Robustly stable feedback min-max model predictive control

Published versio

Fault tolerant control using Gaussian processes and model predictive control

Abstract Essential ingredients for fault-tolerant control are the ability to represent system behaviour following the occurrence of a fault, and the ability to exploit this representation for deciding control actions. Gaussian processes seem to be very promising candidates for the first of these, and model predictive control has a proven capability for the second. We therefore propose to use the two together to obtain fault-tolerant control functionality. Our proposal is illustrated by several reasonably realistic examples drawn from flight control.This research was supported by EU Framework Programme 7, project 314544, RECONFIGURE: Reconfiguration of Control in Flight for Integral Global Upset Recovery, as well as the China Scholarship Council and the Cambridge Overseas Trust.This is the final published version. It first appeared at http://www.degruyter.com/view/j/amcs.2015.25.issue-1/amcs-2015-0010/amcs-2015-0010.xml

Reconfigurable predictive control for redundantly actuated systems with parameterised input constraints

A method is proposed for on-line recon guration of the terminal constraint used to provide theoretical nominal stability guarantees in linear model predictive control (MPC). By parameterising the terminal constraint, its complete reconstruction is avoided when input constraints are modi ed to accommodate faults. To enlarge the region of feasibility of the terminal control law for a certain class of input faults with redundantly actuated plants, the linear terminal controller is de ned in terms of virtual commands. A suitable terminal cost weighting for the recon gurable MPC is obtained by means of an upper bound on the cost for all feasible realisations of the virtual commands from the terminal controller. Conditions are proposed that guarantee feasibility recovery for a de ned subset of faults. The proposed method is demonstrated by means of a numerical example.The research leading to these results has received function from the European Union Seventh Framework Programme FP7/2007{2013 under grant agreement no. 314 544.This is the accepted manuscript. The final version is available from Elsevier at http://www.sciencedirect.com/science/article/pii/S0167691114000127

Incorporating control performance tuning into economic model predictive control

This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/ECC.2015.7330599Economic model predictive control (eMPC), where an economic objective is used directly as the objective function of the control system, has gained much popularity in recent literature. However, with a purely economic objective, the control designer has no influence over the control performance of the process. In this paper, we propose a means of tuning the objective function in order to give some level of control performance. Also, the stability proof for eMPC relies on some strict-dissipativity condition. We also show how this condition can be satisfied when the system is only dissipative with respect to the original objective function.O I. Olanrewaju is sponsored by the Federal Government of Nigeri

Soft Constraints and Exact Penalty Functions in Model Predictive Control

One of the strengths of Model Predictive Control (MPC) is its ability to incorporate constraints in the control formulation. Often a disturbance drives the system into a region where the MPC problem is infeasible and hence no control action can be computed. Feasibility can be recovered by softening the constraints using slack variables. This approach does not necessarily guarantee that the constraints will be satisfied, if possible. Results from the theory of exact penalty functions can be used to guarantee constraint satisfaction. This paper describes a method for computing a lower bound for the constraint violation penalty weight of the exact penalty function. One can then guarantee that the soft-constrained MPC solution will be equal to the hard-constrained MPC solution for a bounded subset of initial states, control inputs and reference trajectories

Predictive control for spacecraft rendezvous in an elliptical orbit using an FPGA

A field programmable gate array (FPGA)-based predictive controller for a spacecraft rendezvous man{\oe}uvre is presented. A linear time varying prediction model is used to accommodate elliptical orbits, and a variable prediction horizon is used to facilitate finite time completion of man{\oe}uvres. The resulting constrained optimisation problems are solved using a primal dual interior point algorithm. The majority of the computational demand is in solving a set of linear equations at each iteration of this algorithm. To accelerate this operation, a custom circuit is implemented, using a combination of Mathworks HDL Coder and Xilinx System Generator for DSP, and used as a peripheral to a MicroBlaze soft core processor. The system is demonstrated in closed loop by linking the FPGA with a simulation of the plant dynamics running in Simulink on a PC, using Ethernet.This work was supported by the Engineering and Physical Sciences Research Council (Grant EP/G030308/1) as well as industrial support from Xilinx, Mathworks and the European Space Agency.European Control Conference 2013 (ECC13), July 17-19, Zurich, Switzerlan

A longitudinal flight control law based on robust MPC and H<inf>2</inf> methods to accommodate sensor loss in the RECONFIGURE benchmark

The feedback gains in state-of-the-art flight control laws for commercial aircraft are scheduled as a function of values such as airspeed, mass, and centre of gravity. If estimates of these are lost due to multiple simultaneous sensor failures, it is necessary for the pilot to either directly command control surface positions, or to revert to an alternative control law. This work develops a robust backup load-factor tracking control law, that does not depend on these parameters, based on application of theory from robust MPC and H2 control. First the methods are applied with loss only of airdata, and subsequently also with loss of mass and CoG estimates. Local linear analysis indicates satisfactory performance over a wide range of operating points. Finally, the resulting control laws are demonstrated on the nonlinear RECONFIGURE benchmark, which is derived from Airbus's high delity, industrially-validated simulator, OSMA.This is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.ifacol.2015.09.65

Model predictive control with prioritised actuators

This paper deals with the control of systems for which there is a clear distinction between preferred and auxiliary actuators, the latter to be used only when the control error is large. Explicit MPC and exact penalty functions are used to show how ℓasso-MPC can implement this idea. Two ℓasso-MPC versions are reviewed, that allow the designer to impose a certain nominal operations zone, namely, a neighbourhood of the set-point in which the auxiliary actuators are never used. For the sake of brevity, the required procedures are shown only for version 1, but it is also discussed how they can be extended to version 2. Limitations due to the presence of constraints are also formalised. The ℓasso-MPC version 1 can be used to embed an existing linear quadratic MPC, while ℓasso-MPC version 2 can be used to obtain multiple levels of priority. The paradigm is demonstrated for version 1 through the control of the linearised lateral dynamics of a Boeing 747. In particular, the approach uses the spoilers only when the control error is larger than a desired threshold.Research supported by the EPSRC grant “Control for Energy and Sustainability”, EP/G066477/1.This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/ECC.2015.733059

Graphical FPGA design for a predictive controller with application to spacecraft rendezvous

A reconfigurable field-programmable gate array (FPGA)-based predictive controller based on Nesterov’s fast gradient method is designed using Simulink and converted to VHDL using Mathworks’ HDL Coder. The implementation is verified by application to a spacecraft rendezvous and capture scenario, with communication between the FPGA and a simulation of the relative dynamics occuring over Ethernet. For a problem with 120 decision variables and 240 constraints, computation times of 0.95 ms are achieved with a clock rate of 50 MHz, corresponding to a speed up of more than 2000 over running the algorithm directly on a MicroBlaze microprocessor implemented on the same FPGA.This work was supported by the Engineering and Physical Sciences Research Council (Grant EP/G030308/1) as well as industrial support from Xilinx, Mathworks and the European Space Agency.52nd IEEE Conference on Decision and Control, December 10-13, 2013, Palazzo dei Congressi, Florence, Italy

Designing output-feedback predictive controllers by reverse-engineering existing LTI controllers

An approach to designing a constrained output-feedback predictive controller that has the same small-signal properties as a pre-existing output-feedback linear time invariant controller is proposed. Systematic guidelines are proposed to select an appropriate (non-unique) realization of the resulting state observer. A method is proposed to transform a class of offset-free reference tracking controllers into the combination of an observer, steady-state target calculator and predictive controller. The procedure is demonstrated with a numerical example.This work was supported by Engineering and Physical Sciences Research Council grant EP/G030308/1, the European Space Agency and EADS Astrium.This is the author's version of an article that has been published in IEEE Transactions on Automatic Control. Changes were made to this version by the publisher prior to publication. The final version of record is available at: http://dx.doi.org/10.1109/TAC.2013.2258781 (c) 2013 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works