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Numerical solution of optimal control problems by direct collocation’, Ed
 In Optimal Control  Calculus of Variation, Optimal Control Theory and Numerical Methods, 111, 129143, International Series of Numerical Mathematics, Birkhäuser
, 1993
"... By an appropriate discretization of control and state variables, a constrained optimal control problem is transformed into a finite dimensional nonlinear program which can be solved by standard SQPmethods [10]. Convergence properties of the discretization are derived. From a solution of this method ..."
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Cited by 41 (2 self)
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By an appropriate discretization of control and state variables, a constrained optimal control problem is transformed into a finite dimensional nonlinear program which can be solved by standard SQPmethods [10]. Convergence properties of the discretization are derived. From a solution of this method known as direct collocation, these properties are used to obtain reliable estimates of adjoint variables. In the presence of active state constraints, these estimates can be significantly improved by including the switching structure of the state constraint into the optimization procedure. Two numerical examples are presented. 1 Statement of problems Systems governed by ordinary differential equations arise in many applications as, e. g., in astronautics, aeronautics, robotics, and economics. The task of optimizing these systems leads to the optimal control problems investigated in this paper. The aim is to find a control vector u(t) and the final time tf that minimize the functional
WorstCase Analysis and Optimization of VLSI Circuit Performances
, 1995
"... In this paper, we present a new approach for realistic worstcase analysis of VLSI circuit performances and a novel methodology for circuit performance optimization. Circuit performance measures are modeled as response surfaces of the designable and uncontrollable (noise) parameters. Worstcase anal ..."
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Cited by 19 (1 self)
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In this paper, we present a new approach for realistic worstcase analysis of VLSI circuit performances and a novel methodology for circuit performance optimization. Circuit performance measures are modeled as response surfaces of the designable and uncontrollable (noise) parameters. Worstcase analysis proceeds by first computing the worstcase circuit performance value and then determining the worstcase noise parameter values by solving a nonlinear programming problem. A new circuit optimization technique is developed to find an optimal design point at which all of the circuit specifications are met under worstcase conditions. This worstcase design optimization method is formulated as a constrained multicriteria optimization. The methodologies described in this paper are applied to several VLSI circuits to demonstrate their accuracy and efficiency. Keywords Worstcase analysis, worstcase design optimization. I. Introduction I NEVITABLE fluctuations in the manufacturing proces...
Optimal Control of the Industrial Robot Manutec r3
, 1994
"... Minimum time and minimum energy pointtopoint trajectories for an industrial robot of the type Manutec r3 are computed subject to state constraints on the angular velocities. The numerical solutions of these optimal control problems are obtained in an efficient way by a combination of a direct coll ..."
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Cited by 8 (2 self)
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Minimum time and minimum energy pointtopoint trajectories for an industrial robot of the type Manutec r3 are computed subject to state constraints on the angular velocities. The numerical solutions of these optimal control problems are obtained in an efficient way by a combination of a direct collocation and an indirect multiple shooting method. This combination links the benefits of both approaches: A large domain of convergence and a highly accurate solution. The numerical results show that the constraints on the angular velocities become active during large parts of the time optimal motion. But the resulting stress on the links can be significantly reduced by a minimum energy trajectory that is only about ten percent slower than the minimum time trajectory. As a byproduct, the reliability of the direct collocation method in estimating adjoint variables and the efficiency of the combination of direct collocation and multiple shooting is demonstrated. The highly accurate solutions ...
A New Technique For Inconsistent QP Problems In The SQP Method
 University at Darmstadt, Department of Mathematics, preprint 1561, Darmstadt
, 1993
"... Successful treatment of inconsistent QP problems is of major importance in the SQP method, since such occur quite often even for well behaved nonlinear programming problems. This paper presents a new technique for regularizing inconsistent QP problems, which compromises in its properties between the ..."
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Cited by 7 (2 self)
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Successful treatment of inconsistent QP problems is of major importance in the SQP method, since such occur quite often even for well behaved nonlinear programming problems. This paper presents a new technique for regularizing inconsistent QP problems, which compromises in its properties between the simple technique of Pantoja and Mayne [34] and the highly successful, but expensive one of Tone [44]. Global convergence of a corresponding algorithm is shown under reasonable weak conditions. Numerical results are reported which show that this technique, combined with a special method for the case of regular subproblems, is quite competitive to highly appreciated established ones. Key words: sequential quadratic programming, SQP method, nonlinear programming AMS(MOS) subject classification: primary 90C30, secondary 65K05 1 NOTATION Superscripts on a vector denote elements of sequences. All vectors are column vectors. For a vectorvalued function g rg(x) denotes the transposed Jacobian eval...
Bivariate density estimation with an application to survival data
 Journal of Computational and Graphical Statistics
, 1997
"... A procedure for estimating a bivariate density based on data that may be censored is described. After the data are transformed to the unit square, the bivariate density is estimated using linear splines and their tensor products. The combined procedure yields an estimate of the bivariate density on ..."
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Cited by 6 (3 self)
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A procedure for estimating a bivariate density based on data that may be censored is described. After the data are transformed to the unit square, the bivariate density is estimated using linear splines and their tensor products. The combined procedure yields an estimate of the bivariate density on the original scale, which mayprovide insight about the dependence structure. The procedure can also be used to estimate densities that are known to be symmetric and to test for independence. Key words: Censoring � Correlated data � Splines � Test of independence. 1
Solving Optimal Control and PursuitEvasion Game Problems of High Complexity
, 1992
"... Optimal control problems which describe realistic technical applications exhibit various features of complexity. First, the consideration of inequality constraints leads to optimal solutions with highly complex switching structures including bangbang, singular, and control and stateconstrained su ..."
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Cited by 4 (1 self)
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Optimal control problems which describe realistic technical applications exhibit various features of complexity. First, the consideration of inequality constraints leads to optimal solutions with highly complex switching structures including bangbang, singular, and control and stateconstrained subarcs. In addition, also isolated boundary points may occur. Techniques are surveyed for the computation of optimal trajectories with multiple subarcs. If the precise computation of the switching structure holds the spotlight, the indirect multiple shooting method is top quality. Second, the differential equations describing the dynamics may be so complicated that they have to be generated by a computer program. In this case, direct methods such as direct collocation are generally superior. Third, the task is often given in applications to solve many optimal control problems, either for parameter homotopies in the course of the solution process itself or for sensitivity investigations of the...
Simulated Annealing Algorithm with MultiMolecule: an Approach to Analog Synthesis
, 1996
"... The research presented in this paper is concerned with the design automation of analog integrated circuits, simply called analog synthesis. A new algorithm, namely a simulated annealing algorithm with multimolecule (SAMM), is proposed to solve analog synthesis problems. Besides inheriting the globa ..."
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Cited by 2 (0 self)
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The research presented in this paper is concerned with the design automation of analog integrated circuits, simply called analog synthesis. A new algorithm, namely a simulated annealing algorithm with multimolecule (SAMM), is proposed to solve analog synthesis problems. Besides inheriting the global convergence of the traditional simulated annealing algorithm (SA), SAMM can avoid the excessively timeconsuming final iterations of SA, which makes it more efficient and suitable for analog synthesis. Several analog synthesis examples are also given in this paper to demonstrate the efficiency and validity of SAMM.
Optimal Pilot Decisions and Flight Trajectories in Air Combat
, 2004
"... The thesis concerns the analysis and synthesis of pilot decisionmaking and the design of optimal flight trajectories. In the synthesis framework, the methodology of influence diagrams is applied for modeling and simulating the maneuvering decision process of the pilot in oneonone air combat. T ..."
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Cited by 1 (0 self)
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The thesis concerns the analysis and synthesis of pilot decisionmaking and the design of optimal flight trajectories. In the synthesis framework, the methodology of influence diagrams is applied for modeling and simulating the maneuvering decision process of the pilot in oneonone air combat. The influence diagram representations describing the maneuvering decision in a one sided optimization setting and in a game setting are constructed. The synthesis of team decisionmaking in a multiplayer air combat is tackled by formulating a decision theoretical information prioritization approach based on a value function and interval analysis. It gives the team optimal sequence of tactical data that is transmitted between cooperating air units for improving the situation awareness of the friendly pilots in the best possible way. In the optimal trajectory planning framework, an approach towards the interactive automated solution of deterministic aircraft trajectory optimization problems is presented. It offers design principles for a trajectory optimization software that can be operated automatically by a nonexpert user. In addition, the representation of preferences and uncertainties in trajectory optimization is considered by developing a multistage influence diagram that describes a series of the maneuvering decisions in a oneonone air combat setting. This influence diagram representation as well as the synthesis elaborations provide seminal ways to treat uncertainties in air combat modeling.
Optimization of Dynamic Systems in Industrial Applications
 Proc. 2nd European Congress on Intelligent Techniques and Soft Computing
, 1994
"... this paper, we focus on technical processes which can be described by dynamic systems, i. e., by the solution of initial or boundary value problems in ordinary differential or differential algebraic equations. In this paper, several recently developed efficient numerical methods are presented. Their ..."
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Cited by 1 (1 self)
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this paper, we focus on technical processes which can be described by dynamic systems, i. e., by the solution of initial or boundary value problems in ordinary differential or differential algebraic equations. In this paper, several recently developed efficient numerical methods are presented. Their impact in engineering is demonstrated by their application to three different classes of problems, namely trajectory optimization, parameter estimation and design optimization.
Optimal control of a magnetic bearing without bias and saturating voltages
 Optimal Control Applications and Methods
, 1998
"... Conventional Active Magnetic Bearings (AMB) are operated using a bias current (or flux) to achieve greater linearity and dynamic capability. Bias, however, results in undesirable rotating losses and consequent rotor heating. While control without bias flux is an attractive alternative, it is conside ..."
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Cited by 1 (1 self)
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Conventional Active Magnetic Bearings (AMB) are operated using a bias current (or flux) to achieve greater linearity and dynamic capability. Bias, however, results in undesirable rotating losses and consequent rotor heating. While control without bias flux is an attractive alternative, it is considerably more complex due to both force slew rate limitations and actuator nonlinearity. In this paper, optimal control of a magnetic bearing without bias is investigated. A single degreeoffreedom system consisting of a mass and two opposing electromagnets is considered. The optimal control problem is examined for a cost function that penalizes both poor regulation and rotational energy lost. Though a standard optimization procedure does not directly yield an analytical solution, it does show that the optimal control is always bangbang including possibly a singular arc. First, the minimum time problem is solved for a simple switching law in three dimensional state space. A nonstandard, physicsbased approach is then employed to obtain an optimal solution for the general problem. The final result is an optimal variable structure feedback controller. This result provides a benchmark which can be used for evaluation of the performance of a practical feedback controller designed via other methods. The practical controller will be designed to support a flexible rotor and achieve robustness and optimally reject disturbance. This result may also be applied to many other applications which contain opposing quadratic actuators. KEY WORDS: active magnetic bearing; opposing quadratic actuators; nonlinear; constrained control; timestate optimization; bangbang; singular arc.