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
2162919642 2000422180 1611009284 2020171016 1984194177 2023939757 2030900255 2148836970 1970751891 2119403022 1991687766 2126000336 2963681938 2257061815 2296356821 2569045184 2738495647 2029859487 1769664844 2471940543
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. 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. With the development of construction techniques, it is possible to build large-span bridges, pipelines, dams, and other essential structures in seismically active regions or in active faults. A new method to find the optimal control forces for active tuned mass damper is presented in this paper. Three algorithms: discrete wavelet transform (DWT), particle swarm optimization (PSO), and linear quadratic regulator (LQR). DWT are used to obtain the local energy distribution of the motivation over the frequency bands. PSO is used to determine the gain matrices through the online update of the weighting matrices used in the LQR controller while eliminating the trial and error. The method is tested on a 10-story structure subject to several historical pulse-like near-fault ground motions. The results presented in this paper indicate that the proposed method is more effective at reducing the displacement response of the structure in real time than conventional LQR controllers. 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. 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 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. This paper discusses design and performance issues of three design techniques for DSTATCOM controller with an aim to improve the robustness. The state feedback controller of DSTATCOM has been designed using Linear Quadratic Regulator (LQR), Linear Quadratic Regulator with prescribed degree of stability and Particle Swarm Optimization (PSO). Weak ac source and unbalanced nonlinear load are considered. The performance of the controller designed through the three methodologies has been compared under different operating conditions. Particle Swarm Optimization based controller is more robust and is suitable for a DSTATCOM working under uncertain parametric conditions like feeder impedance and load that are most common in a distribution system. This controller ensures stability under all possible operating conditions and has superior performance over the other two controller design techniques. The performance of the DSTATCOM controller designed through the three different methodologies is verified by detailed simulation studies. Abstract This paper presents an optimized reconfigurable control design methodology by separating control commands distribution task from flight controller for different types of fault handling. The proposed strategy improves the flight control performance in normal and fault situations. The particle swarm optimization (PSO) based multi-input multi-output (MIMO) linear quadratic regulator (LQR) is used to produce virtual command signals. A modified weighted pseudo-inverse (WPI) based cascaded re- allocation technique is employed for effective implementation of commands to redundant control surfaces in a realistic nonlinear aircraft benchmark model. Control surface fault modelling is performed for the evaluation of optimized reconfiguration based modular flight control strategy. Simulation results show that acceptable fault tolerant control (FTC) performance can be achieved by using swarm intelligence based optimization technique for modular control design. 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 method of Linear Quadratic Regulator (LQR) is employed for controlling accelerator PWM power supply, and improving its dynamic functioning. A method based on the Particle Swarm Optimization is proposed to optimize the weighting matrix Q and R. In order to control the dynamic behavior of the power supply, the fitness function of PSO is acquired considering the needs of the power properties. The results of simulation proved that the proposed method was much better than simple LQR method and LQR-GA method, and the performance of the power supply was improved dramatically. 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. We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown linear system is controlled subject to quadratic costs. Leveraging recent developments in the estimation of linear systems and in robust controller synthesis, we present the first provably polynomial time algorithm that achieves sub-linear regret on this problem. We further study the interplay between regret minimization and parameter estimation by proving a lower bound on the expected regret in terms of the exploration schedule used by any algorithm. Finally, we conduct a numerical study comparing our robust adaptive algorithm to other methods from the adaptive LQR literature, and demonstrate the flexibility of our proposed method by extending it to a demand forecasting problem subject to state constraints. Summary Variable selection for recovering sparsity in nonadditive and nonparametric models with high-dimensional variables has been challenging. This problem becomes even more difficult due to complications in modeling unknown interaction terms among high-dimensional variables. There is currently no variable selection method to overcome these limitations. Hence, in this article we propose a variable selection approach that is developed by connecting a kernel machine with the nonparametric regression model. The advantages of our approach are that it can: (i) recover the sparsity; (ii) automatically model unknown and complicated interactions; (iii) connect with several existing approaches including linear nonnegative garrote and multiple kernel learning; and (iv) provide flexibility for both additive and nonadditive nonparametric models. Our approach can be viewed as a nonlinear version of a nonnegative garrote method. We model the smoothing function by a Least Squares Kernel Machine (LSKM) and construct the nonnegative garrote objective function as the function of the sparse scale parameters of kernel machine to recover sparsity of input variables whose relevances to the response are measured by the scale parameters. We also provide the asymptotic properties of our approach. We show that sparsistency is satisfied with consistent initial kernel function coefficients under certain conditions. An efficient coordinate descent backfitting algorithm is developed. A resampling procedure for our variable selection methodology is also proposed to improve the power. Recent advances in the direct computation of Lyapunov functions using convex optimization make it possible to efficiently evaluate regions of stability for smooth nonlinear systems. Here we present a feedback motion planning algorithm which uses these results to efficiently combine locally-valid linear quadratic regulator (LQR) controllers into a nonlinear feedback policy which probabilistically covers the reachable area of a (bounded) state space with a region of stability, certifying that all initial conditions that are capable of reaching the goal will stabilize to the goal. We carefully investigate the algorithm on a two-dimensional model system and discuss the potential for the control of more complicated underactuated control problems like bipedal walking. An omnidirectional closed-loop gait based on the direct feedback of orientation deviation estimates is presented in this paper. At the core of the gait is an open-loop central pattern generator. The orientation feedback is derived from a 3D nonlinear attitude estimator, and split into the relevant angular deviations in the sagittal and lateral planes using the concept of fused angles. These angular deviations from expected are used by a number of independent feedback mechanisms, including one that controls timing, to perform stabilising corrective actions. The tuning of the feedback mechanisms is discussed, including an LQR-based approach for tuning the transient sagittal response. The actuator control scheme and robot pose representations in use are also addressed. Experimental results on an igus Humanoid Open Platform demonstrate the core concept of this paper, that if the sensor management and feedback chains are carefully constructed, comparatively simple model-free and robot-agnostic feedback mechanisms can successfully stabilise a generic bipedal gait. Evolutionary algorithms have previously shown promise in generating controllers for legged robots. Multiple evaluations across many evolutionary generations are typically required — simulators are frequently used to accommodate this. However, performance degradation is frequently observed when transferring controllers from simulation to reality due to inconsistencies between the two. In this paper we demonstrate a testbed that permits repeated, direct evolution of hexapod controllers as a closed-loop system. The testbed uses a two-stage evolutionary process. In stage 1, a multi-objective evolutionary algorithm spreads a population of controllers across a space of desirable criteria. The second stage allows for specific criteria to be selected for on a per-mission basis, with promising initial controller parameters taken from the first stage. As the optimisation occurs directly on the robot, performance is guaranteed. Furthermore, controllers can be made specific to irregularities in e.g., motor wear, and robot mass distribution, creating controllers that are sensitive to the hardware state of the individual robot. We present a fully adaptive numerical scheme for evolutionary PDEs in Cartesian geometry based on a second-order finite volume discretization. A multiresolution strategy allows local grid refinement while controlling the approximation error in space. For time discretization we use an explicit Runge-Kutta scheme of second-order with a scale-dependent time step. On the finest scale the size of the time step is imposed by the stability condition of the explicit scheme. On larger scales, the time step can be increased without violating the stability requirement of the explicit scheme. The implementation uses a dynamic tree data structure. Numerical validations for test problems in one space dimension demonstrate the efficiency and accuracy of the local time-stepping scheme with respect to both multiresolution scheme with global time stepping and finite volume scheme on a regular grid. Fully adaptive three-dimensional computations for reaction-diffusion equations illustrate the additional speed-up of the local time stepping for a thermo-diffusive flame instability. We consider the problem of learning a structured multi-task regression, where the output consists of multiple responses that are related by a graph and the correlated response variables are dependent on the common inputs in a sparse but synergistic manner. Previous methods such as l1 l2-regularized multi-task regression assume that all of the output variables are equally related to the inputs, although in many real-world problems, outputs are related in a complex manner. In this paper, we propose graph-guided fused lasso (GFlasso) for structured multi-task regression that exploits the graph structure over the output variables. We introduce a novel penalty function based on fusion penalty to encourage highly correlated outputs to share a common set of relevant inputs. In addition, we propose a simple yet efficient proximal-gradient method for optimizing GFlasso that can also be applied to any optimization problems with a convex smooth loss and the general class of fusion penalty defined on arbitrary graph structures. By exploiting the structure of the non-smooth ''fusion penalty'', our method achieves a faster convergence rate than the standard first-order method, sub-gradient method, and is significantly more scalable than the widely adopted second-order cone-programming and quadratic-programming formulations. In addition, we provide an analysis of the consistency property of the GFlasso model. Experimental results not only demonstrate the superiority of GFlasso over the standard lasso but also show the efficiency and scalability of our proximal-gradient method. 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.