Constrained Model Predictive Control

A supervised learning framework is proposed to approximate a model predictive controller (MPC) with reduced computational complexity and guarantees on stability and constraint satisfaction. The framework can be used for a wide class of nonlinear systems. Any standard supervised learning technique (e.g., neural networks) can be employed to approximate the MPC from samples. In order to obtain closed-loop guarantees for the learned MPC, a robust MPC design is combined with statistical learning bounds. The MPC design ensures robustness to inaccurate inputs within given bounds, and Hoeffding’s Inequality is used to validate that the learned MPC satisfies these bounds with high confidence. The result is a closed-loop statistical guarantee on stability and constraint satisfaction for the learned MPC. The proposed learning-based MPC framework is illustrated on a nonlinear benchmark problem, for which we learn a neural network controller with guarantees.

Learning an Approximate Model Predictive Controller With Guarantees

In this paper, the robust state feedback stabilization of uncertain discrete-time constrained nonlinear systems in which the loop is closed through a packet-based communication network is addressed. In order to cope with model uncertainty, time-varying transmission delays, and packet dropouts (typically affecting the performances of networked control systems), a robust control scheme combining model predictive control with a network delay compensation strategy is proposed in the context of non-acknowledged UDP-like networks. The contribution of the paper is twofold. First, the issue of guaranteeing the recursive feasibility of the optimization problem associated to the receding horizon control law has been addressed, such that the invariance of the feasible region under the networked closed-loop dynamics can be guaranteed. Secondly, by exploiting a novel characterization of regional Input-to-State Stability in terms of time-varying Lyapunov functions, the networked closed-loop system has been proven to be Input-to-State Stable with respect to bounded perturbations.

Networked Predictive Control of Uncertain Constrained Nonlinear Systems: Recursive Feasibility and Input-to-State Stability Analysis

In multi-parametric programming, an optimization problem is solved for a range and as a function of multiple parameters In this review, we discuss the main developments of multi-parametric programming over the last two decades from a theoretical, algorithmic and application perspective In addition, we provide an opinionated view of the future research directions in multi-parametric programming

On multi-parametric programming and its applications in process systems engineering

In this paper, an explicit nonlinear model predictive controller (ENMPC) for the stabilization of nonlinear systems is investigated. The proposed ENMPC is constructed using tensored polynomial basis functions and samples drawn from low-discrepancy sequences. Solutions of a finite-horizon optimal control problem at the sampled nodes are used 1) to learn an inner and outer approximation of the feasible region of the ENMPC using support vector machines, and 2) to construct the ENMPC control surface on the computed feasible region using regression or sparse-grid interpolation, depending on the shape of the feasible region. The attractiveness of the proposed control scheme lies in its tractability to higher-dimensional systems with feasibility and stability guarantees, significantly small online computation times, and ease of implementation.

Support Vector Machine Informed Explicit Nonlinear Model Predictive Control Using Low-Discrepancy Sequences

The objective of this work consists in the offline approximation of possibly discontinuous model predictive control laws for nonlinear discrete-time systems, while enforcing hard constraints on state and input variables. Obtaining an offline approximation of the receding horizon control law may lead to a very significant reduction of the online computational burden with respect to algorithms based on iterated optimization, thus allowing the application to fast dynamics plants. The proposed approximation scheme allows to cope with discontinuous control laws, such as those arising from constrained nonlinear finite horizon optimal control problems. A detailed stability analysis of the closed-loop system driven by the approximated state-feedback controller shows that the devised technique guarantees the input-to-state practical stability with respect to the (non-fading) approximation-induced errors. Two examples are provided to show the effectiveness of the method when the approximator is chosen either as a d...

Approximate model predictive control laws for constrained nonlinear discrete-time systems: analysis and offline design

The present paper concerns the design of approximate off-line model predictive control laws for nonlinear discrete-time systems subject to hard constraints on state and input variables. The possibility to obtain an approximate receding horizon control law by performing off-line optimization, leads to a dramatic reduction of the real-time computational complexity with respect to on-line algorithms, and allows the application of the developed control technique to plants with fast dynamics, that require small sampling periods. The main feature of the proposed approximation scheme consists in the possibility to cope with possibly discontinuous state-feedback control laws, while guaranteeing the fulfillment of hard constraints on state and input variables despite the perturbations due to the use of an approximate controller. Finally, the resulting closed-loop system is shown to be input-to-state-stable with respect to the approximation-induced perturbations.

Approximate off-line receding horizon control of constrained nonlinear discrete-time systems

Electromechanical transients in isolated power systems having large and complex structure are challenging phenomena to study due to the intrinsic nonlinearities and to the mutual interactions between the electrical components involved. The problem is faced in this paper of studying the electromechanical transient resulting from a sudden line connection of a thruster motor in a shipboard integrated power system of a cruise liner. This case study has been selected because direct-on-line thruster motor start-up is one of the most perturbing scenario for the shipboard power system voltage and frequency stability. The transient is reproduced by means of a complete system modeling in the Matlab-Simulink environment and results are assessed by comparison with measurements taken on the ship. The good accordance between simulation and experimental results proves the effectiveness of the proposed approach.

Thruster motor start-up transient in an all-electric cruise-liner: Numerical simulation and experimental assessment

The present paper proposes a recursively feasible networked model predictive control scheme for discrete-time constrained interconnected linear systems. A centralized controller, which communicates with the subsystems through a packet-based communication network, is designed to guarantee the uniform boundedness of the trajectories of the overall closed-loop system. In order to cope with disturbances and time-varying transmission delays which typically affect networked control systems, a network delay compensation strategy based on acknowledgments and time-stamping of data packets is adopted. The main contribution of the paper consists in proving that the proposed method guarantees the robust enforcement of hard state and input constraints even in presence of bounded model uncertainty and delayed feedback communication channels, provided that transmission delays are bounded.

Networked MPC for constrained linear systems: a recursive feasibility approach

Inverter-fed Induction motor performance is known to be noticeably affected by the supply voltage waveform. Nevertheless, the prediction of how supply voltage harmonics impact on motor operation in terms of losses, noise and thermal behavior is still a problem that can be hardly approached through simulations and analysis, therefore experimental data constitute an important source for information. In this paper the test results of two high-power induction-motor drives are presented showing their performance under different voltage waveforms. Among the other things, it is shown how low-frequency distortions in the supply voltage may have considerably stronger impacts on motor behavior than PWM harmonics, although the overall THD under PWM supply is higher.

Marco Filippo

Papers

Approximate model predictive control laws for constrained nonlinear discrete-time systems: analysis and offline design

Approximate off-line receding horizon control of constrained nonlinear discrete-time systems

Thruster motor start-up transient in an all-electric cruise-liner: Numerical simulation and experimental assessment

Networked MPC for constrained linear systems: a recursive feasibility approach

Experimental assessment of medium-voltage Induction motor performance under multilevel PWM inverter supply