Symmetric Linear Model Predictive Control

Danielson, Claus; Borrelli, Francesco

doi:10.1109/tac.2014.2373693

Cited by 26 publications

(21 citation statements)

References 27 publications

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“…A symmetry of the constraint linear system (1) and (2) is a state-space transformation Θ and input-space transformation Ω that preserves the dynamics and constraints [4].…”

Section: A Definition Of Symmetrymentioning

confidence: 99%

“…In addition if the cost function matrices satisfy Θ T P Θ = P , Θ T QΘ = Q, and Ω T RΩ = R and the terminal set satisfies ΘX f = X f for all (Θ, Ω) ∈ G then we say that Problem (3) is symmetric with respect to the group G. In [4] it was shown how to select a cost function and terminal set that are symmetric with respect to the symmetry group G of the system (4) and constraints (5).…”

Section: A Definition Of Symmetrymentioning

confidence: 99%

“…Some applications include energy efficient buildings [1]- [3] and battery balancing [4], [5]. In this paper, we are interested in the use of explicit symmetric MPC for the fast control of systems for which the computation of the full explicit and real-time controllers are prohibitively expensive.…”

Section: Introductionmentioning

confidence: 99%

“…However this approach may render the solution suboptimal or even infeasible. Recent advances in symmetric MPC [4] allows for the computation of the explicit solution for large symmetric systems. However, the system must have special symmetry properties which can be hard to satisfy especially with varying external disturbances.…”

Section: Introductionmentioning

confidence: 99%

“…In [18] the authors exploited symmetry to reduce the computational complexity of H 2 and H ∞ controllers. In [4] the authors studied symmetry in linear model predictive control. All of these results rely on the fact that the systems in question have predetermined symmetric properties.…”

Section: Introductionmentioning

confidence: 99%

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Robust approximate symmetric model predictive control

Chuang

Danielson

Borrelli

2015

2015 54th IEEE Conference on Decision and Control (CDC)

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In this paper we study the explicit model predictive control (MPC) design for approximately symmetric systems. The approximately symmetric system is modeled as a symmetric system plus an additive disturbance residing in a symmetric set. The explicit MPC controller is computed using symmetry to minimize the number of critical regions stored in memory while being robust to model mismatch and disturbances. We show through numerical examples that approximating an approximately symmetric systems using a full symmetric system can drastically reduce memory usage and computation time for explicit controllers while still guaranteeing feasibility and input-to-state stability.

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“…A symmetry of the constraint linear system (1) and (2) is a state-space transformation Θ and input-space transformation Ω that preserves the dynamics and constraints [4].…”

Section: A Definition Of Symmetrymentioning

confidence: 99%

Section: A Definition Of Symmetrymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust approximate symmetric model predictive control

Chuang

Danielson

Borrelli

2015

2015 54th IEEE Conference on Decision and Control (CDC)

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An alternating direction method of multipliers algorithm for symmetric model predictive control

Danielson

2020

Optim Control Appl Methods

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SummaryThis article presents an alternating direction method of multipliers (ADMM) algorithm for solving large‐scale model predictive control (MPC) problems that are invariant under the symmetric‐group. Symmetry was used to find transformations of the inputs, states, and constraints of the MPC problem that decompose the dynamics and cost. We prove an important property of the symmetric decomposition for the symmetric‐group that allows us to efficiently transform between the original and decomposed symmetric domains. This allows us to solve different subproblems of a baseline ADMM algorithm in different domains where the computations are less expensive. This reduces the computational cost of each iteration from quadratic to linear in the number of repetitions in the system. In addition, we show that the memory complexity for our ADMM algorithm is also linear in number of repetitions in the system, rather than the typical quadratic complexity. We demonstrate our algorithm for two case studies; battery balancing and heating, ventilation, and air conditioning. In both case studies, the symmetric algorithm reduced the computation‐time from minutes to seconds and memory usage from tens of megabytes to tens or hundreds of kilobytes, allowing the previously nonviable MPCs to be implemented in real time on embedded computers with limited computational and memory resources.

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Research on the control of thrust vectoring turbojet aircraft with uncertainties and input saturation based on fixed‐time control

Liu,

Gao,

Gao

et al. 2024

Intl J Robust & Nonlinear

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One‐dimensional thrust vectoring turbojet vertical takeoff and landing (VTOL) aircraft have attracted research attention due to their high thrust‐to‐weight ratios and their solution for the slow speed response of turbojet engines. However, there are some uncertainties and physical limitations in their systems, such as external disturbances, unknown parameters and input saturation. To improve the accuracy and convergence speed of trajectory tracking, a fixed‐time control method that is robust to saturation is proposed. The system dynamics are established, and an auxiliary system is built within a fixed time control framework to address the influence of input saturation and increase the error convergence rate. Nonsingular fast terminal sliding mode technology is combined with a few adaptive laws to ensure the robustness of the closed‐loop system against dynamic uncertainties and improve the precision of steady‐state control. The stability of the control system is proven based on Lyapunov, and the controller parameters are optimized based on particle swarm optimization (PSO). The proposed method based on fixed‐time stability guarantees that the states of the closed‐loop system can reach the residual set around zero within the designed time, and an expression for the upper bound on the convergence time is given. Finally, numerical simulations demonstrate the superiority of the proposed method based on the error integral criterion.

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Symmetric Linear Model Predictive Control

Cited by 26 publications

References 27 publications

Robust approximate symmetric model predictive control

Robust approximate symmetric model predictive control

An alternating direction method of multipliers algorithm for symmetric model predictive control

Research on the control of thrust vectoring turbojet aircraft with uncertainties and input saturation based on fixed‐time control

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