http://www.ifac-papersonline.net/ en Copyright 09:21 AM Tuesday 21, 2013 IFAC-PapersOnline http://www.ifacpapersonline.com 09:21 AM Tuesday 21, 2013 09:21 AM Tuesday 21, 2013 ET webmaster@ifac-papersonline.net webmaster@ifac-papersonline.net http://www.ifac-papersonline.net/Detailed/41872.html 04:00 PM Wednesday 31, 1969 http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/41873.html 04:00 PM Wednesday 31, 1969 We introduce the concept of Hamiltonian potential function for noncooperative openloop differential games and characterise necessary and sufficient conditions for its existence. We also identify a class of games admitting a Hamiltonian potential and illustrate appropriate examples pertaining to oligopoly games where price or quantity competition goes along with non-cooperative investments either in advertising or in R&D, so as to provide a plausible intuitive interpretation of the meaning of the Hamiltonian potential. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/41874.html 04:00 PM Wednesday 31, 1969 In this article we extend classical deterministic control problems towards stochastic networks. A certain class of such stochastic discrete control problems with finite time horizon is introduced. Algorithms for solving the considered class of problems via the theory of Markov processes and dynamic programming are proposed. We apply the time-expanded network method and present complexity results of the constructive algorithm. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/41875.html 04:00 PM Wednesday 31, 1969 In this paper we discuss the problem of trajectory tracking of non control affine nonlinear systems. The main idea is to approximate the non control affine system by a special class of nonlinear systems, the so called extended Hammerstein systems (EHS). The control affine dynamic part of the EHS is computed such that an optimal control problem and therefore the robustifying feedback part of the tracking controller is already solved in the transformation process. Therefore no positive definite solution of the HJE needs to be computed since it gets a design parameter. The resulting system is then controlled by a trajectory tracking algorithm which ensures robustness against input disturbances and system uncertainties as well. A simulation example shows the efficiency of the proposed method. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/41876.html 04:00 PM Wednesday 31, 1969 In this paper we propose two smooth optimization methods, one that can stabilize a system, and the other that can perform a stabilization as well as solve the optimal H2-norm design problem. For both methods, we make use of the smoothed spectral abscissa, a stabilization measure which originates from the inversion of an H2-norm type function, and that behaves as a smooth approximation of the spectral abscissa. In this way, we can set up an optimization framework in which a stabilizing point can efficiently be found. Taking advantage of its computation via Lyapunov equations, we derive computationally attractive formulae for the first-order and second-order derivatives of this smooth objective, which allows for the use of standard gradient- or Hessian-based optimization techniques. A second optimization framework, also involving the smoothed spectral abscissa, can be designed to deal with the H2-norm synthesis. This method has the advantage that it is not necessary to find a stable point for the system on beforehand, as the stabilization is done simultaneously with the actual minimization of the H2-norm. We apply the discussed methods to the class of systems with low-order, or fixed-order, feedback laws, where the number of controller parameters is smaller than the dimension of the plant. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/41877.html 04:00 PM Wednesday 31, 1969 A new methodology for the design of control systems for real time applications is presented. It is proposed to have a first stage of assisted design of nominal systems with simulation based verification of the achieved performances. The control algorithm will then be improved by robustification to reproduce as good as possible the performances obtained in simulation on the real time process. Finally, a supervisor is implemented to optimize the thermo-energetic process and to compute the best choice for the reference signals. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/41878.html 04:00 PM Wednesday 31, 1969 A linear time-dependent controlled system with given time-dependent acceleration state constraints is considered. Due to such constraints, this system becomes inherently nonlinear. For constant acceleration constraints this difficulty can be circumvented by replacing state constraints with control constraints at the expense of reduced control performance. For time-dependent acceleration constraints this method may fail. In this paper a novel replacing rule is proposed and its success in respecting the constraints and enhancing control performance is illustrated by examples of pursuit-evasion problems. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/41879.html 04:00 PM Wednesday 31, 1969 Semi-infinite programming (SIP) problems arise in several engineering areas such as, for example, robotic trajectory planning, production planning, digital filter design and air pollution control. In spite of being an active research area with many seminal works it lacks available software that could be used by the research community. The only exceptions are the fseminf MATLAB function, available in the Optimization Toolbox, and the NSIPS solver, but neither of them provide an implementation of a method belonging to the well known reduction type class. This paper proposes an implementation of a reduction type algorithm base on a penalty technique and provides a compare between several well known penalty functions. The provided numerical results with a significant number of SIP test problems are reported as performance profiles. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/41880.html 04:00 PM Wednesday 31, 1969 Efficient dedicated methods have been developed for H∞.controller synthesis. However, such methods compute a full order controller which has often to be reduced to be implemented. Solving the reduced order H∞ problem is a hard task, as the corresponding optimization problem is non convex, due to rank constraints. In this paper, a particle swarm optimization method is used to solve such a problem. Experimental tests have been performed for a pendulum in the cart, showing much than satisfactory results. The computed controller is compared with a classical Hankel reduction of the full order H∞ controller, exhibiting a lower H∞ norm and a more robust behavior against measurement noise. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/41881.html 04:00 PM Wednesday 31, 1969 This paper proposes a multi-quantile approach for solving open-loop continuous-variable discrete-time stochastic dynamic programming problems in systems with non-standard probability distribution functions. Instead of using the expected value of the objective function for building the optimization criterion, the decision maker performs a choice on the decision variables over the objective function value quantiles. The proposed procedure relies on a Monte Carlo simulation of the unknown process input outcomes, associated with an open-loop multiobjective optimization. The optimal control comes from a trade-off analysis that considers, for instance, the risk associated with each policy versus its yield. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/41882.html 04:00 PM Wednesday 31, 1969 This paper examines an economy with a large number of industries, each producing a different good. Technological change follows a Poisson process where firms improve their productivity through investment in R&D. The less there are firms in the economy or the more they can coordinate their actions, the higher their profits. Labor is used in production or R&D. All workers are unionized and their wages depend on relative union bargaining power. If this power is high enough, then there is involuntary unemployment. Both workers and firms lobby the central planner of the economy which affects firms' and unions' market power. The main findings of the paper can be summarized the follows. Unions' and firms' market power decreases the level of income at each moment of time. On the other hand, the greater the firm's share of value added or the higher union wages, more incentives the firm has to increase the productivity of labor through R&D. In this respect, there can be an optimal amount of unions' and firms' market power. Concerning the regulation of relative union bargaining power, the central planner can increase its welfare either (a) by increasing the level of income or (b) by speeding up economic growth. If (a) is more effective than (b), then the central planner eliminates union power altogether to have full employment. On the other hand, if (b) is more effective than (a), then the central planner supports labor unions to promote cost-escaping R&D. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/41883.html 04:00 PM Wednesday 31, 1969 A two-stage game-theoretical model of duopoly and vertical product differentiation is examined. It is assumed, that there are two firms on some industrial market which produce homogeneous product differentiated by quality. The results of the research of a two-stage model of duopoly are presented, when at the first stage companies define quality level and at the second stage they compete in product price. It is supposed that consumers are uniformly distributed. This model was extended to the case when consumers are distributed non-uniformly. The research presents the comparative analysis of results in the case of uniform and non-uniform consumers' distribution. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/41884.html 04:00 PM Wednesday 31, 1969 The paper deals with analysis of optimal control problems arising in models of economic growth. The Pontryagin maximum principle is applied for analysis of the optimal investment problem. Specifically, the research is based on existence results and necessary conditions of optimality in problems with infinite horizon. Properties of Hamiltonian systems are examined for different regimes of optimal control. The existence and uniqueness result is proved for a steady state of the Hamiltonian system. Analysis of properties of eigenvalues and eigenvectors is completed for the linearized system in a neighborhood of the steady state. Description of behavior of the nonlinear Hamiltonian system is provided on the basis of results of the qualitative theory of differential equations. This analysis allows us to outline proportions of the main economic factors and trends of optimal growth in the model. A numerical algorithm for construction of optimal trajectories of economic growth is elaborated on the basis of constructions of backward procedures and conjugation of an approximation linear dynamics with the nonlinear Hamiltonian dynamics. High order precision estimates are obtained for the proposed algorithm. These estimates establish connection between precision parameters in the phase space and precision parameters for functional indices. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/41885.html 04:00 PM Wednesday 31, 1969 We investigate the possibility of using public firms to abate polluting emissions in a Cournot oligopoly where production takes place at constant returns to scale and entails a negative environmental externality. We model the problem as a differential game and investigate (i) the open-loop Nash equilibrium of the Cournot game among profit-seeking firms, showing that such equilibrium is strongly time consistent because firms neglect the externality; (ii) the feedback solution of social planning equilibrium where the industry output is entirely controlled by a benevolent planner aiming at the maximisation of social welfare; and (iii) a mixed setup where at least one firm is public (i.e., controlled by the social planner), while the others remain profit-seeking agents. Our analysis shows the conditions whereby having one public firm as a regulatory instrument suffices to drive the industry to the same levels of output, externality and ultimately also social welfare as under social planning. Intuitively, this is due to constant returns, under which the regulator needs no more than a single firm to compensate for the output distortion due to strategic interaction among Cournot firms. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/41886.html 04:00 PM Wednesday 31, 1969 Turnpike behavior in multi-dimensional dynamic optimization problems is analyzed using maximal-yield endothermic chemical processes as an example. The turnpike process is strikingly simple, although the dynamic equations and the behavior of the other state variables and controls are considerably more complex. This feature characterizes the optimal solutions of a large variety of control problems, and is robust to variations in model specifications and constraints. The simple turnpike behavior is explained in terms of Green's Theorem analysis. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/41887.html 04:00 PM Wednesday 31, 1969 We present new a posteriori error estimates for approximate solutions of optimal control problems. Our approach is based on so-called functional a posteriori error estimates that were derived in the last decade for many elliptic and parabolic boundary value problems. They provide guaranteed two-sided bounds of approximation errors for any conforming approximation of a problem considered. In the paper, we consider optimal control problems with distributed control functions that enter right-hand sides of elliptic type state equations and apply functional a posteriori estimates to approximate solutions of state equations. This procedure leads to guaranteed two-sided estimates for the cost functional and also allows to obtain guaranteed a posteriori estimates for state and control functions. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/41888.html 04:00 PM Wednesday 31, 1969 In this paper we show the Nonlinear Model Predictive Control (NMPC) of an airpath of a diesel engine based on a Linear Parameter Varying (LPV) model. We used databased LPV modelling with real data from a dynamical engine test bench in order to obtain a nonlinear model of high quality. Because of the nonlinearity of the model the quadratic program (QP) of the NMPC needs to be set up afresh at each sampling instant, which is the main difference to standard linear MPC. For solving the QP efficiently, we employ the recently developed online active set as implemented in the software package qpOASES. We tested our controller in simulation on the LPV model identified on a mean value model and results show that the NMPC has a better tracking performance in terms of boost pressure and fresh air mass flow compared to the standard linear MPC approach also under the influence of a model plant mismatch. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/41889.html 04:00 PM Wednesday 31, 1969 This paper is concerned with the design of Model Predictive Control (MPC) for Linear Parameter Varying (LPV) discrete-time systems. Sufficient linear matrix inequality (LMI) conditions are provided for the existence of a path-dependent Lyapunov function which generalizes previous results based on affine parameter-dependent Lyapunov functions. At each sampling time the control law is obtained from a convex optimization problem under LMI constraints. As illustrated by examples, the proposed approach yields less conservative results than other available methods for MPC. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/41890.html 04:00 PM Wednesday 31, 1969 In this paper, a chance constrained nonlinear dynamic optimization problem is considered, which will be investigated by using a moving horizon scheme. In each horizon, the chance constraints will be written (transformed) in terms of those (input) random variables with known probability distributions by using monotonicity relations. Some definitions and properties related to the required monotonicity properties are introduced. For the application problem considered these monotonicity properties hold automatically true. The chance constraints and their gradients are evaluated by computing multivariate normal integrals using direct numerical integration. Numerical experimentation results will also be reported. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/41891.html 04:00 PM Wednesday 31, 1969 When designing a regulator for a specific system, a set of different objectives needs to be evaluated. This is usually done by manual tuning of parameters and evaluation of the step response. In recent years gradient-based multiobjective constraint optimization methods have been successfully applied on this problem while, in this report, a multiobjective genetic algorithm approach is applied. By defining a set of cost-functions in the frequency-domain for different frequency intervals, PID regulator settings for two bench-mark models are identified and successfully evaluated. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/41892.html 04:00 PM Wednesday 31, 1969 In a comprehensive control design approach for flexible mechanic structures, such as lightweight vehicles or aircraft, a vital decision is the positioning and design of actuators and sensors for the control tasks. This paper proposes an optimal placement approach that exploits the special structure of flexible mechanical systems and incorporates controllability/observability based measures as well as further knowledge on actuator and sensor properties. It combines the advantages of state of the art positioning criteria such that a balance between low and high frequency modes is assured and at the same time applicability to complex systems in arbitrary system coordinates is guaranteed. These essential properties are illustrated on a clamped beam. The controlled system is studied in terms of the generalized plant description, as it is common in robust control design. Thus it serves as natural extension to the controller design process later on and enables comprehensive control design optimization at an early stage. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/41893.html 04:00 PM Wednesday 31, 1969 We consider a control constrained Linear Quadratic Optimal Control Problem and a general interior penalty, including the logarithmic penalty, parameterized by ε > 0. The purpose of this work is to find an error estimate for the difference between the optimal control solution uε of the penalized problem and the optimal solution u0 of the original problem. An application of the Implicit Function Theorem is not possible in this context. Although, we will be able to apply the so called Restoration Theorem to obtain the desired results. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/41894.html 04:00 PM Wednesday 31, 1969 In this article various definitions and features of transmission zeros for finite-dimensional systems are represented. Then possibilities to generalize these definitions for infinite-dimensional systems are discussed. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/41895.html 04:00 PM Wednesday 31, 1969 The scope of this work is trajectory optimization for space launcher problems, using Pontryagin's Minimum Principle and an indirect shooting method. Due to aerodynamic forces (drag), the considered problem may involve singular arcs, i.e. flight phases with a non maximal thrust. The chosen physical model uses tabulated data, which hinders the usual method of computing the singular control. We introduce an alternate, less problem dependent method for computing the singular control. Numerical experiments are carried out for several test problems and a typical Ariane 5 mission. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/41896.html 04:00 PM Wednesday 31, 1969 The stability property in a game problem of the approach of a conflict-controlled system to a goal set at a fixed terminal moment is investigated. The notion of a stability defect is introduced for sets in the space of game positions. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif