{"title":"Finite difference and simultaneous perturbation stochastic approximation with fixed step sizes in case of multiplicative noises","authors":"Alexander Vakhitov","doi":"10.1109/ECC.2014.6862583","DOIUrl":"https://doi.org/10.1109/ECC.2014.6862583","url":null,"abstract":"Simultaneous perturbation stochastic approximation method was shown to be superior over finite difference (Kiefer-Wolfowitz) method in case of unknown but bounded additive measurement noise. This paper is devoted to analysis of the behaviour of these methods in case of multiplicative noise and fixed step sizes. It gives theoretical bounds for the mean squared error and variance after finite number of iiterations for finite difference and simultaneous perturbation methods. The multiplicative noise is present in cost functions in many different fields, and ability to cope with them is a good side of for an optimization method. Fixed step size algorithms are easy to implement and analyze as well as can be used in nonstationary optimization problems. The simulation includes the case when the algorithms' parameters are chosen as theoretically optimal and the case when they are chosen as practically giving the best results after finite number of iterations. Comparative analysis shows similar performance of both methods in terms of mean squared error and slightly better performance of SPSA in terms of variance. Simulation results are provided to illustrate the theoretical contributions.","PeriodicalId":251538,"journal":{"name":"2014 European Control Conference (ECC)","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134464141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Fast simulation of nonlinear dynamical systems for application in reduced order modelling","authors":"S. A. Nahvi, M. A. Bazaz, M. Nabi, S. Janardhanan","doi":"10.1109/ECC.2014.6862178","DOIUrl":"https://doi.org/10.1109/ECC.2014.6862178","url":null,"abstract":"The Trajectory piecewise linear (TPWL) representation of nonlinear dynamical systems requires an a-priori solution of the nonlinear system trajectory. This paper proposes a new algorithm for finding an approximate nonlinear system trajectory to reduce the computational burden of the TPWL process. Additionally, the new algorithm has an error assessment feature that provides a less heuristic alternative to the conventional methods. It is shown that the TPWL model can be obtained with lesser user intervention using the new algorithm and also comprises of a smaller number of constituent linear systems.","PeriodicalId":251538,"journal":{"name":"2014 European Control Conference (ECC)","volume":"133 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134502342","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
P. Geoffroy, O. Bordron, N. Mansard, M. Raison, O. Stasse, T. Bretl
{"title":"A two-stage suboptimal approximation for variable compliance and torque control","authors":"P. Geoffroy, O. Bordron, N. Mansard, M. Raison, O. Stasse, T. Bretl","doi":"10.1109/ECC.2014.6862557","DOIUrl":"https://doi.org/10.1109/ECC.2014.6862557","url":null,"abstract":"Variable-stiffness actuator is a very appealing mechatronic design that combines the efficiency of stiff actuator in free space with the consistency of elastic actuation in contact. The control of such an actuation system remains a challenge due to its non-linearity and by the fact that it doubles the number of control inputs. In this paper, we propose an original control strategy to compute the whole-body movement of a complex variable-stiffness robot during dynamic task execution. Operational space control is first used to compute both the joint torque and stiffness from operational references. A non-linear model-predictive controller is then proposed to track at higher frequency these references on each joint separately. The effectiveness of this approach is then validated on two models of real actuator with adjustable stiffness, and finally on an explosive motion to make a humanoid robot jump.","PeriodicalId":251538,"journal":{"name":"2014 European Control Conference (ECC)","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133747727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"More efficient interpolating control","authors":"Hoai‐Nam Nguyen, P. Gutman, R. Bourdais","doi":"10.1109/ECC.2014.6862607","DOIUrl":"https://doi.org/10.1109/ECC.2014.6862607","url":null,"abstract":"Recent papers proposed an interpolating control methodology for linear discrete-time systems subject to input and state (output) constraints. The main idea of the approach is to blend a local high-gain optimal controller with a global low-gain vertex controller via interpolation. At each time instant, two linear programming problems of relatively small dimensions are solved online. The approach can be seen as an alternative to optimization based control schemes such as model predictive control. However for high-dimensional systems, computing a feasible set for vertex control is generally challenging, and the ability to determine the feasible set limits the applicability of the approach. The aim of the present paper is to propose a way which removes this difficulty, yields further significant improvements on the computational complexity and on the degree of optimality.","PeriodicalId":251538,"journal":{"name":"2014 European Control Conference (ECC)","volume":"170 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115193116","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Robust cooperative control reconfiguration/recovery in multi-agent systems","authors":"Z. Gallehdari, N. Meskin, K. Khorasani","doi":"10.1109/ECC.2014.6862482","DOIUrl":"https://doi.org/10.1109/ECC.2014.6862482","url":null,"abstract":"In this paper, a reconfigurable control protocol for a linear multi-agent system seeking consensus in presence of actuator faults and saturations and environmental disturbances is investigated. Two controllers, namely the healthy controller and the reconfigured controller, are proposed for the healthy system and the system with faulty agents, respectively. The healthy controller is designed off-line and guarantees that the team achieves consensus in presence of environmental disturbances. On the other hand, the reconfigured/recovered controller is designed on-line subject to constrained control signals and based on the information that the fault detection and identification (FDI) module has provided. The FDI information are assumed to be inaccurate, however the bounds on the uncertainties are assumed to be known.","PeriodicalId":251538,"journal":{"name":"2014 European Control Conference (ECC)","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115368544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Minimal time problem for a fed-batch bioreactor with a non admissible singular arc","authors":"T. Bayen, F. Mairet, M. Mazade","doi":"10.1109/ECC.2014.6862444","DOIUrl":"https://doi.org/10.1109/ECC.2014.6862444","url":null,"abstract":"In this paper, we consider an optimal control problem for a system describing a fed-batch bioreactor with one species and one substrate. Our aim is to find an optimal feedback control in order to steer the system to a given target in minimal time. The growth function is of Haldane type implying the existence of a singular arc. Unlike many studies on the minimal time problem governed by an affine system w.r.t. the control with one input, we assume that the singular arc is non-necessary controllable. This brings interesting issues in terms of optimal synthesis. Thanks to the Pontryagin Maximum Principle, we provide the optimal synthesis of the problem, It turns out that singular extremal trajectories are no longer optimal on a subset of the singular arc.","PeriodicalId":251538,"journal":{"name":"2014 European Control Conference (ECC)","volume":"158 6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115511440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Parameter Set-mapping using kernel-based PCA for linear parameter-varying systems","authors":"S. Z. Rizvi, J. Mohammadpour, R. Tóth, N. Meskin","doi":"10.1109/ECC.2014.6862571","DOIUrl":"https://doi.org/10.1109/ECC.2014.6862571","url":null,"abstract":"This paper proposes a method for reduction of scheduling dependency in linear parameter-varying (LPV) systems. In particular, both the dimension of the scheduling variable and the corresponding scheduling region are shrunk using kernel-based principal component analysis (PCA). Kernel PCA corresponds to linear PCA that is performed in a high-dimensional feature space, allowing the extension of linear PCA to nonlinear dimensionality reduction. Hence, it enables the reduction of complicated coefficient dependencies which cannot be simplified in a linear subspace, giving kernel PCA an advantage over other linear techniques. This corresponds to mapping the original scheduling variables to a set of lower dimensional variables via a nonlinear mapping. However, to recover the original coefficient functions of the model, this nonlinear mapping is needed to be inverted. Such an inversion is not straightforward. The reduced scheduling variables are a nonlinear expansion of the original scheduling variables into a high-dimensional feature space, an inverse mapping for which is not available. Therefore, we cannot generally assert that such an expansion has a “pre-image” in the original scheduling region. While certain pre-image approximation algorithms are found in the literature for Gaussian kernel-based PCA, we aim to generalize the pre-image estimation algorithm to other commonly used kernels, and formulate an iterative pre-image estimation rule. Finally, we consider the case study of a physical system described by an LPV model and compare the performance of linear and kernel PCA-based LPV model reduction.","PeriodicalId":251538,"journal":{"name":"2014 European Control Conference (ECC)","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124297498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Sliding mode based attitude and acceleration controller for a velocity-varying skid-to-turn missile","authors":"Yongwoo Lee, Youdan Kim, G. Moon, Byung-Eul Jun","doi":"10.1109/ECC.2014.6862251","DOIUrl":"https://doi.org/10.1109/ECC.2014.6862251","url":null,"abstract":"Sliding mode based roll-pitch-yaw integrated attitude and acceleration controller for a fin-controlled skid-to-turn(STT) missile is proposed. In terms of aerodynamics, the missile model has severe nonlinearities and coupling effect between input channels and roll-pitch-yaw angles that make the controller design challenging. Moreover, the controller should be designed for the entire flight envelope consisting of boost-phase and gliding-phase where rapid velocity variation exists, and therefore parametric robustness with respect to rapid velocity change is strongly required. The attitude autopilot controls the Euler angles of the missile, and is configured as a single-loop. On the other hand, the acceleration autopilot, which is of two-loop structure, is used for the control of STT maneuver. The proposed autopilots use multiple sliding surfaces to generate control inputs for multiple channels simultaneously. Numerical simulation is performed to verify the performance of the proposed controllers.","PeriodicalId":251538,"journal":{"name":"2014 European Control Conference (ECC)","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114637388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"ℋ2 optimal output feedback control for a general discrete-time system","authors":"S. Tudor, C. Oara","doi":"10.1109/ECC.2014.6862331","DOIUrl":"https://doi.org/10.1109/ECC.2014.6862331","url":null,"abstract":"For a generalized discrete-time system, possibly improper or polynomial, we give realization based formulas for the ℋ2 optimal output feedback controller, under the same general hypotheses as in the proper case. The solution is provided in term of two descriptor algebraic Riccati equations and features the same elegant simplicity as the standard case.","PeriodicalId":251538,"journal":{"name":"2014 European Control Conference (ECC)","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114932942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Evaluation of the NEPSAC nonlinear predictive controller on a thermal process","authors":"R. D. De Keyser, Andres Hernandez","doi":"10.1109/ECC.2014.6862319","DOIUrl":"https://doi.org/10.1109/ECC.2014.6862319","url":null,"abstract":"Nonlinear dynamics are commonly encountered in industrial applications, where manufacturing of higher quality products very often requires that the process works within a wide range of operating conditions close to the boundaries. Nonlinear Model Predictive Control (NMPC) appears as a solution due to its capability to find optimal control actions for the case of nonlinear processes with constraints. In this contribution, the control problem is solved using the Nonlinear Extended Prediction Self-Adaptive Control (NEPSAC) approach to model predictive control (MPC), which besides of being a fast algorithm also avoids explicit local linearization by directly using the nonlinear model for prediction. The effectiveness of the mentioned nonlinear controller and the procedure to express a nonlinear model suitable for prediction is illustrated on a simulation example of a highly nonlinear thermal process. Furthermore, the benefits of NEPSAC are clearly shown by comparing its performance to linear controllers such as linear MPC, PI and PID controllers.","PeriodicalId":251538,"journal":{"name":"2014 European Control Conference (ECC)","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116998246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}