A dual gradient projection quadratic programming algorithm tailored for model predictive control

Axehill, Daniel; Hansson, Anders

doi:10.1109/cdc.2008.4738961

Cited by 43 publications

(69 citation statements)

References 13 publications

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“…The primal problem (4.39) can be solved by using for example a dual as type solver as proposed in Axehill and Hansson (2006), or a dual gradient projection method as in Axehill (2008); Axehill and Hansson (2008). In these types of methods, the primal problem is solved by constructing the corresponding dual problem and applying primal methods to solve the dual problem.…”

Section: Methods To Handle General Constraintsmentioning

confidence: 99%

“…Furthermore, it is shown that also the dual problem can be interpreted as a cftoc problem using a suitable variable transformation. This dual problem is used in the solvers in Axehill and Hansson (2006); Axehill (2008); Axehill and Hansson (2008).…”

Section: Dual Problemmentioning

confidence: 99%

“…λ t := P t x t − Ψ t 6: end for 7: λ N := P N x N − Ψ N the one presented in Axehill (2008); Axehill and Hansson (2008). In such problems the matrices G t+1 in the Riccati recursion might be singular, and hence the feedback gain matrices K t+1 might be non-unique.…”

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confidence: 99%

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On Structure Exploiting Numerical Algorithms for Model Predictive Control

Nielsen

2015

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One of the most common advanced control strategies used in industry today is Model Predictive Control (mpc), and some reasons for its success are that it can handle multivariable systems and constraints on states and control inputs in a structured way. At each time-step in the mpc control loop the control input is computed by solving a constrained finite-time optimal control (cftoc) problem on-line. There exist several optimization methods to solve the cftoc problem, where two common types are interior-point (ip) methods and active-set (as) methods. In both these types of methods, the main computational effort is known to be the computation of the search directions, which boils down to solving a sequence of Newton-system-like equations. These systems of equations correspond to unconstrained finite-time optimal control (uftoc) problems. Hence, high-performance ip and as methods for cftoc problems rely on efficient algorithms for solving the uftoc problems.The solution to a uftoc problem is computed by solving the corresponding Karush-Kuhn-Tucker (kkt) system, which is often done using generic sparsity exploiting algorithms or Riccati recursions. When an as method is used to compute the solution to the cftoc problem, the system of equations that is solved to obtain the solution to a uftoc problem is only changed by a low-rank modification of the system of equations in the previous iteration. This structured change is often exploited in as methods to improve performance in terms of computation time. Traditionally, this has not been possible to exploit when Riccati recursions are used to solve the uftoc problems, but in this thesis, an algorithm for performing low-rank modifications of the Riccati recursion is presented.In recent years, parallel hardware has become more commonly available, and the use of parallel algorithms for solving the cftoc problem and the underlying uftoc problem has increased. Some existing parallel algorithms for computing the solution to this type of problems obtain the solution iteratively, and these methods may require many iterations to converge. Some other parallel algorithms compute the solution directly (non-iteratively) by solving parts of the system of equations in parallel, followed by a serial solution of a dense system of equations without the sparse structure of the mpc problem. In this thesis, two parallel algorithms that compute the solution directly (non-iteratively) in parallel are presented. These algorithms can be used in both ip and as methods, and they exploit the sparse structure of the mpc problem such that no dense system of equations needs to be solved serially. Furthermore, one of the proposed parallel algorithms exploits the special structure of the mpc problem even in the parallel computations, which improves performance in terms of computation time even more. By using these algorithms, it is possible to obtain logarithmic complexity growth in the prediction horizon length.v Populärvetenskaplig sammanfattningModellprediktiv reglering (eng. Model Predictive...

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Section: Methods To Handle General Constraintsmentioning

confidence: 99%

Section: Dual Problemmentioning

confidence: 99%

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On Structure Exploiting Numerical Algorithms for Model Predictive Control

Nielsen

2015

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“…This method is also used in this work to form an explicit relationship between the state variables and the control inputs. (Axehill and Hansson, 2008) proposed a gradient projection method to improve the active set method and solve the MPC problem. It allowed the working set changes to be faster than a generic active set method.…”

Section: Fast Mpc With Online Solvermentioning

confidence: 99%

1-Bit processing based model predictive control for fractionated satellite missions

Bai

2014

Acta Astronautica

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In this thesis, a 1-bit processing based Model Predictive Control (OBMPC) structure is proposed for a fractionated satellite attitude control mission. Despite the appealing advantages of the MPC algorithm towards constrained MIMO control applications, implementing the MPC algorithm onboard a small satellite is certainly challenging due to the limited onboard resources. The proposed design is based on the 1-bit processing concept, which takes advantage of the affine relation between the 1-bit state feedback and multi-bit parameters to implement a multiplier free MPC controller.As multipliers are the major power consumer in online optimization, the OBMPC structure is proven to be more efficient in comparison to the conventional MPC implementation in term of power and circuit complexity. The system is in digital control nature, affected by quantization noise introduced by Δ∑ modulators. The stability issues and practical design criteria are also discussed in this work.Some other aspects are considered in this work to complete the control system. Firstly, the implementation of the OBMPC system relies on the 1-bit state feedbacks. Hence, 1-bit sensing components are needed to implement the OBMPC system. While the ∆∑ modulator based Microelectromechanical systems (MEMS) gyroscope is considered in this work, it is possible to implement this concept into other sensing components.Secondly, as the proposed attitude mission is based on the wireless inter-satellite link (ISL), a state estimator is required. However, conventional state estimators will once again introduce multi-bit signals, and compromise the simple, direct implementation of the OBMPC controller. Therefore, the 1-bit state estimator is also designed in this work to satisfy the requirements of the proposed fractionated attitude control mission.The simulation for the OBMPC is based on a 2U CubeSat model in a fractionated satellite structure, in which the payload and actuators are separated from the controller and controlled via the ISL. Matlab simulations and FPGA implementation based performance analysis shows that the OBMPC is feasible for fractionated satellite missions and is advantageous over the conventional MPC controllers. V VI

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“…Several methods have been proposed in recent years, demonstrating that the computation times can be pushed into a range where online optimization can be used for the control of high-speed systems (Ferreau, Bock, & Diehl, 2008;Wang & Boyd, 2010). Significant reduction of the computational complexity can be achieved by exploiting the particular structure and sparsity inherent in the MPC problem (Axehill & Hansson, 2008;Milman & Davison, 2008;Wang & Boyd, 2010;Wright, 1997). In a real-time environment, all available methods for fast online MPC resort to early termination, sacrificing guarantees on either feasibility or stability of the applied control action.…”

Section: Introductionmentioning

confidence: 99%