scholarly journals Robust Parametric Control of Spacecraft Rendezvous

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Dake Gu ◽  
Yindong Liu
Keyword(s):  
Cost Function ◽  
Relative Motion ◽  
Model Uncertainty ◽  
Optimization Problem ◽  
Control Law ◽  
Eigenstructure Assignment ◽  
Parametric Control ◽  
Autonomous Rendezvous ◽  
Simulation Results ◽  
The Cost

This paper proposes a method to design the robust parametric control for autonomous rendezvous of spacecrafts with the inertial information with uncertainty. We consider model uncertainty of traditional C-W equation to formulate the dynamic model of the relative motion. Based on eigenstructure assignment and model reference theory, a concise control law for spacecraft rendezvous is proposed which could be fixed through solving an optimization problem. The cost function considers the stabilization of the system and other performances. Simulation results illustrate the robustness and effectiveness of the proposed control.

Suboptimality of a Decentralized Feedback Control Law

1999 ◽  
Vol 121 (2) ◽  
pp. 305-308
Author(s):  
El Kebi´r Boukas ◽  
A. Swierniak ◽  
H. Yang
Keyword(s):  
Feedback Control ◽  
Linear System ◽  
Upper Bound ◽  
Optimization Problem ◽  
Control Law ◽  
Relative Cost ◽  
Numerical Example ◽  
Uncertain Linear System ◽  
The Absolute ◽  
The Cost

In this note, a new estimating method for the upper bound of the cost of the uncertain linear system used by Trinh and Aldeen (1993) is proposed. We have also estimated the absolute cost loss and relative cost loss of this kind of optimization problem. To show the usefulness of our results a numerical example has been developed.

scholarly journals Proliferation of non-linear excitations in the piecewise-linear perceptron

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Antonio Sclocchi ◽  
Pierfrancesco Urbani
Keyword(s):  
Cost Function ◽  
Optimization Problem ◽  
Hard Spheres ◽  
Piecewise Linear ◽  
Power Laws ◽  
Universality Class ◽  
Local Minima ◽  
Convex Optimization Problem ◽  
Non Linear ◽  
The Cost

We investigate the properties of local minima of the energy landscape of a continuous non-convex optimization problem, the spherical perceptron with piecewise linear cost function and show that they are critical, marginally stable and displaying a set of pseudogaps, singularities and non-linear excitations whose properties appear to be in the same universality class of jammed packings of hard spheres. The piecewise linear perceptron problem appears as an evolution of the purely linear perceptron optimization problem that has been recently investigated in [1]. Its cost function contains two non-analytic points where the derivative has a jump. Correspondingly, in the non-convex/glassy phase, these two points give rise to four pseudogaps in the force distribution and this induces four power laws in the gap distribution as well. In addition one can define an extended notion of isostaticity and show that local minima appear again to be isostatic in this phase. We believe that our results generalize naturally to more complex cases with a proliferation of non-linear excitations as the number of non-analytic points in the cost function is increased.

scholarly journals Gradient Span Analysis Method: Application to the Multipoint Aerodynamic Shape Optimization of a Turbine Cascade

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
Hadrien Montanelli ◽  
Marc Montagnac ◽  
François Gallard
Keyword(s):  
Cost Function ◽  
Optimization Problem ◽  
Stokes Equations ◽  
Single Point ◽  
Operating Conditions ◽  
Design Variables ◽  
Wide Range ◽  
The Cost ◽  
Multipoint Optimization ◽  
Utopia Point

This paper presents the application of the gradient span analysis (GSA) method to the multipoint optimization of the two-dimensional LS89 turbine distributor. The cost function (total pressure loss) and the constraint (mass flow rate) are computed from the resolution of the Reynolds-averaged Navier–Stokes equations. The penalty method is used to replace the constrained optimization problem with an unconstrained problem. The optimization process is steered by a gradient-based quasi-Newton algorithm. The gradient of the cost function with respect to design variables is obtained with the discrete adjoint method, which ensures an efficient computation time independent of the number of design variables. The GSA method gives a minimal set of operating conditions to insert into the weighted sum model to solve the multipoint optimization problem. The weights associated to these conditions are computed with the utopia point method. The single-point optimization at the nominal condition and the multipoint optimization over a wide range of conditions of the LS89 blade are compared. The comparison shows the strong advantages of the multipoint optimization with the GSA method and utopia-point weighting over the traditional single-point optimization.

scholarly journals Linear Quadratic Optimal Control Design: A Novel Approach Based on Krotov Conditions

2019 ◽  
Vol 2019 ◽  
pp. 1-17
Author(s):  
Avinash Kumar ◽  
Tushar Jain
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Riccati Equation ◽  
Nonconvex Optimization ◽  
Optimization Problem ◽  
A Priori ◽  
Control Law ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Quadratic Optimal Control

This paper revisits the problem of synthesizing the optimal control law for linear systems with a quadratic cost. For this problem, traditionally, the state feedback gain matrix of the optimal controller is computed by solving the Riccati equation, which is primarily obtained using calculus of variations- (CoV-) based and Hamilton–Jacobi–Bellman (HJB) equation-based approaches. To obtain the Riccati equation, these approaches require some assumptions in the solution procedure; that is, the former approach requires the notion of costates and then their relationship with states is exploited to obtain the closed-form expression of the optimal control law, while the latter requires a priori knowledge regarding the optimal cost function. In this paper, we propose a novel method for computing linear quadratic optimal control laws by using the global optimal control framework introduced by V. F. Krotov. As shall be illustrated in this article, this framework does not require the notion of costates and any a priori information regarding the optimal cost function. Nevertheless, using this framework, the optimal control problem gets translated to a nonconvex optimization problem. The novelty of the proposed method lies in transforming this nonconvex optimization problem into a convex problem. The convexity imposition results in a linear matrix inequality (LMI), whose analysis is reported in this work. Furthermore, this LMI reduces to the Riccati equation upon imposing optimality requirements. The insights along with the future directions of the work are presented and gathered at appropriate locations in this article. Finally, numerical results are provided to demonstrate the proposed methodology.

Predictive Control Based on Fuzzy Expert PID Tuning Control

2012 ◽  
Vol 466-467 ◽  
pp. 1207-1211 ◽  
Author(s):  
Zheng Zai Qian ◽  
Gong Cai Xin ◽  
Jin Niu Tao
Keyword(s):  
Predictive Control ◽  
Model Uncertainty ◽  
Adaptive Controller ◽  
Automatic Tuning ◽  
Pid Controllers ◽  
Generalized Predictive Control ◽  
Control Law ◽  
Pid Tuning ◽  
Simulation Results ◽  
Expert Pid

In decade years, several simple methods for the automatic tuning of PID controllers have been proposed. There have been different approaches to the problem of deriving a PID-like adaptive controller. All of these can be classified into two broad categories: model-based; or expert systems. In this paper a new expert adaptive controller is proposed in which the underlying control law is a PID structure. The design is based on the fuzzy logic and the generalized predictive control theory. The proposed controller can be applied to a large class of systems which is model uncertainty or strong non-linearity. Simulation results have also been illustrated. It shows that the proposed expert PID-like controller performed well than generally used PID.

scholarly journals Weak-constraint inverse modeling using HYSPLIT-4 Lagrangian dispersion model and Cross-Appalachian Tracer Experiment (CAPTEX) observations – effect of including model uncertainties on source term estimation

2018 ◽  
Vol 11 (12) ◽  
pp. 5135-5148 ◽  
Author(s):  
Tianfeng Chai ◽  
Ariel Stein ◽  
Fong Ngan
Keyword(s):  
Cost Function ◽  
Inverse Modeling ◽  
Model Uncertainty ◽  
Source Term ◽  
Dispersion Model ◽  
Tracer Experiment ◽  
Inverse System ◽  
Lagrangian Dispersion ◽  
Uncertainty Parameters ◽  
The Cost

Abstract. A Hybrid Single-Particle Lagrangian Integrated Trajectory version 4 (HYSPLIT-4) inverse system that is based on variational data assimilation and a Lagrangian dispersion transfer coefficient matrix (TCM) is evaluated using the Cross-Appalachian Tracer Experiment (CAPTEX) data collected from six controlled releases. For simplicity, the initial tests are applied to release 2, for which the HYSPLIT has the best performance. Before introducing model uncertainty terms that will change with source estimates, the tests using concentration differences in the cost function result in severe underestimation, while those using logarithm concentration differences result in overestimation of the release rate. Adding model uncertainty terms improves results for both choices of the metric variables in the cost function. A cost function normalization scheme is later introduced to avoid spurious minimal source term solutions when using logarithm concentration differences. The scheme is effective in eliminating the spurious solutions and it also helps to improve the release estimates for both choices of the metric variables. The tests also show that calculating logarithm concentration differences generally yields better results than calculating concentration differences, and the estimates are more robust for a reasonable range of model uncertainty parameters. This is further confirmed with nine ensemble HYSPLIT runs in which meteorological fields were generated with varying planetary boundary layer (PBL) schemes. In addition, it is found that the emission estimate using a combined TCM by taking the average or median values of the nine TCMs is similar to the median of the nine estimates using each of the TCMs individually. The inverse system is then applied to the other CAPTEX releases with a fixed set of observational and model uncertainty parameters, and the largest relative error among the six releases is 53.3 %. At last, the system is tested for its capability to find a single source location as well as its source strength. In these tests, the location and strength that yield the best match between the predicted and the observed concentrations are considered as the inverse modeling results. The estimated release rates are mostly not as good as the cases in which the exact release locations are assumed known, but they are all within a factor of 3 for all six releases. However, the estimated location may have large errors.

Kinematic Optimization of the Arm of a Working Machine

2014 ◽  
Author(s):  
Antonio Alba ◽  
Francesco Bucchi ◽  
Francesco Frendo ◽  
Marco Gabiccini
Keyword(s):  
Cost Function ◽  
Optimization Problem ◽  
Link Length ◽  
Weighting Method ◽  
Kinematic Synthesis ◽  
Multi Objective ◽  
Optimization Methodology ◽  
The Cost ◽  
Joint Limits ◽  
Kinematic Optimization

The aim of this work is to develop an optimization methodology for the design of the arm of a small-sized working machine. The workspace and a reference maneuver are firstly defined together with a pre-defined redundant kinematic topology. The kinematic synthesis is framed as a constrained multi-objective problem with respect to link length variables. The constraints consider the capability of the machine to follow the assigned trajectory and to fulfill the joint limits. The cost function incorporates the solution of the inverse kinematics and uses several indices, e.g., total link lengths, manipulability, energy consumption. The multi-objective optimization problem is solved employing the weighting method, converting the initial problem into a single-objective one. The final scalar cost function is minimized by the Nelder-Mead method. On the basis of the outcomes of numerical simulations, the effectiveness and versatility of the developed procedure for the design of novel working machine arms is verified.

Optimal control of nonlinear systems with dynamic programming

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Isaac Tawiah ◽  
Yinglei Song
Keyword(s):  
Optimal Control ◽  
Optimization Problem ◽  
Optimal Control Problems ◽  
Optimal Solution ◽  
Functional Approach ◽  
Equality Constraints ◽  
Control Problems ◽  
Iterative Approach ◽  
Simulation Results ◽  
The Cost

Abstract In this paper, a generalized technique for solving a class of nonlinear optimal control problems is proposed. The optimization problem is formulated based on the cost-to-go functional approach and the optimal solution can be obtained by Bellman’s technique. Specifically, a continuous nonlinear system is first discretized and a set of equality constraints can be obtained from the discretization. We show that, under a certain condition, the optimal solution of a problem in this class can be approximated by a solution of the set of equality constraints within any precision and the system is guaranteed to be stable under a control signal obtained from the solution. An iterative approach is then applied to numerically solve the set of equality constraints. The technique is tested on a nonlinear control problem from the class and simulation results show that the approach is not only effective but also leads to a fast convergence and accurate optimal solution.

Underdetermined Blind Sources Separation Based on Nonnegative Tri-Matrix Factorization

2014 ◽  
Vol 971-973 ◽  
pp. 1843-1846 ◽  
Author(s):  
Jing Zhang ◽  
Ye Zhang
Keyword(s):  
Cost Function ◽  
Matrix Factorization ◽  
Simulation Results ◽  
Update Rules ◽  
The Cost ◽  
Source Signals ◽  
Multiplicative Update

In this paper, a nonnegative tri-Matrix factorization (NTMF) algorithm is proposed for underdetermined blind sources separation with the assumption of that the source signals are nonnegative and sparse. By incorporating the regularization and sparse penalty into the cost function, a novel multiplicative update rules is proposed to solve the problem of UBSS based on NTMF. The simulation results are presented to show the validity and competitive performances of the proposed algorithm.

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