| 1. |
- Gerdin, Markus, et al.
(författare)
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Global Identifiability of Complex Models, Constructed from Simple Submodels
- 2007
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Ingår i: Modeling, Estimation and Control. - Linköping : Linköping University Electronic Press. - 9783540735694 ; , s. 123-133
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- It is a typical situation in modern modeling that a total model is built up from simpler submodels, or modules, for example residing in a model library. The total model could be quite complex, while the modules are well understood and analysed. A procedure to decide global parameter identifiability for such a collection of model equations of differential-algebraic nature is suggested. It is shown how to make use of the natural modularization of the model structure. Basically, global identifiability is obtained if and only if each module is identifiable, and the connecting signals can be retrieved from the external signals, without knowledge of the values of the parameters.
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| 2. |
- Gerdin, Markus, 1977-, et al.
(författare)
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On Identifiability of Object-Oriented Models
- 2006
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Ingår i: Proceedings of the 14th IFAC Symposium on System Identification. - 9783902661029 ; , s. 820-825
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Konferensbidrag (refereegranskat)abstract
- When estimating unknown parameters, it is important that the model is identifiable so that the parameters can be estimated uniquely. For nonlinear differential-algebraic equation models with polynomial equations, a differential algebra approach to examine identifiability is available. This approach can be slow, so the present paper describes how this method can be modularized for object-oriented models. A characteristic set of equations is computed for components in model libraries, and stored together with the components. When an object-oriented model is built using such models, identifiability can be examined using the stored equations.
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| 3. |
- Gerdin, Markus, et al.
(författare)
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On Identifiability of Object-Oriented Models
- 2005
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- When estimating unknown parameters, it is important that the model is identifiable so that the parameters can be estimated uniquely. For nonlinear differential-algebraic equation models with polynomial equations, a differential algebra approach to examine identifiability is available. This approach can be slow, so the present paper describes how this method can be modularized for object-oriented models. A characteristic set of equations is computed for components in model libraries, and stored together with the components. When an object-oriented model is built using such models, identifiability can be examined using the stored equations.
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| 4. |
- Gerdin, Markus, 1977-, et al.
(författare)
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On Parameter and State Estimation for Linear Differential-Algebraic Equations
- 2007
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Ingår i: Automatica. - Linköping : Elsevier. - 0005-1098 .- 1873-2836. ; 43:3, s. 416-425
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Tidskriftsartikel (refereegranskat)abstract
- The current demand for more complex models has initiated a shift away from state-space models towards models described by differential-algebraic equations (DAEs). These models arise as the natural product of object-oriented modeling languages, such as Modelica. However, the mathematics of DAEs is somewhat more involved than the standard state-space theory. The aim of this work is to present a well-posed description of a linear stochastic differential-algebraic equation and more importantly explain how well-posed estimation problems can be formed. We will consider both the system identification problem and the state estimation problem. Besides providing the necessary theory we will also explain how the procedures can be implemented by means of efficient numerical methods.
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| 5. |
- Gerdin, Markus, 1977-, et al.
(författare)
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Well-Posedness of Filtering Problems for Stochastic Linear DAE Models
- 2005
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Ingår i: Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference. - Linköping : Linköping University Electronic Press. - 0780395670 ; , s. 350-355
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Konferensbidrag (refereegranskat)abstract
- Modern modeling tools often give descriptor or DAE models, i.e., models consisting of a mixture of differential and algebraic relationships. The introduction of stochastic signals into such models in connection with filtering problems raises several questions of well-posedness. The main problem is that the system equations may contain hidden relationships affecting variables defined as white noise. The result might be that certain physical variables get infinite variance or contain formal differentiations of white noise. The paper gives conditions for well-posedness in terms of certain subspaces defined by the system matrices.
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| 6. |
- Glad, Torkel, 1947-
(författare)
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Computing the Settling Time for Nonlinear Step Responses
- 2007
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Ingår i: Proceedings of the 7th IFAC Symposium on Nonlinear Control Systems. - 9783902661289 ; , s. 119-122
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Konferensbidrag (refereegranskat)abstract
- The settling time for the step response of a nonlinear system can be computed using the Poincaré-Dulac normal form. It is then possible to use a simple approximate formula, whose error can be estimated. The data needed can all be calculated from the leading coefficients of series expansions of the Poincaré-Dulac transformation and the equilibrium curve.
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| 7. |
- Glad, Torkel, 1947-, et al.
(författare)
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Controllers for Amplitude Limited Model Error Models
- 2005
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Ingår i: Proceedings of the 16th IFAC World Congress. - Linköping : Linköping University Electronic Press. - 9783902661753 ; , s. 662-662
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Konferensbidrag (refereegranskat)abstract
- In this paper, systems where information about model accuracy is contained in a model error model are considered. The validity of such a model is typically restricted to input signals that are limited in amplitude. It is then natural to require the same amplitude restriction when designing controllers. The resulting implications for controller design are investigated in both the continuous and the discrete time case.
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| 8. |
- Glad, Torkel, 1947-, et al.
(författare)
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Hamilton-Jacobi Equations for Nonlinear Descriptor Systems
- 2006
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Ingår i: Proceedings of the 2006 American Control Conference. - 1424402107 - 1424402093 ; , s. 1027-1031
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Konferensbidrag (refereegranskat)abstract
- Optimal control problems for nonlinear descriptor systems are considered. Anapproach where the descriptor system is conceptually reduced to a state spaceform is compared to an approach where the Hamilton-Jacobi equation is directly formulated for the descriptor system. The two approaches are shown to give essentially the same systems of equations to be solved. A certain unknown function is present only in the second approach but is shown to be computable from the quantities common to both approches.
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| 9. |
- Glad, Torkel, 1947-, et al.
(författare)
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Hamilton-Jacobi Equations for Nonlinear Descriptor Systems
- 2005
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Optimal control problems for nonlinear descriptor systems are considered. Anapproach where the descriptor system is conceptually reduced to a state spaceform is compared to an approach where the Hamilton-Jacobi equation is directly formulated for the descriptor system. The two approaches are shown to give essentially the same systems of equations to be solved. A certain unknown function is present only in the second approach but is shown to be computable from the quantities common to both approches.
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| 10. |
- Glad, Torkel, 1947-, et al.
(författare)
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Mathematical Analysis of the Tippe Top
- 2005
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Ingår i: Regular and Chaotic Dynamics. - : Maik Nauka/Interperiodica. - 1560-3547. ; 10:4, s. 333-362
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Tidskriftsartikel (refereegranskat)abstract
- A rigorous, and possibly complete analysis of the phase space picture of the tippe top solutions for all initial conditions when the top does not jump and all relations between parameters α and γ, is for the first time presented here. It is based on the use the Jellett's integral of motion λ and the analysis of the energy function. Theorems about stability and attractivity of the asymptotic manifold are proved in detail. Lyapunov stability of (periodic) asymptotic solutions with respect to arbitrary perturbations is shown.
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| 11. |
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| 12. |
- Glad, Torkel, 1947-, et al.
(författare)
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Phase Space of Rolling Solutions of the Tippe Top
- 2007
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Ingår i: Symmetry, Integrability and Geometry. - 1815-0659. ; 3, s. 41-55
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Tidskriftsartikel (refereegranskat)abstract
- Equations of motion of an axially symmetric sphere rolling and sliding on a plane are usually taken as model of the tippe top. We study these equations in the nonsliding regime both in the vector notation and in the Euler angle variables when they admit three integrals of motion that are linear and quadratic in momenta. In the Euler angle variables (θ, ϕ, ψ) these integrals give separation equations that have the same structure as the equations of the Lagrange top. It makes it possible to describe the whole space of solutions by representing them in the space of parameters (D, λ, E) being constant values of the integrals of motion.
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| 13. |
- Glad, Torkel, 1947-, et al.
(författare)
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Uncertain LTI-Models for Linear Control Design of Nonlinear Systems
- 2007
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Much attention in robust identification and control has been focused on linear low order models approximating high order linear systems. We consider the more realistic situation with a linear model approximating a non-linear system. We describe how a linear time invariant (LTI) model with unstructured uncertainty, i.e. a "band" of Nyquist curves can be developed using a non-linear model error model. Applying standard linear robust control design to this uncertain LTI model will lead to a (non-linear) closes loop system with performance robustness guarantees (in terms of gain from disturbances to output) well in line with the objectives of the linear design. Clearly the design can be successful only if the linear model is a reasonable good approximation of the system. A particular aspect of the design process is to define a workable definition of "practical stability" for robust control design, with possibly non-linear model errors. We use affine power norms for that purpose.
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| 14. |
- Härkegård, Ola, 1973-, et al.
(författare)
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Resolving Actuator Redundancy : Optimal Control vs. Control Allocation
- 2005
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Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 41:1, s. 137-144
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Tidskriftsartikel (refereegranskat)abstract
- This paper considers actuator redundancy management for a class of overactuated nonlinear systems. Two tools for distributing the control effort among a redundant set of actuators are optimal control design and control allocation. In this paper, we investigate the relationship between these two design tools when the performance indexes are quadratic in the control input. We show that for a particular class of nonlinear systems, they give exactly the same design freedom in distributing the control effort among the actuators. Linear quadratic optimal control is contained as a special case. A benefit of using a separate control allocator is that actuator constraints can be considered, which is illustrated with a flight control example.
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| 15. |
- Härkegård, Ola, et al.
(författare)
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Vector Backstepping Design for Flight Control
- 2007
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Ingår i: Proceedings of the 2007 AIAA Guidance, Navigation, and Control Conference and Exhibit. - Reston, Virigina : American Institute of Aeronautics and Astronautics. - 9781624100154
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- A backstepping design for an aircraft described by rigid body dynamics is proposed. The system states are the unit velocity vector and the angular velocity in a body-fixed coordinate system. The result can be viewed as a multi-variable controller for angle of attack, sideslip angle, and velocity vector roll rate. The backstepping design is performed on the rigid body dynamics described on vector form. The resulting controller achieves convergence to a desired state from almost all starting points. Guidelines are given for tuning the controller to affect the characteristics of the short period mode, the roll mode and the dutch roll mode. A coupled high angle of attack, high roll rate maneuver is simulated using a simplified aircraft model to illustrate the design.
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| 16. |
- Lyzell, Christian, 1980-, et al.
(författare)
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Identification Aspects of Ritt's Algorithm for Discrete-Time Systems
- 2009
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Ingår i: Proceedings of the 15th IFAC Symposium on System Identification. - Linköping : Linköping University Electronic Press. ; , s. 681-686
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Konferensbidrag (refereegranskat)abstract
- In system identification, the challenge of parameter estimation often lies in solving a non-convex optimization problem. In many cases, this implies that it is difficult to guarantee that the global optimum will be found. The tools of differential algebra, for example, Gr\"{o}bner bases and Ritt's algorithm, have turned out to be quite useful when dealing with certain nonlinear model structures. Some examples of successful applications are the determination of controllability, observability and global identifiability of these model structures. In this paper, difference algebraic techniques, which mimics the differential algebraic methods, will be presented. Besides making it possible to handle discrete-time systems, this opens up the possibility of dealing with noise. It turns out that the classical instrumental variables method plays a role.
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| 17. |
- Ohlsson, Henrik, 1981-, et al.
(författare)
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Using Manifold Learning for Nonlinear System Identification
- 2007
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Ingår i: Proceedings of the 7th IFAC Symposium on Nonlinear Control Systems. - Linköping : Linköping University Electronic Press. - 9783902661289 ; , s. 170-175
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Konferensbidrag (refereegranskat)abstract
- A high-dimensional regression space usually causes problems in nonlinear system identification.However, if the regression data are contained in (or spread tightly around) some manifold, thedimensionality can be reduced. This paper presents a use of dimension reduction techniques tocompose a two-step identification scheme suitable for high-dimensional identification problems withmanifold-valued regression data. Illustrating examples are also given.
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| 18. |
- Sjöberg, Johan, 1978-, et al.
(författare)
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Computing the Controllability Function for Nonlinear Descriptor Systems
- 2006
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Ingår i: Proceedings of the 2006 American Control Conference. - 1424402107 - 1424402093 ; , s. 1027-1031
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Konferensbidrag (refereegranskat)abstract
- The computation of the controllability function for nonlinear descriptor systems is considered. Three different methods are derived. The first method is based on the necessary conditions for optimality from the Hamilton-Jacobi-Bellman theory for descriptor systems. The second method uses completion of squares to find the solution. The third method gives a series expansion solution, which with a finite number of terms can serve as an approximate solution.
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| 19. |
- Sjöberg, Johan, 1978-, et al.
(författare)
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Computing the Controllability Function for Nonlinear Descriptor Systems
- 2005
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The computation of the controllability function for nonlinear descriptor systems is considered. Three different methods are derived. The first method is based on the necessary conditions for optimality from the Hamilton-Jacobi-Bellman theory for descriptor systems. The second method uses completion of squares to find the solution. The third method gives a series expansion solution, which with a finite number of terms can serve as an approximate solution.
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| 20. |
- Sjöberg, Johan, 1978-, et al.
(författare)
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Model Reduction of Nonlinear Differential-Algebraic Equations
- 2007
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Ingår i: Proceedings of the 7th IFAC Symposium on Nonlinear Control Systems. - 9783902661289 ; , s. 176-181
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Konferensbidrag (refereegranskat)abstract
- In this work, a computational method to compute balanced realizations for nonlinear differential-algebraic equation systems is derived. The work is a generalization of an earlier work for nonlinear control-affine systems, and is based on analysis of the controllability and observability functions.
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| 21. |
- Sjöberg, Johan, 1978-, et al.
(författare)
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Power Series Solution of the Hamilton-Jacobi-Bellman Equation for DAE Models with a Discounted Cost
- 2008
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Ingår i: Proceedings of the 47th IEEE Conference on Decision and Control. - Linköping : Linköping University Electronic Press. - 9781424431243 - 9781424431236 ; , s. 4761-4766
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Konferensbidrag (refereegranskat)abstract
- This paper considers infinite horizon optimal feedback control of nonlinear models with discounted cost. The paper includes two extensions of existing results about optimal feedback control. First, it is proven that for real analytic statespace models, a time-invariant real analytic feedback solution exists, even when the cost function includes a discount factor, provided certain regularity conditions. Second, the result is generalized to nonlinear DAE models. The feedback solution is valid in a neighborhood of the origin. In both cases, explicit formulas for the series expansions of the cost function and control law are given.
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| 22. |
- Sjöberg, Johan, 1978-, et al.
(författare)
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Power Series Solution of the Hamilton-Jacobi-Bellman Equation for Descriptor Systems
- 2005
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Ingår i: Proceedings of the 44th IEEE Conference on Decision and Control. - Linköping : Linköping University Electronic Press. - 0780395670 ; , s. 6869-6874
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Konferensbidrag (refereegranskat)abstract
- Optimal control problems for a class of nonlinear descriptor systems are considered. It is shown that they possess a well-defined analytical feedback solution in a neighborhood of the origin, provided stabilizability and some other regularity conditions are satisfied. Explicit formulas for the series expansions of the cost function and control law are given.
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| 23. |
- Sjöberg, Johan, 1978-, et al.
(författare)
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Power Series Solution of the Hamilton-Jacobi-Bellman Equation for Time-Varying Differential-Algebraic Equations
- 2006
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Ingår i: Proceedings of the 45th IEEE Conference on Decision and Control. - 1424401712 ; , s. 870-875
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Konferensbidrag (refereegranskat)abstract
- Optimal control problems for a class of nonlinear time-varying differentialalgebraic equations are considered. It is shown that they possess a welldefined feedback solution in a neighborhood of the origin. Explicit formulasfor the series expansions of the cost function and control law are given.
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| 24. |
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| 25. |
- Sjöberg, Johan, 1978-, et al.
(författare)
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Rational Approximation of Nonlinear Optimal Control Problems
- 2008
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Ingår i: Proceedings of the 17th IFAC World Congress. - 9783902661005 ; , s. 11340-11345
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Konferensbidrag (refereegranskat)abstract
- In this paper rational approximation of solutions to nonlinear optimal control problems is considered. A computational procedure is presented that makes it possible to compute a rational function that approximates the true optimal cost function. It is shown that the rational function has the same series expansion around the origin as the true solution. Finally, two examples are given that compares the new method with the power series approximation, which is a rather well-known method to find approximative solutions.
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| 26. |
- Tidefelt, Henrik, 1978-, et al.
(författare)
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Index Reduction of Index 1 DAE under Uncertainty
- 2008
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Ingår i: Proceedings of the 17th IFAC World Congress. - 9783902661005 ; , s. 5053-5058
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Konferensbidrag (refereegranskat)abstract
- This paper examines an index reduction method for linear time-invariant differential algebraic equations, with uncertainty in the equation coefficients. When the bottom block of a block upper triangular leading matrix contains no elements that can be distinguished from zero, the natural action to take is to replace all numbers in the block by exact zeros, and then proceed with index reduction by differentiation. Conditions are given under which zeroing of an uncertain small block gives a small deviation in the solution.
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