(243g) A Deep Learning-Based Approach for Explicit Offset-Free Tracking Nonlinear Model Predictive Control

Nonlinear model predictive control (NMPC) has been applied in numerous industrial applications in recent years due to its ability to directly handle constrained multivariate dynamic systems [1]. However, issues can arise with NMPC in practice including: (i) complexity of implementation on low-memory devices; (ii) potentially high computational burden due to the iterative solution of an optimal control problem online; (iii) reduced computational efficiency when applied to problems with long prediction horizons; and (iv) challenges in guaranteeing closed-loop properties [2]. Explicit MPC is capable of addressing these issues by replacing the online optimal control problem with an explicitly precomputed control law [3]. Although many readily available explicit MPC methods exist for linear systems [3,4], the extension to nonlinear systems is not straightforward and has received considerably less attention.

Motivated by the latest advances in the field of deep learning [5], we propose an explicit NMPC strategy that uses a deep neural network (DNN) to directly learn the NMPC solution. Recent work has shown the ability of DNN to cope with larger state dimensions, nonlinear dynamics, and long-horizon problems using less resources than various alternative approaches [6]. The DNN is trained with data pairs for the mapping between the system state and the optimal control inputs, which are generated offline by solving the NMPC problem for a given number of samples. A main contribution of our work is how we deal with potential infeasibilities of the NMPC problem due to the presence of state constraints. These constraints are softened using penalty functions [7], which guarantee that the NMPC problem is feasible for every state sample in the training set. Subsequently, the region of attraction of the approximate explicit NMPC controller is classified using support vector machines [8], which can be straightforwardly trained with closed-loop simulation data. To ensure that the controller can be incorporated within hierarchical control strategies, we extend the DNN-based method to the reference tracking problem by treating the reference signals as additional states in the explicit NMPC. By including a disturbance model, we can also ensure that all feasible references are tracked without steady-state offset using a suitable update rule for the reference signal.

We demonstrate the proposed explicit NMPC approach for control of a kHz-excited atmospheric pressure plasma jet (APPJ) in helium [9]. APPJs have found a growing number of applications in the processing of heat-sensitive (bio)materials and plasma medicine including the deactivation of antibiotic resistant bacteria, shrinkage of cancerous tumors, and facilitating faster healing rates in chronic wounds [10]. Safe, reproducible, and therapeutically effective operation of APPJs remains a challenging problem due their highly nonlinear dynamics, the presence of safety-critical constraints, and uncertainty such as intrinsic variability in the plasma characteristics and exogenous disturbances [11]. Extensive simulation results show that the DNN-based controller closely matches the exact NMPC law, even though the system dynamics are modeled by stiff differential-algebraic equations, illustrating the improved representative power of DNNs over other function approximation techniques including shallow NNs. Experimental results also reveal that the proposed explicit NMPC controller exhibits faster disturbance rejection and improved constraint handling capabilities when compared to an embedded multi-loop PI controller that was tuned using internal model control (IMC) principles.

References

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