Nonlinear Model Predictive Control

Provably stable formualtions

Relaxing the N-reachability assumption

Non conventional NMPC formulation where the previous current control is a part of the initial extended state

The cost function formulation where \(f_c\) stands for the r.h.s of the original ODE.

Closed-loop evolution of the open-loop optimal cost under different instantiation of the formuation and different targeted state. \(d\) is the distance to the target.

Computation times showing that the novel more appropriate formualtion is not even longer to compute.

For more details, refer to the [paper].

Weighted increment-based formulation for economic MPC

Definition of the cost function. \(\Delta_k\) denotes the discrete increment of the state between instants \(k\) and \(k+1\).

Impact of \(\alpha\) in stabilizing the trajectories near the steady optimal unknown state.

For more details, refer to the [paper].

Formulation with exponentially increasing penalty

Evolution of the stability indicator when applying the formulation to control the highly instable triple integrator system.

The ratio being systematically lower than one shows that the proposed formualtion produce better response than the traditional final constraint-based provably stable formulation.

For more details, refer to the paper.

NMPC admissibility dashboard

The degree of freesdom of the NMPC implementation.

Package can be downloaded at my GitHub repository.

Typical resulting admissibility dashboards for two different assumption regarding the computational aspects called the implementation acceleration.

For more details, refer to the [paper].

Real-time considerations

GPU-Based parmeterized NMPC applied to semi-active suspension system

description

CPU vs GPU pNMPC computation times.

For more details, refer to the [paper].

Stochastic MPC by supervised clustering

Schematic view of the proposed stochastic NMPC. The features used in the clustering results from the solution of a bunch of deterministic optimal control problems. This provides a supervised clustering of the uncertainities leading to the selection of consistent small number \(n_{cl}\) of representative instantiation of the uncertainties. The latter serve in approximating the expectation and the vairance of the closed-loop indicators.

The approximated stochastic NMPC based on the \(n_{cl}\) continuously updated instances.

Cost Function

Statistics of therapy issue over a high number of scenarios. Comparison of nominal deterministic vs proposed stochastic NMPC implementation

For more details, refer to the [paper].

Hierarchical NMPC: Application to cryogenic refrigerators

Schematic view of the cryogenic refrigerator which is decomposed into four systems serving in the hierarchical design of the NMPC controller

Block diagram of the hierarchical control algorithm. \(r\) denotes the vector of set-points to subsystem that is to be computed by the master through fixed-point iterations.

Details of the fixed-point iteration in the specific case of two subsystem for the sake of illustration. \(v\) denotes the vector of coupling signals.

(a)

(b)

Achieved closed-loop cost under different settings of the controller. (a) without distributing the computation time over the system’s lifetime (b) under different setting of the distribution-in-time implementation.

For more details, refer to the [paper]. Notice that this work is an extension of [a previous work] which tackled only a network of unconstained linear dynamical system. The work presented here extends the previous one to networks of possibly nonlinear system involving general constraints.