(593c) GPU-Accelerated Nonlinear Model Predictive Control with Infiniteopt.Jl

Model predictive control (MPC) is a widely used control strategy in applications such as power plants, petroleum refineries, and manufacturing [1, 2], where an optimal control problem (OCP) is repeatedly solved over a rolling time horizon to determine optimal control inputs [3]. While linear MPC (LMPC) is commonly implemented for its computational efficiency, many real-world systems like separation units [4] and air conditioning systems [5] exhibit highly nonlinear behaviour [3, 6]. Various schemes have been developed to approximate these dynamics, such as neural network surrogate models [7, 8] or partitioning the system into subregions with tailored LMPC controllers [6]. However, these approaches often introduce modelling error that can degrade controller performance, especially for systems with fast or sensitive dynamics that require greater control precision. Nonlinear MPC (NMPC) provides an attractive approach by directly incorporating high-fidelity models and constraints that better capture system behaviour across a wide range of operating conditions [3]. However, in many applications, real-time NMPC is challenging to implement due to the significant computational cost of solving nonlinear programs (NLPs) that are often nonconvex [3, 6].

NPMC formulations are often solved via direct transcription which results in NLPs with highly recurrent constraint and objective structures that traditional algebraic modelling languages (AMLs) like JuMP and Pyomo do not exploit [9]. To address this, Pulsipher and Shin introduced InfiniteExaModels.jl, an extension of InfiniteOpt.jl (an AML for infinite-dimensional optimization [10]) that leverages the capabilities of the ExaModels.jl ecosystem (an AML for NLPs with recurrent structure [9]) to more efficiently transcribe, differentiate, and solve transcribed infinite-dimensional optimization (InfiniteOpt) problems [11]. Gondosiswanto and Pulsipher further refined the abstraction (the InfiniteSIMD-NLP abstraction) behind InfiniteExaModels.jl to solve InfiniteOpt problems entirely on GPUs, accelerating NLP solution times by one to two orders-of-magnitude across a range InfiniteOpt benchmark problems (including NMPC problems) using the MadNLP.jl interior-point solver with NVDIA’s cuDSS linear solver [12]. This framework provides an attractive means to accelerate NMPC performance without using reduced models, but this was not verified with closed-loop NMPC.

Interestingly, Pacaud and Shin recently showed that, for many NLP problems solved on GPU via the ExaModels framework, the symbolic factorization of the Karush-Kuhn-Tucker (KKT) system via cuDSS’s sparse Cholesky factorization is the main computational bottleneck [4, 13]. This observation is significant since most NMPC formulations exhibit a consistent sparsity pattern across iterations which means that the symbolic factorization can be treated as a one-time offline cost and reused for online NMPC [4], this presents yet another opportunity to further reduce NMPC solutions times beyond those demonstrated in [12]. Despite the aforementioned opportunities, their utility for NPMC remains untested, in part because no comprehensive framework has been available to facilitate GPU-accelerated NMPC.

Hence, we present an NMPC-tailored framework, implemented in Julia, that builds on the capabilities of InfiniteExaModels.jl to significantly accelerate the solution of NMPC problems on GPU. The framework automatically caches the symbolic factorization of the KKT system and provides efficient warmstarting to facilitate significant speedup for NMPC problems solved via direct transcription. Moreover, it leverages the InfiniteOpt.jl AML to provide an intuitive modelling API for NMPC problems that automates transcription. The effectiveness of the proposed GPU-NMPC framework is demonstrated via case studies in distillation column control, reactor control, and 2D temperature control. This framework has great potential for real-time NMPC applications, enabling more efficient control of systems with fast, complex dynamics and demanding constraints.

References

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