On the Use of Supervised Clustering in Stochastic NMPC Design

Abstract

In this paper, a supervised clustering based-heuristic is proposed for the real-time implementation of approximate solutions to stochastic nonlinear model predictive control frameworks. The key idea is to update on-line a low cardinality set of uncertainty vectors to be used in the expression of the stochastic cost and constraints. These vectors are the centers of uncertainty clusters that are built using the optimal control sequences, cost and constraints indicators as supervision labels. The use of a moving clustering data buffer which accumulates recent past computations enables to reduce the computational burden per sampling period while making available at each period a relevant amount of samples for the clustering task. A relevant example is given to illustrate the contribution and the associated algorithms.

A Heuristic for Dynamic Output Predictive Control Design for Uncertain Nonlinear Systems

“…Note that if the distribution of the control values was more continuously distributed between u min = 0.049 and u max = 0.449, a regressor would have been more appropriate to address the identification problem. 3 for this specific example.…”

“…In what follows, The histogram of control values over the prediction horizon of the n q = 500 sampled scenarios (including hence 125000 values) is shown in Figure 5. This histogram suggests that classification tools are best suited for the learning of the control using ML tools compared to regression tools 3 . Indeed, the following three-valued set of label values can be used:…”

“…In a nutshell, SNMPC frameworks implement the basic NMPC scheme with the standard deterministic cost and constraints being replaced by their expected values, considered as functions of the model's uncertainties. While the conceptual simplicity of this shift in paradigm is appealing, its consequence on the computational burden appears as a deal breaker despite some recent attempts [3], [9], [16]. Indeed, SNMPC requires the on-line computation of the expectation of nonlinear functions of several variables.…”

Learning against uncertainty in control engineering

“…This means that even if the gradient descent converges ultimately to the right solution, this might need a number of simulations [involved in (5)] that grows exponentially in the state dimension. This is the price to pay if one would like to stick to the ideal promises of RL which is to deliver the stochastically optimal state feedback strategy defined as a function of the state over the set of interest X.…”

Explicit approximation of stochastic optimal feedback control for combined therapy of cancer

“…Stochastic model predictive control (SMPC) offers an attractive alternative through the use of a set of scenarios in the on-line computation in order to minimize the approximate version of the expectation of the cost function [13,12,2]. This lead to a solution for each initial state but does not give a global overview on the performance on a whole region of the state space.…”