| 1. |
- Andersen, Martin, et al.
(författare)
-
Distributed Robust Stability Analysis of Interconnected Uncertain Systems
- 2012
-
Ingår i: Proceedings of the 51st IEEE Conference on Decision and Control. - 0743-1546. - 9781467320641 - 9781467320658 ; , s. 1548-1553
-
Konferensbidrag (refereegranskat)abstract
- This paper considers robust stability analysis of a large network of interconnected uncertain systems. To avoid analyzing the entire network as a single large, lumped system, we model the network interconnections with integral quadratic constraints. This approach yields a sparse linear matrix inequality which can be decomposed into a set of smaller, coupled linear matrix inequalities. This allows us to solve the analysis problem efficiently and in a distributed manner. We also show that the decomposed problem is equivalent to the original robustness analysis problem, and hence our method does not introduce additional conservativeness.
|
|
| 2. |
- Andersen, Martin S., et al.
(författare)
-
Robust Stability Analysis of Sparsely Interconnected Uncertain Systems
- 2014
-
Ingår i: IEEE Transactions on Automatic Control. - : IEEE. - 0018-9286 .- 1558-2523. ; 59:8, s. 2151-2156
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper, we consider robust stability analysis of large-scale sparsely interconnected uncertain systems. By modeling the interconnections among the subsystems with integral quadratic constraints, we show that robust stability analysis of such systems can be performed by solving a set of sparse linear matrix inequalities. We also show that a sparse formulation of the analysis problem is equivalent to the classical formulation of the robustness analysis problem and hence does not introduce any additional conservativeness. The sparse formulation of the analysis problem allows us to apply methods that rely on efficient sparse factorization techniques, and our numerical results illustrate the effectiveness of this approach compared to methods that are based on the standard formulation of the analysis problem.
|
|
| 3. |
- Annergren, Mariette, et al.
(författare)
-
A Distributed Primal-dual Interior-point Method for Loosely Coupled Problems Using ADMM
-
Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- In this paper we propose an efficient distributed algorithm for solving loosely coupled convex optimization problems. The algorithm is based on a primal-dual interior-point method in which we use the alternating direction method of multipliers (ADMM) to compute the primal-dual directions at each iteration of the method. This enables us to join the exceptional convergence properties of primal-dual interior-point methods with the remarkable parallelizability of ADMM. The resulting algorithm has superior computational properties with respect to ADMM directly applied to our problem. The amount of computations that needs to be conducted by each computing agent is far less. In particular, the updates for all variables can be expressed in closed form, irrespective of the type of optimization problem. The most expensive computational burden of the algorithm occur in the updates of the primal variables and can be precomputed in each iteration of the interior-point method. We verify and compare our method to ADMM in numerical experiments.
|
|
| 4. |
- Falcone, Paolo, 1977, et al.
(författare)
-
Predictive Approaches to Rear Axle Regenerative Braking Control in Hybrid Vehicles
- 2009
-
Ingår i: 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference.
-
Konferensbidrag (refereegranskat)abstract
- We consider the problem of controlling the regenerative braking at rear axle in hybrid vehicles. In particular, thefocus of this work is the maximization of regenerative braking in cornering maneuvers on low friction surfaces. In such cases, excessive braking at the rear axle might induce instability.We present and compare two predictive control approaches,where the objective is maximizing the regenerative braking and distributing the friction braking at the four wheels, while (i) delivering the braking force requested by the driver, (ii) preserving vehicle stability and (iii) fulfilling system constraints (e.g., bounds on regenerative braking set by the hybrid powertrain).We present simulation results in combined braking andcornering scenarios, showing that the proposed approaches are able to distribute the requested braking at the four wheels in order to counteract undesired effects, on vehicle stability, introduced by regenerative braking.
|
|
| 5. |
- Falcone, Paolo, 1977, et al.
(författare)
-
Regenerative Braking and Yaw Dynamics Optimal Control in Hybrid Vehicles
- 2009
-
Ingår i: 21st International Symposium on Dynamics of Vehicles on Roads and Tracks, 17-21 August 2009, Stockholm, Sweden.
-
Konferensbidrag (refereegranskat)abstract
- In hybrid vehicles, regenerative braking is used in order to recover energy when vehiclebrakes. Energy is recovered by converting the vehicle kinetic energy into electric energy tobe stored in electricity buffers, i.e., batteries or capacitors. The recovered energy can then beused for powering the vehicle and thus reduce the fuel consumption. In particular, in order togenerate a braking force, the wheels can be connected to the electric motor, thus providingmotion energy to the generator and charging the electric buffer. When regenerative brakingis applied, the connection of the wheels to the generator results in a load torque (i.e., a braketorque), slowing the vehicle down, and at the same time enables energy recovery.In this paper, we consider hybrid drivelines where the electric motor is connected to therear axle, i.e., the regenerative braking takes place by braking the rear wheels, and focus onthe implications of the regenerative braking on the vehicle dynamics.The scenario considered in this paper (i.e., regenerative braking at the rear axle) is challengingfrom both the brake force delivery and distribution and the vehicle stabilizationperspectives [1]. In fact, we first observe that the maximum force the regenerative brakingcan deliver is limited and, in general, less than the friction braking. In particular, a brakingforce request from the driver might not be delivered entirely through regenerative brakingand a combination of friction and regenerative braking might be necessary. Secondly, werecall that an “optimum” brake proportioning between front and rear axles exists, such thatthe braking performance is maximized and the vehicle stability is preserved (see [2] for adetailed explanation). Clearly, maximizing the braking at one axle might conflict with a brakeforce distribution determined according to some “optimum” brake proportioning. Moreover,preserving the vehicle stability and comfort on slippery surfaces while maximizing the energyrecovering is a significant challenge as well. In particular, on low friction surfaces, the braketorque from regenerative braking might be large enough to lock-up the rear wheel. This wouldinduce an oversteering behavior and might even lead to instability, i.e., vehicle spinning [1].Even though instability does not occur, the driver might perceive a reduction of comfort asconsequence of braking at the rear wheels. In particular, on low friction surfaces, where thevehicle can easily operate at the limit of tire force capabilities, a sudden reduction of lateralforce might be experienced as consequence of braking.In this paper, we consider testing scenarios where the driver demands a braking force whilethe vehicle is performing a cornering manoeuvres on slippery surfaces, i.e., snow or ice. Thecontrol objective is to maximize the energy recovery (i.e., the regenerative braking), while (i)delivering the requested braking force by introducing front and rear friction braking as well,if necessary, (ii) preserving the vehicle stability and (iii) limit the lateral force reduction. Weshow how this problem can be effectively formulated as a Model Predictive Control (MPC)problem. In particular, we design a cost function in order to achieve our control objectives.Every time step, based on measurements of the demanded brake force, the vehicle yaw turningrate and longitudinal and lateral velocities, we repeatedly solve an optimization problem inorder to find the braking policy minimizing the cost function while fulfilling design and systemconstraints. As shown in [3], such control approach can be high computational demandingand even prevent real-time implementation. In order to implement our MPC algorithms inreal-time, we resort to the low complexity MPC formulation used in [4], [5], [6] to solveautonomous path following problems.REFERENCES[1] M. Hancock and F. Assadian. Impact of regenerative braking on vehicle stability. IET The Institution of Engineeringand Technology, Hybrid Vehicle Conference, 2006.[2] T. Gillespie. Fundamentals of Vehicle Dynamics, chapter 3, pages 60–67. Society of Automotive Engineers (SAE),1992.[3] F. Borrelli, P. Falcone, T. Keviczky, J. Asgari, and D. Hrovat. MPC-based approach to active steering for autonomousvehicle systems. Int. J. Vehicle Autonomous Systems, 3(2/3/4):265–291, 2005.[4] P. Falcone, F. Borrelli, J. Asgari, H. E. Tseng, and D. Hrovat. Predictive active steering control for autonomous vehiclesystems. IEEE Trans. on Control System Technology, 15(3), 2007.[5] P. Falcone, F. Borrelli, J. Asgari, H. E. Tseng, and D. Hrovat. Linear time varying model predictive control and itsapplication to active steering systems: Stability analisys and experimental validation. International Journal of Robustand Nonlinear Control., 18:862–875, 2008.[6] P. Falcone. Nonlinear Model Predictive Control for Autonomous Vehicles. PhD thesis, Universit`a del Sannio,Dipartimento di Ingegneria, Piazza Roma 21, 82100, Benevento, Italy, June 2007.
|
|
| 6. |
- Karami, Farzaneh, et al.
(författare)
-
Automated Model Generation for Analysis of Large-scale Interconnected Uncertain Systems
- 2015
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The first challenge in robustness analysis of large-scale interconnected uncertain systems is to provide a model of such systems in a standard-form that is required within different analysis frameworks. This becomes particularly important for large-scale systems, as analysis tools that can handle such systems heavily rely on the special structure within such model descriptions. We here propose an automated framework for providing such models of large-scale interconnected uncertain systems that are used in Integral Quadratic Constraint (IQC) analysis. Specifically, in this paper we put forth a methodological way to provide such models from a block-diagram and nested description of interconnected uncertain systems. We describe the details of this automated framework using an example.
|
|
| 7. |
- Khoshfetrat Pakazad, Sina, 1985-, et al.
(författare)
-
Decomposition and Projection Methods for Distributed Robustness Analysis of Interconnected Uncertain Systems
- 2013
-
Konferensbidrag (refereegranskat)abstract
- We consider a class of convex feasibility problems where the constraints that describe the feasible set are loosely coupled. These problems arise in robust stability analysis of large, weakly interconnected uncertain systems. To facilitate distributed implementation of robust stability analysis of such systems, we describe two algorithms based on decomposition and simultaneous projections. The first algorithm is a nonlinear variant of Cimmino's mean projection algorithm, but by taking the structure of the constraints into account, we can obtain a faster rate of convergence. The second algorithm is devised by applying the alternating direction method of multipliers to a convex minimization reformulation of the convex feasibility problem. We use numerical results to show that both algorithms require far less iterations than the accelerated nonlinear Cimmino algorithm.
|
|
| 8. |
- Khoshfetrat Pakazad, Sina, 1985-, et al.
(författare)
-
Distributed Interior-point Method for Loosely Coupled Problems
- 2014
-
Konferensbidrag (refereegranskat)abstract
- In this paper, we put forth distributed algorithms for solving loosely coupled unconstrained and constrained optimization problems. Such problems are usually solved using algorithms that are based on a combination of decomposition and first order methods. These algorithms are commonly very slow and require many iterations to converge. In order to alleviate this issue, we propose algorithms that combine the Newton and interior-point methods with proximal splitting methods for solving such problems. Particularly, the algorithm for solving unconstrained loosely coupled problems, is based on Newton's method and utilizes proximal splitting to distribute the computations for calculating the Newton step at each iteration. A combination of this algorithm and the interior-point method is then used to introduce a distributed algorithm for solving constrained loosely coupled problems. We also provide guidelines on how to implement the proposed methods efficiently and briefly discuss the properties of the resulting solutions.
|
|
| 9. |
- Khoshfetrat Pakazad, Sina, 1985-, et al.
(författare)
-
Distributed Robustness Analysis of Interconnected Uncertain Systems Using Chordal Decomposition
- 2014
-
Ingår i: Proceedings of the 19th IFAC World Congress, 2014. - : International Federation of Automatic Control. - 9783902823625 ; , s. 2594-2599
-
Konferensbidrag (refereegranskat)abstract
- Large-scale interconnected uncertain systems commonly have large state and uncertainty dimensions. Aside from the heavy computational cost of solving centralized robust stability analysis techniques, privacy requirements in the network can also introduce further issues. In this paper, we utilize IQC analysis for analyzing large-scale interconnected uncertain systems and we evade these issues by describing a decomposition scheme that is based on the interconnection structure of the system. This scheme is based on the so-called chordal decomposition and does not add any conservativeness to the analysis approach. The decomposed problem can be solved using distributed computational algorithms without the need for a centralized computational unit. We further discuss the merits of the proposed analysis approach using a numerical experiment.
|
|
| 10. |
- Khoshfetrat Pakazad, Sina, 1985-, et al.
(författare)
-
Distributed Semidefinite Programming with Application to Large-scale System Analysis
-
Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Distributed algorithms for solving coupled semidefinite programs (SDPs) commonly require manyiterations to converge. They also put high computational demand on the computational agents. In thispaper we show that in case the coupled problem has an inherent tree structure, it is possible to devisean efficient distributed algorithm for solving such problems. This algorithm can potentially enjoy thesame efficiency as centralized solvers that exploit sparsity. The proposed algorithm relies on predictorcorrectorprimal-dual interior-point methods, where we use a message-passing algorithm to compute thesearch directions distributedly. Message-passing here is closely related to dynamic programming overtrees. This allows us to compute the exact search directions in a finite number of steps. Furthermorethis number can be computed a priori and only depends on the coupling structure of the problem. Weuse the proposed algorithm for analyzing robustness of large-scale uncertain systems distributedly. Wetest the performance of this algorithm using numerical examples.
|
|
