| 1. |
- Nielsen, Isak, et al.
(författare)
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Low-rank Modifications of Riccati Factorizations with Applications to Model Predictive Control
- 2013
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Ingår i: Proceedings of 52nd IEEE Conference on Decision and Control. - : IEEE conference proceedings. - 9781467357173 - 9781467357142 ; , s. 3684-3690
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Konferensbidrag (refereegranskat)abstract
- In optimization algorithms used for on-line Model Predictive Control (MPC), the main computational effort is spent while solving linear systems of equations to obtain search directions. Hence, it is of greatest interest to solve them efficiently, which commonly is performed using Riccati recursions or generic sparsity exploiting algorithms. The focus in this work is efficient search direction computation for active-set methods. In these methods, the system of equations to be solved in each iteration is only changed by a low-rank modification of the previous one. This highly structured change of the system of equations from one iteration to the next one is an important ingredient in the performance of active-set solvers. It seems very appealing to try to make a structured update of the Riccati factorization, which has not been presented in the literature so far. The main objective of this paper is to present such an algorithm for how to update the Riccati factorization in a structured way in an active-set solver. The result of the work is that the computational complexity of the step direction computation can be significantly reduced for problems with bound constraints on the control signal. This in turn has important implications for the computational performance of active-set solvers used for linear, nonlinear as well as hybrid MPC.
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| 2. |
- Ankelhed, Daniel, et al.
(författare)
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A Partially Augmented Lagrangian Method for Low Order H-Infinity Controller Synthesis Using Rational Constraints
- 2011
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- When designing robust controllers, H-infinity synthesis is a common tool touse. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the (augmented) system, the problem becomes nonconvex and it is relatively hard to solve. These problems become very complex, even when the order of the system is low.The approach used in this work is based on formulating the constraint onthe maximum order of the controller as a polynomial (or rational) equation.This equality constraint is added to the optimization problem of minimizingan upper bound on the H-innity norm of the closed loop system subjectto linear matrix inequality (LMI) constraints. The problem is then solvedby reformulating it as a partially augmented Lagrangian problem where theequality constraint is put into the objective function, but where the LMIsare kept as constraints.The proposed method is evaluated together with two well-known methodsfrom the literature. The results indicate that the proposed method hascomparable performance in most cases, especially if the synthesized con-troller has many parameters, which is the case if the system to be controlledhas many input and output signals.
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| 3. |
- Ankelhed, Daniel, et al.
(författare)
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A Partially Augmented Lagrangian Method for Low Order H-Infinity Controller Synthesis Using Rational Constraints
- 2012
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Ingår i: IEEE Transactions on Automatic Control. - 0018-9286 .- 1558-2523. ; 57:11, s. 2901-2905
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Tidskriftsartikel (refereegranskat)abstract
- This technical note proposes a method for low order H-infinity synthesis where the constraint on the order of the controller is formulated as a rational equation. The resulting nonconvex optimization problem is then solved by applying a partially augmented Lagrangian method. The proposed method is evaluated together with two well-known methods from the literature. The results indicate that the proposed method has comparable performance and speed.
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| 4. |
- Ankelhed, Daniel, et al.
(författare)
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A Primal-Dual Method for Low Order H-Infinity Controller Synthesis
- 2010
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Ingår i: Proceedings of Reglermöte 2010. - Lund : Linköping University Electronic Press.
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- When designing robust controllers, H-infinity synthesis is a common tool to use. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the (augmented) system, the problem becomes nonconvex and it is relatively hard to solve. These problems become very complex, even when the order of the system is low.The approach used in this work is based on formulating the constraint on the maximum order of the controller as a polynomial (or rational) equation. By using the fact that the polynomial (or rational) is non-negative on the feasible set, the problem is reformulated as an optimization problem where the nonconvex function is to be minimized over a convex set defined by linear matrix inequalities.The proposed method is evaluated together with a well-known method from the literature. The results indicate that the proposed method performs slightly better.
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| 5. |
- Ankelhed, Daniel, et al.
(författare)
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A Primal-Dual Method for Low Order H-Infinity Controller Synthesis
- 2009
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Ingår i: Proceedings of the 48th IEEE Conference on Decision and Control held jointly with the 28th Chinese Control Conference. - : IEEE. - 9781424438716 - 9781424438723 ; , s. 6674-6679
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Konferensbidrag (refereegranskat)abstract
- When designing robust controllers, H-infinity synthesisis a common tool to use. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the (augmented) system, the problem becomes nonconvex and it is relatively hard to solve. These problems become very complex,even when the order of the system is low.The approach used in this work is based on formulating the constraint on the maximum order of the controller as a polynomial (or rational) equation. By using the fact that the polynomial (or rational) is non-negative on the feasible set, the problem is reformulated as an optimization problem where the nonconvex function is to be minimized over a convex set defined by linear matrix inequalities.The proposed method is evaluated together with a wellknown method from the literature. The results indicate that the proposed method performs slightly better.
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| 6. |
- Ankelhed, Daniel, et al.
(författare)
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A Quasi-Newton Interior Point Method for Low Order H-Infinity Controller Synthesis
- 2011
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Ingår i: IEEE Transactions on Automatic Control. - 0018-9286 .- 1558-2523. ; 56:6, s. 1462-1467
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Tidskriftsartikel (refereegranskat)abstract
- This technical note proposes a method for low order H-infinity synthesis where the constraint on the order of the controller is formulated as a rational equation. The resulting nonconvex optimization problem is then solved by applying a quasi-Newton primal-dual interior point method. The proposed method is evaluated together with a well-known method from the literature. The results indicate that the proposed method has comparable performance and speed.
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| 7. |
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| 8. |
- Ankelhed, Daniel
(författare)
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An Efficient Implementation of Gradient and Hessian Calculations of the Coefficients of the Characteristic Polynomial of I-XY
- 2011
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This is a report about a project in robust multivariable control. In the project we investigated how to decrease the computational complexity of calculating the gradient and Hessian of coefficients of the characteristic polynomial of the matrix I-XY that often appear in H-infinity controller synthesis. Compared to a straight-forward implementation, our new implementation managed to decrease the number of operations required to calculated the gradient and Hessian by several orders of magnitude by utilizing the structure of the problem.
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| 9. |
- Ankelhed, Daniel, 1980-
(författare)
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On design of low order H-infinity controllers
- 2011
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- When designing controllers with robust performance and stabilization requirements, H-infinity synthesis is a common tool to use. These controllers are often obtained by solving mathematical optimization problems. The controllers that result from these algorithms are typically of very high order, which complicates implementation. Low order controllers are usually desired, since they are considered more reliable than high order controllers. However, if a constraint on the maximum order of the controller is set that is lower than the order of the so-called augmented system, the optimization problem becomes nonconvex and it is relatively difficult to solve. This is true even when the order of the augmented system is low.In this thesis, optimization methods for solving these problems are considered. In contrast to other methods in the literature, the approach used in this thesis is based on formulating the constraint on the maximum order of the controller as a rational function in an equality constraint. Three methods are then suggested for solving this smooth nonconvex optimization problem.The first two methods use the fact that the rational function is nonnegative. The problem is then reformulated as an optimization problem where the rational function is to be minimized over a convex set defined by linear matrix inequalities (LMIs). This problem is then solved using two different interior point methods.In the third method the problem is solved by using a partially augmented Lagrangian formulation where the equality constraint is relaxed and incorporated into the objective function, but where the LMIs are kept as constraints. Again, the feasible set is convex and the objective function is nonconvex.The proposed methods are evaluated and compared with two well-known methods from the literature. The results indicate that the first two suggested methods perform well especially when the number of states in the augmented system is less than 10 and 20, respectively. The third method has comparable performance with two methods from literature when the number of states in the augmented system is less than 25.
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| 10. |
- Ankelhed, Daniel, 1980-
(författare)
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On low order controller synthesis using rational constraints
- 2009
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In order to design robust controllers, H-infinity synthesis is a common tool to use. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the plant, the problem is no longer convex and it is then relatively hard to solve. These problems become very complex, even when the order of the system to be controlled is low.The approach used in the thesis is based on formulating the constraint on the maximum order of the plant as a polynomial equation. By using the fact that the polynomial is non-negative on the feasible set, the problem is reformulated as an optimization problem where the nonconvex polynomial function is to be minimized over a convex set defined by linear matrix inequalities.To solve this optimization problem, two methods have been proposed. The first method is a barrier method and the second one is a method based on a primal-dual framework. These methods have been evaluated on several problems and compared with a well-known method found in the literature. To motivate this choice of method, we have made a brief survey of available methods available for solving the same or related problems.The proposed methods emerged as the best methods among the three for finding lower order controllers with the same or similar performance as the full order controller. When the aim is to find the lowest order controller with no worse than +50% increase in the closed loop H-infinity norm, then the three compared methods perform equally well.
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