Complexity Reduction in Explicit MPC through Model Reduction

Hovland, Svein; Gravdahl, Jan Tommy

doi:10.3182/20080706-5-kr-1001.01304

Cited by 15 publications

(6 citation statements)

References 13 publications

(11 reference statements)

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“…The main challenge is propagating the order-reduction error dynamics and taking them into account for MPC constraint satisfaction. Earlier works [8,14,15,28] avoided this issue and relied on softening the MPC constraints on-the-fly to accommodate possible violations. Stability was only guaranteed for open-loop stable systems [15].…”

Section: Related Workmentioning

confidence: 99%

Robust output feedback control with guaranteed constraint satisfaction

Sadraddini

Tedrake

2020

Proceedings of the 23rd International Conference on Hybrid Systems: Computation and Control

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We propose a method to control linear time-varying (LTV) discretetime systems subject to bounded process disturbances and measurable outputs with bounded noise, and polyhedral constraints over system inputs and states. We search over control policies that map the history of measurable outputs to the current control input. We solve the problem in two stages. First, using the original system, we build a linear system that predicts future observations using the past observations. The bounded errors are characterized using zonotopes. Next, we propose control laws based on affine maps of such output prediction errors, and show that controllers can be synthesized using convex linear/quadratic programs. Furthermore, we can add constraints on trajectories and guarantee their satisfaction for all allowable sequences of observation noise and process disturbances. Our method does not require any assumptions about system controllability and observability. The controller design does not directly take into account the state-space dynamics, and its implementation does not require an observer. Instead, partial observability is often sufficient to design a correct controller. We provide the polytopic representation of observability errors and reachable sets in the form of zonotopes. Illustrative examples are included. CCS CONCEPTS• Mathematics of computing → Mathematical optimization;• Computing methodologies → Planning under uncertainty; Computational control theory.

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Section: Related Workmentioning

confidence: 99%

Robust output feedback control with guaranteed constraint satisfaction

Sadraddini

Tedrake

2020

Proceedings of the 23rd International Conference on Hybrid Systems: Computation and Control

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“…Example 2. As a second example, we considered the fuel cell breathing control system in [12] and [7] with 8 state variables and 1 input and prediction horizon N = 6 and discretized the model with sampling time T d = 1 sec. Table II provides an insightful illustration of the particular situation that Algorithm 2 may encounter.…”

Section: Algorithm 2 Downward Exploration Of the Combinatorial Treementioning

confidence: 99%

Further results on the exploration of combinatorial tree in multi-parametric quadratic programming

Ahmadi-Moshkenani¹,

Olaru

Johansen³

2016

2016 European Control Conference (ECC)

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A combinatorial approach has been recently proposed for multi-parametric quadratic programming and has shown to be more effective in finding the complete solution than existing geometric methods for higher-order systems. In this paper, we propose a method for exploring the combinatorial tree which exploits some of the underlying geometric properties of adjacent critical regions as the supplementary information in combinatorial approach to exclude a noticeable number of feasible candidate active sets from combinatorial tree. This method is particularly well-suited for cases where many combinations of active constraints are feasible but not optimal. Results indicate that this method can find all critical regions corresponding to non-degenerate multi-parametric programming. A postprocessing algorithm can be applied to complete the proposed method in the cases in which some critical regions might not be enumerated due to degeneracies in the problem.

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“…Already for a linear prediction model it is hard to define 'relatively small systems' precisely since the complexity is highly depending on the application at hand. But to get a flavor of what relatively small means, one can observe that many applications of explicit MPC employ prediction models of state dimension five or lower, while only in exceptions the dimension is higher than ten, Hovland and Gravdahl [2008].…”

Section: Bounded Rate Of Variationmentioning

confidence: 99%

Explicit LPV-MPC with Bounded Rate of Parameter Variation

Besselmann

Löfberg

Morari

2009

IFAC Proceedings Volumes

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Abstract:Recently it was shown how one can reformulate the MPC problem for LPV systems to a series of mpLPs by a closed-loop minimax MPC algorithm based on dynamic programming. A relaxation technique is employed to reformulate constraints which are polynomial in the scheduling parameters to parameter-independent constraints. The algorithm allows the computation of explicit control laws for LPV systems and enables the controller to exploit information about the scheduling parameter. This improves the control performance compared to a standard robust approach where no uncertainty knowledge is used, while keeping the benefits of fast online computations. In this paper the explicit LPV-MPC scheme is extended to incorporate limits on the rate of parameter variation in the controller design. Taking these limits into account can further improve control performance since impossible trajectories of the scheduling parameter do not have to be considered during control law computations.

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Complexity Reduction in Explicit MPC through Model Reduction

Cited by 15 publications

References 13 publications

Robust output feedback control with guaranteed constraint satisfaction

Robust output feedback control with guaranteed constraint satisfaction

Further results on the exploration of combinatorial tree in multi-parametric quadratic programming

Explicit LPV-MPC with Bounded Rate of Parameter Variation

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