comparison to non-dominated sorting GA. As far as the authors' knowledge is concerned, it is the first time that a multi-objective derivative of the PSO algorithm is applied for optimal design of LQR controllers.
@cite_4 @cite_22
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This paper introduces an application of Multi-Objective Evolution Algorithm (MOEA) to design Q and R weighting matrices in Linear Quadratic regulators (LQR). Considering the difficulty of designing weighting matrices for a linear quadratic regulator, a multi-objective evolutionary algorithm based approach is proposed. The LQR weighting matrices, state feedback control rate and consequently the optimal controller are obtained by means of establishing the multi-objective optimization model of LQR weighting matrices and applying MOEA to it, which makes control system meet multiple performance indexes simultaneously. Controller of double inverted pendulum system is designed using the proposed approach. Simulation results show that it has shorter adjusting time and smaller amplitude value deviating from steady-state than a Non-dominated Sorting Genetic Algorithm LQR ( NSGA- LQR )weighting matrices design approach. Aiming at the difficulty of designing weighting matrices for linear quadratic regulator (LQR), a multi-objective evolution algorithm (MOEA) based approach is proposed. The LQR weighting matrices, state feedback control rate and optimal controller are obtained by means of establishing the multi-objective optimization model of LQR weighting matrices and applying MOEA to it, which makes control system meet multiple performance indexes simultaneously. Controller of double inverted pendulum system is designed using the proposed approach. Simulation results show that it has shorter adjusting time, smaller amplitude value deviating from steady-state than the pole assignment LQR weighting matrices design approach. So the validity of the proposed approach is confirmed. In this paper, considering some important indices such as closed-loop pole locations, speed of response and combining them into an objective function an optimization problem is defined in order to select the weighting matrices in Linear Quadratic Regulator (LQR) controller. To solve this optimization problem the Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) are utilized and compared. The proposed method is applied to rotational inverted pendulum. Simulation results show the relative superiority of PSO over GA. This paper established a mathematical model of the inverted pendulum system and put forward a design method of LQR based on PSO. A LQR is designed by this method according to the computer simulation experiments. The simulation results show that the inverted pendulum system with the LQR has good performance. Then the real-time control of the pendulum has been accomplished successfully based on the real-time control model built in Simulink. The LQR designed in the computer simulation experiments is applied to real-time controls. The real-time control experiments also validated the correctness of the theoretical analysis and the rightness of the computer simulation. The application of LQR controller in inverted pendulum system is common, but the choice of weight matrix Q and R of LQR controller has always been a difficult. This paper presents a new method to achieve the double inverted pendulum system LQR controller parameters optimization through the particle swarm optimization algorithm. The simulation result shows that the method used in the choice of matrix Q and R achieves very good results. In the field of evolutionary multi-criterion optimization, the hypervolume indicator is the only single set quality measure that is known to be strictly monotonic with regard to Pareto dominance: whenever a Pareto set approximation entirely dominates another one, then the indicator value of the dominant set will also be better. This property is of high interest and relevance for problems involving a large number of objective functions. However, the high computational effort required for hypervolume calculation has so far prevented the full exploitation of this indicator's potential; current hypervolume-based search algorithms are limited to problems with only a few objectives. This paper addresses this issue and proposes a fast search algorithm that uses Monte Carlo simulation to approximate the exact hypervolume values. The main idea is not that the actual indicator values are important, but rather that the rankings of solutions induced by the hypervolume indicator. In detail, we present HypE, a hypervolume estimation algorithm for multi-objective optimization, by which the accuracy of the estimates and the available computing resources can be traded off; thereby, not only do many-objective problems become feasible with hypervolume-based search, but also the runtime can be flexibly adapted. Moreover, we show how the same principle can be used to statistically compare the outcomes of different multi-objective optimizers with respect to the hypervolume----so far, statistical testing has been restricted to scenarios with few objectives. The experimental results indicate that HypE is highly effective for many-objective problems in comparison to existing multi-objective evolutionary algorithms. HypE is available for download at http: www.tik.ee.ethz.ch sop download supplementary hype . A scheduling policy strongly influences the performance of a manufacturing system. However, the design of an effective scheduling policy is complicated and time consuming due to the complexity of each scheduling decision, as well as the interactions among these decisions. This paper develops four new multi-objective genetic programming-based hyperheuristic (MO-GPHH) methods for automatic design of scheduling policies, including dispatching rules and due-date assignment rules in job shop environments. In addition to using three existing search strategies, nondominated sorting genetic algorithm II, strength Pareto evolutionary algorithm 2, and harmonic distance-based multi-objective evolutionary algorithm, to develop new MO-GPHH methods, a new approach called diversified multi-objective cooperative evolution (DMOCC) is also proposed. The novelty of these MO-GPHH methods is that they are able to handle multiple scheduling decisions simultaneously. The experimental results show that the evolved Pareto fronts represent effective scheduling policies that can dominate scheduling policies from combinations of existing dispatching rules with dynamic regression-based due-date assignment rules. The evolved scheduling policies also show dominating performance on unseen simulation scenarios with different shop settings. In addition, the uniformity of the scheduling policies obtained from the proposed method of DMOCC is better than those evolved by other evolutionary approaches. Feature selection (FS) is an important data preprocessing technique, which has two goals of minimising the classification error and minimising the number of features selected. Based on particle swarm optimisation (PSO), this paper proposes two multi-objective algorithms for selecting the Pareto front of non-dominated solutions (feature subsets) for classification. The first algorithm introduces the idea of non-dominated sorting based multi-objective genetic algorithm II into PSO for FS. In the second algorithm, multi-objective PSO uses the ideas of crowding, mutation and dominance to search for the Pareto front solutions. The two algorithms are compared with two single objective FS methods and a conventional FS method on nine datasets. Experimental results show that both proposed algorithms can automatically evolve a smaller number of features and achieve better classification performance than using all features and feature subsets obtained from the two single objective methods and the conventional method. Both the continuous and the binary versions of PSO are investigated in the two proposed algorithms and the results show that continuous version generally achieves better performance than the binary version. The second new algorithm outperforms the first algorithm in both continuous and binary versions. In this paper, a proposed particle swarm optimization called multi-objective particle swarm optimization (MOPSO) with an accelerated update methodology is employed to tune Proportional-Integral-Derivative (PID) controller for an AR.Drone quadrotor. The proposed approach is to modify the velocity formula of the general PSO systems in order for improving the searching efficiency and actual execution time. Three PID control parameters, i.e., the proportional gain Kp, integral gain K; and derivative gain Kd are required to form a parameter vector which is considered as a particle of PSO. To derive the optimal PID parameters for the Ar.Drone, the modified update method is employed to move the positions of all particles in the population. In the meanwhile, multi-objective functions defined for PID controller optimization problems are minimized. The results verify that the proposed MOPSO is able to perform appropriately in Ar.Drone control system. This paper presents the design of an active suspension control of a two-axle railway vehicle using an optimized linear quadratic regulator. The control objective is to minimize the lateral displacement and yaw angle of the wheelsets when the vehicle travels on straight and curved tracks with lateral irregularities. In choosing the optimum weighting matrices for the LQR, the Particle Swarm Optimization (PSO) method has been applied and the results of the controller performance with weighting matrices chosen using this method is compared with the commonly used, trial and error method. The performance of the passive and active suspension has also been compared. The results show that the active suspension system performs better than the passive suspension system. For the active suspension, the LQR employing the PSO method in choosing the weighting matrices provides a better control performance and a more systematic approach compared to the trial and error method. The main focus of this paper is to develop an optimization method for the automatic fighter tracking (AFT) problem. The AFT problem is similar to a general evader-pursuer maneuvering automation problem between the dynamic systems of two highly interactive objects. This paper proposes a particle swarm optimizer-based variable feedback gain controller (PSO-based VFGC) for dealing with AFT problems. The PSO-based VFGC is designed to obtain the control value of a pursuer through an error-feedback gain controller. Once conditions of system closed-loop stability have been satisfied, the optimal feedback gains can be obtained through PSO, and the actual control values can be derived from the obtained values. Simulation results confirm the capabilities of the proposed method by comparing the results against two other methods in the field: the weight matrix value defined Ricatti equation, and the linear matrix inequality (LMI) based linear quadratic regulator (LQR). The performance of the proposed method is superior to that of its alternatives. Many-objective problems (MAPs) have put forward a number of challenges to classical Pareto-dominance based multi-objective evolutionary algorithms (MOEAs) for the past few years. Recently, researchers have suggested that MOEA D (multi-objective evolutionary algorithm based on decomposition) can work for MAPs. However, there exist two difficulties in applying MOEA D to solve MAPs directly. One is that the number of constructed weight vectors is not arbitrary and the weight vectors are mainly distributed on the boundary of weight space for MAPs. The other is that the relationship between the optimal solution of subproblem and its weight vector is nonlinear for the Tchebycheff decomposition approach used by MOEA D. To deal with these two difficulties, we propose an improved MOEA D with uniform decomposition measurement and the modified Tchebycheff decomposition approach (MOEA D-UDM) in this paper. Firstly, a novel weight vectors initialization method based on the uniform decomposition measurement is introduced to obtain uniform weight vectors in any amount, which is one of great merits to use our proposed algorithm. The modified Tchebycheff decomposition approach, instead of the Tchebycheff decomposition approach, is used in MOEA D-UDM to alleviate the inconsistency between the weight vector of subproblem and the direction of its optimal solution in the Tchebycheff decomposition approach. The proposed MOEA D-UDM is compared with two state-of-the-art MOEAs, namely MOEA D and UMOEA D on a number of MAPs. Experimental results suggest that the proposed MOEA D-UDM outperforms or performs similarly to the other compared algorithms in terms of hypervolume and inverted generational distance metrics on different types of problems. The effects of uniform weight vector initializing method and the modified Tchebycheff decomposition are also studied separately. The initial state of an Unmanned Aerial Vehicle (UAV) system and the relative state of the system, the continuous inputs of each flight unit are piecewise linear by a Control Parameterization and Time Discretization (CPTD) method. The approximation piecewise linearization control inputs are used to substitute for the continuous inputs. In this way, the multi-UAV formation reconfiguration problem can be formulated as an optimal control problem with dynamical and algebraic constraints. With strict constraints and mutual interference, the multi-UAV formation reconfiguration in 3-D space is a complicated problem. The recent boom of bio-inspired algorithms has attracted many researchers to the field of applying such intelligent approaches to complicated optimization problems in multi-UAVs. In this paper, a Hybrid Particle Swarm Optimization and Genetic Algorithm (HPSOGA) is proposed to solve the multi-UAV formation reconfiguration problem, which is modeled as a parameter optimization problem. This new approach combines the advantages of Particle Swarm Optimization (PSO) and Genetic Algorithm (GA), which can find the time-optimal solutions simultaneously. The proposed HPSOGA will also be compared with basic PSO algorithm and the series of experimental results will show that our HPSOGA outperforms PSO in solving multi-UAV formation reconfiguration problem under complicated environments. In this paper, state feedback control design for tracking control of a flexible link manipulator is considered. The computation of state feedback control gains is conventionally handled by pole placement method or LQR method via Riccati equation. Unfortunately, they still possess trial-and-error approach in choosing their parameters. Particularly, choosing elements of Q and R matrices in the state feedback control design using LQR method has to be done by trial. Therefore, an intelligent method to resolve this problem is proposed by adopting PSO-based optimization. Experimental work is carried out to evaluate effectiveness of the proposed method. In this paper, the state feedback control design problem for tracking control of a flexible link manipulator is considered. The calculation of state feedback control gains is conventionally handled by pole placement method or LQR method via Riccati equation. Unfortunately, they still possess trial and error approach of choosing some parameters. Particularly, choosing elements of Q and R matrices in the state feedback control using LQR method has to be done by trial. Therefore, an intelligent method to resolve this problem is proposed by adopting PSO algorithm. The experimental work is carried out to evaluate the effectiveness of the proposed method. Evolutionary algorithms (EAs) are increasingly popular approaches to multi-objective optimization. One of their significant advantages is that they can directly optimize the Pareto front by evolving a population of solutions, where the recombination (also called crossover) operators are usually employed to reproduce new and potentially better solutions by mixing up solutions in the population. Recombination in multi-objective evolutionary algorithms is, however, mostly applied heuristically. In this paper, we investigate how from a theoretical viewpoint a recombination operator will affect a multi-objective EA. First, we employ artificial benchmark problems: the Weighted LPTNO problem (a generalization of the well-studied LOTZ problem), and the well-studied COCZ problem, for studying the effect of recombination. Our analysis discloses that recombination may accelerate the filling of the Pareto front by recombining diverse solutions and thus help solve multi-objective optimization. Because of this, for these two problems, we find that a multi-objective EA with recombination enabled achieves a better expected running time than any known EAs with recombination disabled. We further examine the effect of recombination on solving the multi-objective minimum spanning tree problem, which is an NP-hard problem. Following our finding on the artificial problems, our analysis shows that recombination also helps accelerate filling the Pareto front and thus helps find approximate solutions faster. We present an approach to learning control policies for physical robots that achieves high efficiency by adjusting existing policies that have been learned on similar source systems, such as a similar robot with different physical parameters, or an approximate dynamics model simulator. This can be viewed as calibrating a policy learned on a source system, to match a desired behaviour in similar target systems. Our approach assumes that the trajectories described by the source robot are feasible on the target robot. By making this assumption, we only need to learn a mapping from the source robot state and action spaces to the target robot action space, which we call a policy adjustment model. We demonstrate our approach in simulation in the cart-pole balancing task and a two link double pendulum. We also validate our approach with a physical cart-pole system, where we adjust a learned policy under changes to the weight of the pole. The authors present algorithms for robotic (eye-in-hand configuration) real-time visual tracking of arbitrary 3D objects traveling at unknown velocities in a 2D space (depth is given as known). Visual tracking is formulated as a problem of combining control with computer vision. A mathematical formulation of the control problem that includes information from a novel feedback vision sensor and represents everything with respect to the camera frame is presented. The sum-of-squared differences (SSD) optical flow is used to compute the vector of discrete displacements each instant of time. These displacements can be fed either directly to a PI (proportional-integral) controller or to a pole assignment controller or discrete steady-state Kalman filter. In the latter case, the Kalman filter calculates the estimated values of the system's states and the exogenous disturbances, and a discrete LQG (linear-quadratic Gaussian) controller computes the desired motion of the robotic system. The outputs of the controllers are sent to the Cartesian robotic controller. Performance results are presented. > Optimizing shared vehicle systems (bike-sharing car-sharing ride-sharing) is more challenging compared to traditional resource allocation settings due to the presence of complex network externalities. In particular, changes in the demand supply at any location (via dynamic pricing, rebalancing of empty vehicles, etc.) affect future supply throughout the system within short timescales. Such externalities are well captured by steady-state Markovian models, which are therefore widely used to analyze and design shared vehicle systems. However, using such models to design pricing control policies is computationally difficult since the resulting optimization problems are high-dimensional and non-convex. To this end, we develop a general approximation framework for designing pricing policies in shared vehicle systems, based on a novel convex relaxation which we term elevated flow relaxation. Our approach provides the first efficient algorithms with rigorous approximation guarantees for a wide range of objective functions (throughput, revenue, welfare). For any shared vehicle system with @math stations and m vehicles, our framework provides a pricing policy with an approximation ratio of 1+(n-1) m. This guarantee is particularly meaningful when m n, the average number of vehicles per station is large, as is often the case in practice. Further, the simplicity of our approach allows us to extend it to more complex settings. Apart from pricing, shared vehicle systems enable other control levers for modulating demand and supply, e.g. rebalancing empty vehicles, redirecting riders to nearby vehicles, etc. Our approach yields efficient algorithms with the same approximation guarantees for all these problems, and in the process, obtains as special cases several existing heuristics and asymptotic guarantees. We also extend our approach to obtain bi-criterion guarantees in multi-objective settings; we illustrate this with the example of Ramsey pricing. From a technical perspective, our work develops a new approach for obtaining control policies with approximation guarantees in steady-state Markovian models. Our approach can be distilled into the following three-step program: (i) construct an upper bound via a relaxation to the original problem that encodes essential conservation laws of the system, (ii) identify a family of control policies inducing known steady-state distributions that achieve the value of the relaxed solution in an appropriate scaling limit (in our case, state-independent policies in the limit m++), and (iii) characterize the performance loss between the finite system (i.e. fixed m) and the scaling limit. This technique may be of independent interest for other settings. Abstract This paper proposes a push and pull search (PPS) framework for solving constrained multi-objective optimization problems (CMOPs). To be more specific, the proposed PPS divides the search process into two different stages: push and pull search stages. In the push stage, a multi-objective evolutionary algorithm (MOEA) is used to explore the search space without considering any constraints, which can help to get across infeasible regions very quickly and to approach the unconstrained Pareto front. Furthermore, the landscape of CMOPs with constraints can be probed and estimated in the push stage, which can be utilized to conduct the parameter setting for the constraint-handling approaches to be applied in the pull stage. Then, a modified form of a constrained multi-objective evolutionary algorithm (CMOEA), with improved epsilon constraint-handling, is applied to pull the infeasible individuals achieved in the push stage to the feasible and non-dominated regions. To evaluate the performance regarding convergence and diversity, a set of benchmark CMOPs and a real-world optimization problem are used to test the proposed PPS (PPS-MOEA D) and state-of-the-art CMOEAs, including MOEA D-IEpsilon, MOEA D-Epsilon, MOEA D-CDP, MOEA D-SR, C-MOEA D and NSGA-II-CDP. The comprehensive experimental results show that the proposed PPS-MOEA D achieves significantly better performance than the other six CMOEAs on most of the tested problems, which indicates the superiority of the proposed PPS method for solving CMOPs.