Rohan C. Shekhar

Robust variable horizon MPC with move blocking

Abstract This paper introduces a new formulation of variable horizon model predictive control (VH-MPC) that utilises move blocking for reducing computational complexity. Various results pertaining to move blocking are derived, following which, a generalised blocked VH-MPC controller is formulated for linear discrete-time systems. Robustness to bounded disturbances is ensured through the use of tightened constraints. The resulting time-varying control scheme is shown to guarantee robust recursive feasibility and finite-time completion. An example is then presented for a particular choice of blocking regime, as would be applicable to vehicle manœuvring problems. Simulations demonstrate the efficacy of the formulation.

Robust periodic economic MPC for linear systems

Economic Model Predictive Control differs from conventional tracking model predictive control by directly addressing a plants economic cost as the stage cost, consequently leading to better economic performance. This paper extends current economic model predictive control theory to linear time-invariant systems with periodic disturbances and cost functions, under mild assumptions. To ensure an increased region of attraction and to continuously guarantee feasibility of the controller despite changing economic conditions, a periodic terminal condition is used in place of terminal constraints. The approach draws on constraint tightening techniques in order to guarantee robust satisfaction of constraints as well as convergence of the controller. A Lyapunov based approach is used to show stability of the proposed controller and characterise a region about the optimal trajectory to which the system converges.

Fast model-based extremum seeking on Hammerstein plants

Partial plant knowledge may be used to develop model-based extremum seekers, however existing results rely on a type of time-scale separation which leads to slow optimization relative to the plant dynamics. In this work, a fast model-based extremum seeking scheme is proposed for a Hammerstein plant, and semi-global stability results are provided. Simulation results are used to validate the theoretical results.

Economic Model Predictive Control and Applications for Diesel Generators

When developing control systems for diesel generators, tuning of the controller’s parameters to achieve acceptable performance is a significant challenge, particularly while satisfying input, emission, and safety constraints in the face of unknown system disturbances. Robust economic model predictive control (EMPC) can simplify this process by directly addressing the generator’s objectives, while systematically handling constraints in a robust way. This paper details how robust EMPC can be implemented as the control solution for diesel generators. To illustrate the process, two distinct generator applications are considered. The first application is a power tracking diesel generator, operating under emissions constraints. Such an application is found in series hybrid electric vehicles. The second application concerns diesel generators onboard submarines. In this application, engine speed and exhaust temperatures must be kept constant, despite significant system disturbances. An experimental study highlights the effectiveness of the EMPC as a solution for both applications.

Optimal move blocking strategies for model predictive control

This paper presents a systematic methodology for designing move blocking strategies to reduce the complexity of a model predictive controller for linear systems, with explicit optimisation of the blocking structure using mixed-integer programming. Given a move-blocked predictive controller with a terminal invariant set constraint for stability, combined with an input parameterisation to preserve recursive feasibility, two different optimisation problems are formulated for blocking structure selection. The first problem calculates the maximum achievable reduction in the number of input decision variables and prediction horizon length, subject to the controllers region of attraction containing a specified subset of the state space. Then, for a given fixed horizon length and block count determined by hardware capabilities, the second problem seeks to maximise the volume of an inner approximation to the region of attraction. Numerical examples show that the resulting blocking structures are able to optimally reduce controller complexity and improve region of attraction volume.

Discrete-time extremum-seeking for Wiener-Hammerstein plants

This paper presents a new formulation of extremum-seeking control for discrete-time Wiener-Hammerstein plants. A novel method of analysis using Linear Parameter-Varying (LPV) system theory demonstrates semi-global stability of the control scheme. Assuming only limited plant knowledge, the stability result ensures convergence of the plant output in steady state to a point in an arbitrarily small neighbourhood of the extremum, for appropriately chosen controller parameters. The behaviour of the control scheme is analysed on a simple simulated system, prior to being implemented on an internal combustion engine. Experiments demonstrate how the scheme is able to maximise engine output torque in the presence of an uncertain fuel composition by modifying the spark timing.

Robust stable economic MPC with applications in engine control

Economic Model Predictive Controllers have shown to improve a plants economic performance using state dependant economic stage costs. Recent extensions have provided continual feasibility guarantees, despite changes in economic parameters, however, perfect plant models have been assumed. This assumption is invalid in practise due to modelling errors or un-modelled disturbances and can therefore lead to infeasibility of the optimisation problem. This paper proposes a robust economic model predictive controller, which takes advantage of constraint tightening techniques to guarantee feasibility despite modelling errors. Input-to-state stability is proven using a Lyapunov function. The advantages of this method are highlighted against alternative control structures in the application of power tracking for diesel engines in series hybrid type applications.

Optimal constraint tightening policies for robust variable horizon model predictive control

This paper develops a technique for improving the region of attraction of a robust variable horizon model predictive controller. It considers a constrained discrete-time linear system acted upon by a bounded, but unknown time-varying state disturbance. Using constraint tightening for robustness, it is shown how the tightening policy, parameterised as direct feedback on the disturbance, can be optimised to increase the volume of an inner approximation to the controllers true region of attraction. Numerical examples demonstrate the benefits of the policy in increasing region of attraction volume and decreasing the maximum prediction horizon length.

Robust Model Predictive Control of Unmanned Aerial Vehicles Using Waysets

This paper introduces a new formulation of model predictive control for robust trajectory guidance of unmanned aerial vehicles. It generalizes the ubiquitous concept of waypoints to waysets, in order to provide robustness to bounded state disturbances in the presence of obstacles. Using a variable horizon formulation of model predictive control, it shows how wayset guidance combined with constraint tightening can guarantee robust recursive feasibility and finite-time completion of a control maneuver. Simulations on a point mass fixed-wing unmanned aerial vehicle model moving through a field of obstacles with wind disturbances demonstrate significant computational benefits from using waysets when compared to existing mixed-integer optimization methods that employ long prediction horizons. Using the controller’s robustness to mitigate linearization error, an additional example implements the strategy on a simulated quadrotor, demonstrating how waysets can be used to control more complex nonlinear systems.

Extremum Seeking Methods for Online Automotive Calibration

The automotive calibration process is becoming increasingly difficult as the degrees of freedom in modern engines rises with the number of actuators. This is coupled with the desire to utilise alternative fuels to gasoline and diesel for the promise of lower \(\mathrm {CO}_2\) levels in transportation. However, the range of fuel blends also leads to variability in the combustion properties, requiring additional sensing and calibration effort for the engine control unit (ECU). Shifting some of the calibration effort online whereby the engine controller adjusts its operation to account for the current operating conditions may be an effective alternative if the performance of the controller can be guaranteed within some performance characteristics. This tutorial chapter summarises recent developments in extremum seeking control, and investigates the potential of these methods to address some of the complexity in developing fuel-flexible controllers for automotive powertrains.